From f52335467fb81b3ed6c4725a3f77fa012b702c1a Mon Sep 17 00:00:00 2001 From: Astryd Park Date: Tue, 13 Jan 2026 12:18:43 +0000 Subject: [PATCH 01/46] Clear up the branch to store the source code --- Hackathons.md | 27 - LICENSE-2.0.txt | 202 - QuantumBrush.jar | Bin 89234 -> 0 bytes QuantumBrush_lib/core-4.4.1.jar | Bin 1049912 -> 0 bytes README.md | 183 - config/python_path.txt | 2 - effect/GoL/GoL.py | 230 - effect/GoL/GoL_requirements.json | 46 - effect/GoL/__init__.py | 0 effect/__init__.py | 0 effect/acrylic/__init__.py | 0 effect/acrylic/acrylic.py | 49 - effect/acrylic/acrylic_requirements.json | 39 - effect/apply_effect.py | 260 - effect/chemical/__init__.py | 0 effect/chemical/chemical.py | 206 - effect/chemical/chemical_requirements.json | 43 - effect/chemical/data/h2_circuit.qpy | Bin 17949 -> 0 bytes effect/chemical/data/h2_parameters.json | 366522 --------------- effect/clone/__init__.py | 0 .../clone/__pycache__ 2/clone.cpython-311.pyc | Bin 7787 -> 0 bytes effect/clone/clone.py | 132 - effect/clone/clone_requirements.json | 25 - effect/damping/__init__.py | 0 effect/damping/damping.py | 148 - effect/damping/damping_requirements.json | 38 - effect/heisenbrush/__init__.py | 0 effect/heisenbrush/heisenbrush.py | 177 - .../heisenbrush/heisenbrush_requirements.json | 40 - effect/heisenbrush2/__init__.py | 0 effect/heisenbrush2/heisenbrush2.py | 176 - .../heisenbrush2_requirements.json | 41 - effect/pointillism/__init__.py | 3 - effect/pointillism/docs/PointlisimBrush.ipynb | 721 - effect/pointillism/docs/USAGE_GUIDE.md | 175 - .../pointillism/docs/images/dots_applied.png | Bin 914989 -> 0 bytes .../docs/images/negative_coupling_example.png | Bin 976134 -> 0 bytes .../docs/images/positive_coupling_example.png | Bin 957216 -> 0 bytes .../docs/images/stroke_example.png | Bin 1115877 -> 0 bytes effect/pointillism/pointillism.py | 435 - .../pointillism/pointillism_requirements.json | 56 - effect/qdrop/__init__.py | 0 effect/qdrop/qdrop.py | 146 - effect/qdrop/qdrop_requirements.json | 43 - effect/steerable/.gitignore | 1 - effect/steerable/__init__.py | 0 effect/steerable/helper.py | 340 - effect/steerable/steerable.py | 308 - effect/steerable/steerable_requirements.json | 58 - effect/utils.py | 355 - screenshots/after.png | Bin 1021781 -> 0 bytes screenshots/before.png | Bin 929934 -> 0 bytes screenshots/control.png | Bin 337564 -> 0 bytes screenshots/manager.png | Bin 967245 -> 0 bytes setup.sh | 416 - update.sh | 359 - 56 files changed, 372002 deletions(-) delete mode 100644 Hackathons.md delete mode 100644 LICENSE-2.0.txt delete mode 100644 QuantumBrush.jar delete mode 100644 QuantumBrush_lib/core-4.4.1.jar delete mode 100644 README.md delete mode 100644 config/python_path.txt delete mode 100644 effect/GoL/GoL.py delete mode 100644 effect/GoL/GoL_requirements.json delete mode 100644 effect/GoL/__init__.py delete mode 100644 effect/__init__.py delete mode 100644 effect/acrylic/__init__.py delete mode 100644 effect/acrylic/acrylic.py delete mode 100644 effect/acrylic/acrylic_requirements.json delete mode 100644 effect/apply_effect.py delete mode 100644 effect/chemical/__init__.py delete mode 100644 effect/chemical/chemical.py delete mode 100644 effect/chemical/chemical_requirements.json delete mode 100644 effect/chemical/data/h2_circuit.qpy delete mode 100644 effect/chemical/data/h2_parameters.json delete mode 100644 effect/clone/__init__.py delete mode 100644 effect/clone/__pycache__ 2/clone.cpython-311.pyc delete mode 100644 effect/clone/clone.py delete mode 100644 effect/clone/clone_requirements.json delete mode 100644 effect/damping/__init__.py delete mode 100644 effect/damping/damping.py delete mode 100644 effect/damping/damping_requirements.json delete mode 100644 effect/heisenbrush/__init__.py delete mode 100644 effect/heisenbrush/heisenbrush.py delete mode 100644 effect/heisenbrush/heisenbrush_requirements.json delete mode 100644 effect/heisenbrush2/__init__.py delete mode 100644 effect/heisenbrush2/heisenbrush2.py delete mode 100644 effect/heisenbrush2/heisenbrush2_requirements.json delete mode 100644 effect/pointillism/__init__.py delete mode 100644 effect/pointillism/docs/PointlisimBrush.ipynb delete mode 100644 effect/pointillism/docs/USAGE_GUIDE.md delete mode 100644 effect/pointillism/docs/images/dots_applied.png delete mode 100644 effect/pointillism/docs/images/negative_coupling_example.png delete mode 100644 effect/pointillism/docs/images/positive_coupling_example.png delete mode 100644 effect/pointillism/docs/images/stroke_example.png delete mode 100644 effect/pointillism/pointillism.py delete mode 100644 effect/pointillism/pointillism_requirements.json delete mode 100644 effect/qdrop/__init__.py delete mode 100644 effect/qdrop/qdrop.py delete mode 100644 effect/qdrop/qdrop_requirements.json delete mode 100644 effect/steerable/.gitignore delete mode 100644 effect/steerable/__init__.py delete mode 100644 effect/steerable/helper.py delete mode 100644 effect/steerable/steerable.py delete mode 100644 effect/steerable/steerable_requirements.json delete mode 100644 effect/utils.py delete mode 100644 screenshots/after.png delete mode 100644 screenshots/before.png delete mode 100644 screenshots/control.png delete mode 100644 screenshots/manager.png delete mode 100755 setup.sh delete mode 100644 update.sh diff --git a/Hackathons.md b/Hackathons.md deleted file mode 100644 index 01c310e..0000000 --- a/Hackathons.md +++ /dev/null @@ -1,27 +0,0 @@ -# Welcome to the creative side of quantum computing! -**[Quantum Brush](https://github.com/moth-quantum/QuantumBrush)** is the Java (`OpenJDK 21+`) application which contains creative digital pixel/colour/selection modification algorithms powered by quantum computing. This lightweight programme supports various visual quantum algorithms with local simulation, which is good for future quantum art enthusiasts and Python developers so that they can try to make their own quantum brushes. Now is your chance. -If you want to read the paper before you go, the preprint is [here](https://github.com/moth-quantum/QuantumBrush). - -## Why: Motivation and brief introduction -MOTH aims to demonstrate how quantum technology can support creative industries even nowadays in the NISQ-era, while actively building its use cases. History proved art, science and technology evolves together, whilst each introduces new, unique viewpoints onto 'the new world'. While we are moving onto the FTQC-era, we can still explore the creative side of quantum technology, setting up quantum algorithm for quantum emulation and hardware, so that in the future, these will be advanced into unimaginable, exciting new era of computation. - -## How: Description -Quantum Brush is one of the example. It is a collection/application of digital brushes. The app itself is written with Java and there is a backend operated by Python, where you will mostly contribute with your own brush. The communication between the app (Java) and the brush (Python) is conducted with JSON documents. All templates are in the Quantum Brush [repository](https://github.com/moth-quantum/QuantumBrush) and you can read through `README.md` there. -There is a Jupyter Notebook tutorial where you can get a glimpse of how the brushes work, how you can setup the JSON document, and how data structure will work. It is created on Google CoLab and here is the [link](https://colab.research.google.com/drive/1_guH4IbEmCFA3bPTWEVa8jI_d1-TP63V?usp=sharing). -Based on the template and the tutorial, you can make your own brush, `brushName.py` with its following requirements, `brushName_requirements.json`, underneath the folder `brushName`. Position it underneath the `effect` folder in `$HOME/QuantumBrush`, and test it out on the application. -To install the application, go [here](https://github.com/moth-quantum/QuantumBrush) and download `install.sh` underneath the Releases tab. And follow the instructions on the another `README.md` there. - -## What: Goals -1. Make your own Quantum Brush -2. (Bonus!) Improve UI/UX of the Quantum Brush application: Now, Quantum Brush is in the stage of private distribution for clients and internal usage. We want to take this further in the future. Beforehand, can you help us with tidying up the UI/UX so the onboarding process can be smoother? - -## Who: Eligibility and license -**Anyone** who heard of quantum art, has an interest in creative computing, actively researches quantum algorithms, wants to improve their skills while contributing to open-source software is all welcomed. Basic knowledge of version control (Git), logic management between different computer languages (Java, Python), user experience, are required. Or you can build up these skills with learning-by-doing! -Participants who are selected as a winner will become an official contributor on Quantum Brush's GitHub repository, with your GitHub handle and profile picture on it. -The license follows APACHE license 2.0, the permissive open source license. You can do something you want to do with the software, if you: -- Include the original copyright and license notice, and -- State all changes/contributions, and -- Include the NOTICE file if needed. -If you require further information or have any questions, book a session with one of the creators of Quantum Brush, Astryd Park. -### c.f. -Cover artwork by [Atelier Roman Lipski](https://www.romanlipski.com/) with Quantum Brush. \ No newline at end of file diff --git a/LICENSE-2.0.txt b/LICENSE-2.0.txt deleted file mode 100644 index d645695..0000000 --- a/LICENSE-2.0.txt +++ /dev/null @@ -1,202 +0,0 @@ - - Apache License - Version 2.0, January 2004 - http://www.apache.org/licenses/ - - TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION - - 1. 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z#Pv04ykt%HZ-1|wwi{4sRmL!e;=AOECQ?Y8t?&cc%Zsi71=N@_C$gN79sQ7q^@LXb;NP5%7TyzTTet>#_<+gI6UA z%PV(*{P+>P=YnczP;gzTzbz#xEsOO1?uN}4JYZx_*y!@=>{P1DA%6R_C0UdNgr>Ya z395RWF7>yiq!EQ*v7gBp532SF@PVqn*P8n4GSWz*Q@?ZzI{1JM^|yCQ{rNgLwg#?` Q;GYZNxyR@`?BGxT58y@)hyVZp diff --git a/README.md b/README.md deleted file mode 100644 index 1f4cbf2..0000000 --- a/README.md +++ /dev/null @@ -1,183 +0,0 @@ -πŸ” Hello! I am a creative image modification tool powered by quantum computing. -- Brush collection powered by quantum algorithms. -- Lightweight program which supports quantum simulation and hardware communication both. -- Work with high-res images with quantum backend to draw, modify and have fun! - -πŸ‘©πŸ»β€πŸ’» Author: MOTH Quantum (This app is built with ❀️ by [Astryd Park](https://www.github.com/artreadcode)) - ---- - -πŸ“‹ Contents -1. [Usage Instruction](https://github.com/moth-quantum/quantumbrush?tab=readme-ov-file#usage-instruction) -2. [Installation Instruction](https://github.com/moth-quantum/quantumbrush?tab=readme-ov-file#installation-instructions) -3. [Examples](https://github.com/moth-quantum/quantumbrush?tab=readme-ov-file#examples) -4. [One more thing](https://github.com/moth-quantum/quantumbrush?tab=readme-ov-file#one-more-thing) -5. [Technical Stack](https://github.com/moth-quantum/quantumbrush?tab=readme-ov-file#technical-stack) - ---- - -# Usage Instruction -This application is tested with MacOS Sequoia (15.5) && Eclipse IDE (2025-03) && Python 3.11+ && OpenJDK 21.0.7 LTS. Technically, the application must support every machines (Windows, Linux and MacOS) with the suitable Java and Python versions. It requires OpenJDK and Python to execute, so they must be previously installed. - -However, Luckily, the installer provides automatic OpenJDK + Python installation through `miniconda` thus you actually don’t need to do anything! `install.sh` creates condo environment `’quantumbrush’` and store all necessary libraries there. More of this is described under [Installation Instructions](https://github.com/moth-quantum/quantumbrush?tab=readme-ov-file#instllation-instruction). - -Quantum Brush is basically a graphics software powered by quantum-computing-imagination. There’s nothing which makes user experience difficult. The program has three windows. Treat them equally well. - -0. Import any Image! This is the guidance which are free images. - - [Free art website](https://www.nga.gov/artworks/free-images-and-open-access) - - [Art canvas image 1](https://unsplash.com/photos/a-white-wall-with-some-white-paint-on-it-YS0YJLU_h2k) - - [Art canvas image 2](https://unsplash.com/photos/white-wall-paint-with-black-line-R53t-Tg6J4c) - - [Art canvas image 3](https://unsplash.com/photos/white-printer-paper-on-white-surface-HZm2XR0whdw) - -1. Canvas - -![The image of Canvas](/screenshots/before.png) - This is the place where your image/canvas is displayed and you interact with it by `mouseClicked` and `mouseDragged`. `mouseClicked` will create a yellow dot. `mouseDragged` will create a red line. Look at the screenshot above. - Those elements are crucial for quantum algorithms, so treat it nicely. - - ⚠️ CAVEAT: Because of this special requirements, after you work on other windows, you MUST click the title bar of the canvas or it will wrongly leave yellow dots. This might make quantum brush algorithms to misbehave so be careful! - - Now, what will you do if you want to do something with quantum brush algorithms? As a sidekick, there is a control panel. - -2. Control panel - -![The image of Control Panel](/screenshots/control.png) - - This window is for modifying parameters for quantum brush algorithms. It depends on which brush did you choose. For example, Heisenbrush (Ver.Continuous) here has a radius, lightness, saturation and strength. It also contains tiny descriptions of each brush. - - After creating & modifying each brush stroke, we must group those paths and level them up to a system called 'stroke'. When you press 'Create', the program will say you can open up Stroke Manager to run the quantum algorithms. It depends on your choice. You can make bunch of strokes BEFORE you run them on quantum simulations/hardware (in the near future) OR you can directly open up the manager window and run the algorithms. This program is designed to not interfere with creative workflow. - - Have you decided to move along to Stroke Manager? - -3. Stroke Manager - - Open up Stroke Manager from *Tools* on the menu bar. - -![The image of Stroke Manager](/screenshots/manager.png) - - Here, you can see the list of ’strokes’ that you created. You can change the timeline of them, for example, run the recent stroke on the simulator than the old one. - - When you click 'Run', Python process will run in the background. You can close the window and come back to actually apply the processed result on the divided section. If the result is satisfactory, press the 'Apply to Canvas' button. - -# Installation Instructions - -These instructions are primarily for MacOS. They will likely also work for Linux. - -1. Download the install script `install.sh` [here](https://github.com/moth-quantum/QuantumBrush/releases/download/v0.0.3/install.sh). -2. Open up the terminal. On a Mac, to open the ’Terminal’ app, press command+Space, type terminal and press Enter. -3. Write `sh ~/Downloads/install.sh` (or copy-paste from here) and then press Enter to run the install script. -4. If the installer shows `{someQuestion}? (Y/y)`, you can press `y` and Enter! -5. After it install the program, you can choose whether the installer will set up the environment for you or not. Just press `y` for peaceful mind. -6. The `QuantumBrush` folder can down be found in your Home folder. - -To update you will need to run a similar process, but this time using the `update.sh` file in the QuantumBrush folder. - -1. Open a terminal, as in step 2 above. -2. Write `sh ~/QuantumBrush/update.sh` (or copy-paste from here) and then press Enter to run the update script. - -# Examples - -The combination of the stroke and the quantum brush that we choose, the result is this! - -![Example of Quantum Brush](/screenshots/after.png) -c.f. Image credit: [Pavilion by the Lake](https://www.metmuseum.org/art/collection/search/40429) - You can see the tech-savvy details on our paper and understand deeply about quantum-powered creativity! - -- Our paper is on Arxiv now! Check it out [here](https://arxiv.org/abs/2509.01442). - -# One more thing... - -Users can create their own quantum brush and contribute to this open-source project! The dummy brush looks like this (Have a look at the `template` folder underneath `effect`, too.: - -``` -QuantumBrush - |_ effect - |_ {brushName} - |_ {brushName}.py - |_ {brushName}.json - |_ __init__.py -``` - -Any users who have brilliant idea regarding visual effects using quantum mechanics can fork this repository, include their own brush and raise a pull request. After the review, we will add your work with credit in the `dist` branch. - -The current nature of quantum computing requires lot of dependencies. If it needs to be manually installed, look at the line __*318*__ of `setup.sh`. You will notice there's an automatic block of script to install dependencies with `conda run -n quantumbrush pip install`. Don't forget to add yours here so that your work won't crash. Recommended workflow is **A)** Sketch your idea, **B)** Think about which technical stack is needed and **C)** Fork the repository, modify the `setup.sh` or jump right into development. - -You can see all debugging results if you open up the `View Live Debug Log` underneath Tools in the Control Panel window. - -1. `__init__.py` is just an empty file for existance. -2. `{brushName}.py` is a brush algorithm file. Make your `run(...)` function to be linked to the `effects/apply_effect.py` in the future. -3. `{brushName}_requirements.json` is a file contains initialised parameters for the brush. This is the example from `template.json`. It contains the default values for each parameter, data type of each and other metadata which is your name or a description. `id` is extra important because this will be used to communicate between each script. - - ``` json - { - "name": "Super cool effect", - "id": "id_without_spaces", # Set this well so that it could be called from other scripts. - "author": "creator", # Your name - "version": "1.0.0", - "description": "Small description of the effect.", - "dependencies": { - "numpy": ">=2.1.0" - }, - "user_input": { - "Radius": { - "type": "int", - "min": 0, - "max": 100, - "default": 20 - }, - "Strength": { - "type": "float", - "min": 0.0, - "max": 1.0, - "default": 1.0 - }, - "Color": { - "type": "color", - "default": "#FF0000" - } - }, - "stroke_input": { - "image_rgba": "array", - "path": "array", - "clicks": "array" - }, - "flags": { - "smooth_path": true - } - ``` - -While development, check `apply_effect.py` underneath the `effect` folder so that you can have a glimpse of how backend communicates. Happy quantum! - -# Technical Stack - -- Format: Standalone Processing (Java) application for multiple OS -- Supported: - - ``` - (base) astrydpark@Astryds-MacBook-Pro ~ % java -version - openjdk version "21.0.7" 2025-04-15 LTS - OpenJDK Runtime Environment Temurin-21.0.7+6 (build 21.0.7+6-LTS) - OpenJDK 64-Bit Server VM Temurin-21.0.7+6 (build 21.0.7+6-LTS, mixed mode, sharing) - ``` - -- Works on Python 3.11+ (Automatic background: Recent version of Miniconda environment called β€˜`quantumbrush`') - -Project location: `$HOME/QuantumBrush` - -Used IDE version: Eclipse 2025-03 - -# License - -Copyright [2025] [MOTH Quantum] - -Licensed under the Apache License, Version 2.0 (the "License"); -you may not use this file except in compliance with the License. -You may obtain a copy of the License at - - http://www.apache.org/licenses/LICENSE-2.0 - -Unless required by applicable law or agreed to in writing, software -distributed under the License is distributed on an "AS IS" BASIS, -WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -See the License for the specific language governing permissions and -limitations under the License. diff --git a/config/python_path.txt b/config/python_path.txt deleted file mode 100644 index d8e7d80..0000000 --- a/config/python_path.txt +++ /dev/null @@ -1,2 +0,0 @@ -/Users/astrydpark/miniconda3/envs/quantumbrush/bin/python3.11 - diff --git a/effect/GoL/GoL.py b/effect/GoL/GoL.py deleted file mode 100644 index e61a920..0000000 --- a/effect/GoL/GoL.py +++ /dev/null @@ -1,230 +0,0 @@ -import numpy as np -from qiskit import QuantumCircuit, generate_preset_pass_manager -from qiskit_aer import Aer -from qiskit.quantum_info import Pauli, SparsePauliOp, Statevector,partial_trace -from qiskit.circuit.library import RXGate, RZGate,XGate,ZGate,IGate,StatePreparation -import importlib.util -from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister -from qiskit_aer import Aer, statevector_simulator -from qiskit.quantum_info import partial_trace -import colorsys - -spec = importlib.util.spec_from_file_location("utils", "effect/utils.py") -utils = importlib.util.module_from_spec(spec) -spec.loader.exec_module(utils) -#%% -mapping = ['hsv','hvs','shv','svh','vhs','vsh'] - -def hsv_to_statevector(hsv,mapping = 'hsv'): - """ - Maps an RGB value to a qubit statevector and saturation. - - Args: - rgb: A tuple of (r, g, b) values, where each is in the range [0, 255]. - - Returns: - A tuple of (statevector, saturation), where statevector is a - numpy array representing the qubit state, and saturation is a float. - """ - h, s, v = hsv - hsv = {'h':h,'s':s,'v':v} - # Map Hue to phase (phi) and Value to amplitude (theta) - phi = hsv[mapping[0]] * 2 * np.pi - theta = hsv[mapping[1]] * np.pi - - # Create the statevector [alpha, beta] - alpha = np.cos(theta / 2) - beta = np.exp(1j * phi) * np.sin(theta / 2) - - statevector = np.array([alpha, beta]) - return statevector, hsv[mapping[2]] - -def statevector_to_hsv(statevector, semiclassical, mapping = 'hvs'): - """ - Maps a qubit statevector and saturation back to an RGB value. - - Args: - statevector: A numpy array representing the qubit state. - saturation: The saturation value (as a float). - - Returns: - A tuple of (r, g, b) values in the range [0, 255]. - """ - - alpha, beta = statevector[0], statevector[1] - - # Inverse mapping from statevector to H and V - # Ensure alpha is real and non-negative for acos to be in [0, pi] - theta = 2 * np.arccos(np.abs(alpha)) - # Handle the case where beta is zero to avoid division by zero - if np.abs(beta) > 1e-9: - phi = np.angle(beta) - np.angle(alpha) - else: - phi = 0 - - h = phi / (2 * np.pi) - # Normalize h to be in [0, 1] - if h < 0: - h += 1 - v = theta / np.pi - return {mapping[0]:h,mapping[1]:v,mapping[2]:semiclassical} -#%% -def find_closest_pure_state(density_matrix): - """ - Finds the closest pure state to a given density matrix for a single qubit. - - The closest pure state is the eigenvector corresponding to the largest - eigenvalue of the density matrix. - - Args: - density_matrix: A 2x2 NumPy array representing the density matrix. - It must be Hermitian with a trace of 1. - - Returns: - A tuple containing: - - closest_pure_state_vector (np.ndarray): The state vector |ψ⟩. - - closest_pure_state_density_matrix (np.ndarray): The density matrix |ψ⟩⟨ψ|. - - Raises: - ValueError: If the input is not a valid 2x2 density matrix. - """ - # --- Input Validation --- - if not isinstance(density_matrix, np.ndarray) or density_matrix.shape != (2, 2): - raise ValueError("Input must be a 2x2 NumPy array.") - if not np.isclose(np.trace(density_matrix), 1): - raise ValueError("The trace of the density matrix must be 1.") - if not np.allclose(density_matrix, density_matrix.conj().T): - raise ValueError("The density matrix must be Hermitian.") - - # --- Core Algorithm --- - # For a Hermitian matrix, eigh is preferred as it's more efficient - # and guarantees real eigenvalues and orthonormal eigenvectors. - eigenvalues, eigenvectors = np.linalg.eigh(density_matrix) - purity = np.matmul(density_matrix, density_matrix).trace().real - # Find the index of the largest eigenvalue - largest_eigenvalue_index = np.argmax(eigenvalues) - - # The corresponding eigenvector is the state vector of the closest pure state - closest_pure_state_vector = eigenvectors[:, largest_eigenvalue_index] - - - return closest_pure_state_vector, purity - -def liveliness(nhood): - v=nhood - a = v[0][0]+v[1][0]+v[2][0]+v[3][0]+v[5][0]+v[6][0]+v[7][0]+v[8][0] - return np.abs(a) -def SCGOL(nhood): - a = liveliness(nhood) - value = nhood[4] - alive = np.array([1.0,0.0]) - dead = np.array([0.0,1.0]) - B = np.array([[0,0],[1,1]]) - D = np.array([[1,1],[0,0]]) - S = np.array([[1,0],[0,1]]) - if a <= 1: - value = dead - elif (a > 1 and a <= 2): - value = ((np.sqrt(2)+1)*2-(np.sqrt(2)+1)*a)*dead+(a-1)*value#(((np.sqrt(2)+1)*(2-a))**2+(a-1)**2) - elif (a > 2 and a <= 3): - value = (((np.sqrt(2)+1)*3)-(np.sqrt(2)+1)*a)*value+(a-2)*alive#(((np.sqrt(2)+1)*(3-a))**2+(a-2)**2) - elif (a > 3 and a < 4): - value = ((np.sqrt(2)+1)*4-(np.sqrt(2)+1)*a)*alive+(a-3)*dead#(((np.sqrt(2)+1)*(4-a))**2+(a-3)**2) - elif a >= 4: - value = dead - value = value/np.linalg.norm(value) - return value - -def game_of_life(nhood): - qr = QuantumRegister(9,'qr') - qc = QuantumCircuit(qr,name='conway') - v = np.array(nhood).reshape(9,2) - for qubit,state in enumerate(v): - qc.initialize(state,qubit) - for q in [0,1,2,3,4,5,6,7,8]: - pass - if q!=4: - qc.crx(np.pi/2,4,q) - qc.cry(2*np.pi/(q+1),q,(q+1)%9) - qc.crz(2*np.pi/((q+4)%9+1),q,(q+1)%9) - if q!=4: - qc.cx(q,4) - - - job = Aer.get_backend('statevector_simulator').run(qc) - results = job.result().get_statevector() - value = partial_trace(results,[0,1,2,3,5,6,7,8]) - value,purity = find_closest_pure_state(value.data) #make sure vlaue is a normalized complex vector of length 2. - - return value,purity - -def run(params): - """ - Executes the effect pipeline based on the provided parameters. - - Args: - parameters (dict): A dictionary containing all the relevant data. - - Returns: - Image: the new numpy array of RGBA values or None if the effect failed - """ - - # Extract image to work from - image = params["stroke_input"]["image_rgba"] - map = mapping[params["user_input"]["Mapping"]] - # It's a good practice to check any of the request variables - assert image.shape[-1] == 4, "Image must be RGBA format" - - height = image.shape[0] - width = image.shape[1] - # Convert the image to HSV colorspace as a copy - rgb_norm = image[:, :, :3].astype(np.float32) / 255.0 - - image_hsv = np.apply_along_axis( - lambda c: colorsys.rgb_to_hsv(c[0], c[1], c[2]), - axis=2, - arr=rgb_norm - ) - - # Extract the lasso path - path = params["stroke_input"]["path"] - - radius = params["user_input"]["Radius"] - if radius > 0: - copy_region = utils.points_within_radius(path, radius, border = (height, width)) - else: - copy_region = utils.points_within_lasso(path, border = (height, width)) - def extract_neighbourhoods(x, y): - neighbours = [] - for dx in [-1, 0, 1]: - for dy in [-1, 0, 1]: - ni, nj = (x + dx) % width, (y + dy) % height # Wrap around edges - neighbours.append((ni, nj)) - return neighbours - - - for iterations in range(params["user_input"]["Iterations"]): - copy_selection = {} - statevector_selection = {} - semiclassical = {} - after_iteration = {} - for i in copy_region: - neighbourhood = extract_neighbourhoods(i[0],i[1]) - nhood = np.zeros((9,2), dtype=np.complex128) - nhood_s = np.zeros((9,2), dtype=np.float64) - for n,coord in enumerate(neighbourhood): - if coord not in copy_selection: - copy_selection[coord] = np.array(image_hsv[coord[0], coord[1],:3]) - statevector_selection[coord],semiclassical[coord] = hsv_to_statevector(copy_selection[coord],mapping=map) - nhood[n] = statevector_selection[coord] - nhood_s[n] = semiclassical[coord], 1-semiclassical[coord] - v, purity = game_of_life(nhood) - new_sc = SCGOL(nhood_s)[0] - hsv = statevector_to_hsv(v,semiclassical=new_sc, mapping=map) - after_iteration[(i[0],i[1])] = np.array([hsv['h'],hsv['s'],hsv['v']]) - for key in after_iteration: - image_hsv[key[0], key[1],:3] = after_iteration[key] - for key in after_iteration: - image[key[0], key[1],:3] = np.round(np.array(colorsys.hsv_to_rgb(*after_iteration[key]))*255).astype(np.uint8) - return image -#%% \ No newline at end of file diff --git a/effect/GoL/GoL_requirements.json b/effect/GoL/GoL_requirements.json deleted file mode 100644 index 6d9c7e3..0000000 --- a/effect/GoL/GoL_requirements.json +++ /dev/null @@ -1,46 +0,0 @@ -{ - "name": "Game of Life", - "id": "GoL", - "author": "Daniel", - "version": "1.0.0", - "long_description": "This brush/lasso tool implements N iterations of a quantum cellular automata with a nearest neighbour neighbourhood with the result being the new state of the cell.\n Runtime is linear with the number of iterations and number of pixels.\nMapping refers to which color parameters (hue, luminosity and saturation) are mapped to which function in the game of life, as such there are 6 permutations to choose from.\nRadius determines the width of the stroke, if it is 0 then it behaves as a lasso.", - "description": "This brush/lasso implements N iterations of a quantum cellular automata with a nearest neighbour neighbourhood with the result being the new state of the cell.\n πŸ”Έ Runtime is proportional to (number of iterations)x(number of pixels).\n πŸ”Ή Radius determines the width of the stroke, if it is 0 then it behaves as a lasso.\n πŸ”Ή Mapping refers to which color parameters (hue, saturation and value) are mapped to which function in the game of life, as such there are 6 permutations to choose from. The labelling is 0:'hsv',1:'hvs',2:'shv',3:'svh',4:'vhs',5:'vsh'. The interaction of the various parameters is unpredictable, and as such one should pick by taste. Generally the last letter will have the strongest effect.\n πŸ”Ή Iterations is the number of steps of the cellular automata takes.", - "dependencies": { - "numpy": ">=2.1.0", - "colorsys": "", - "qiskit": ">=1.0.0", - "qiskit_ibm_runtime": ">=0.20.0", - "qiskit_aer": ">=0.17.0" - }, - "user_input": { - "Iterations": { - "type": "int", - "label": "Iterations", - "default": 1, - "min": 1, - "max": 10, - "step": 1 - }, - "Mapping": { - "type": "int", - "label": "Mapping", - "default": 0, - "min": 0, - "max": 5, - "step": 1 - }, - "Radius": { - "type": "int", - "min": 0, - "max": 100, - "default": 0 - } - }, - "stroke_input": { - "image_rgba": "array", - "path": "array" - }, - "flags": { - "smooth_path": true - } -} diff --git a/effect/GoL/__init__.py b/effect/GoL/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/effect/__init__.py b/effect/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/effect/acrylic/__init__.py b/effect/acrylic/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/effect/acrylic/acrylic.py b/effect/acrylic/acrylic.py deleted file mode 100644 index a75d778..0000000 --- a/effect/acrylic/acrylic.py +++ /dev/null @@ -1,49 +0,0 @@ -import numpy as np -import time # Added proper import for sleep functionality -import importlib.util - -spec = importlib.util.spec_from_file_location("utils", "effect/utils.py") -utils = importlib.util.module_from_spec(spec) -spec.loader.exec_module(utils) - -def run(params): - """ - Executes the effect pipeline based on the provided parameters. - - Args: - parameters (dict): A dictionary containing all the relevant data. - - Returns: - Image: the new numpy array of RGBA values or None if the effect failed - """ - - # Extract image to work from - image = params["stroke_input"]["image_rgba"] - assert image.shape[-1] == 4, "Image must be RGBA format" - - width = image.shape[1] - height = image.shape[0] - - # All the requirements that were requested are also available - radius = params["user_input"]["Radius"] - assert radius > 0, "Radius must be greater than 0" - - assert params["user_input"]["Color"].shape[0] == 3, "Color must be RGB format" - assert params["user_input"]["Alpha"] >= 0 and params["user_input"]["Alpha"] <= 1, "Alpha must be between 0 and 1" - - path = params["stroke_input"]["path"] - - blur = params["user_input"]["Blur Edges"] - - alpha = params["user_input"]["Alpha"] - - #We can also use some helpful functions from utils - region, distance = utils.points_within_radius(path, radius, border = (height, width), return_distance=True) - - patch = image[region[:, 0], region[:, 1]].astype(np.float32) / 255 - patch[...,:3] = params["user_input"]["Color"] / 255 # Set RGB channels - patch[...,3] = alpha - - image[region[:, 0], region[:, 1]] = utils.apply_patch_to_image(image[region[:, 0], region[:, 1]], patch, blur=blur, distance=distance) - - return image diff --git a/effect/acrylic/acrylic_requirements.json b/effect/acrylic/acrylic_requirements.json deleted file mode 100644 index d35a8f6..0000000 --- a/effect/acrylic/acrylic_requirements.json +++ /dev/null @@ -1,39 +0,0 @@ -{ - "name": "Basic", - "id": "acrylic", - "author": "MOTH", - "version": "1.0.0", - "description": "The Basic brush paints a consistent, uniform color across the canvas.\n\nThe effect is controlled by several parameters:\n πŸ”Ή Radius β†’ determines the size of the brush\n πŸ”Ή Color β†’ sets the base color of the brush\n πŸ”Ή Alpha β†’ controls the opacity of the brush strokes\n πŸ”Ή Blur Edges β†’ ON = smooth, feathered edges; OFF = hard edges\n\nUsage:\n πŸ”Έ Click and drag on the canvas to paint with the selected color.\n ", - "dependencies": { - "numpy": ">=2.1.0" - }, - "user_input": { - "Radius": { - "type": "int", - "min": 0, - "max": 100, - "default": 20 - }, - "Alpha": { - "type": "float", - "min": 0.0, - "max": 1.0, - "default": 1.0 - }, - "Color": { - "type": "color", - "default": "#FF0000" - }, - "Blur Edges": { - "type": "bool", - "default": true - } - }, - "stroke_input": { - "image_rgba": "array", - "path": "array" - }, - "flags": { - "smooth_path": true - } -} \ No newline at end of file diff --git a/effect/apply_effect.py b/effect/apply_effect.py deleted file mode 100644 index 60d46c4..0000000 --- a/effect/apply_effect.py +++ /dev/null @@ -1,260 +0,0 @@ -from copy import copy -import json -import importlib -import importlib.util -from pathlib import Path -import traceback -import numpy as np -from PIL import Image -import numpy as np -import sys -import argparse -import os -import time -from utils import * -import contextlib - -app_path = Path(sys.path[0] + "/..") # Path to the app folder - -def process_variable(var_type: str, variable: any): - match var_type: - case "str": - return str(variable) - case "float": - return float(variable) - case "int": - return int(variable) - case "bool": - return bool(variable) - case "array": - if isinstance(variable, np.ndarray): - return variable - elif isinstance(variable, list): - try: - return np.array(variable) - except Exception as e: - raise ValueError(f"Error converting to numpy array: {e}") - else: - raise ValueError("Invalid array format") - case "color": - # Assuming color is represented as a hex string - if isinstance(variable, str) and variable.startswith("#") and len(variable) in {7, 9}: - # Convert hex to RGB(A) numpy array - hex_color = variable.lstrip("#") - if len(hex_color) == 6: # RGB - return np.array([int(hex_color[i:i+2], 16) for i in (0, 2, 4)]) - elif len(hex_color) == 8: # RGBA - return np.array([int(hex_color[i:i+2], 16) for i in (0, 2, 4, 6)]) - - raise ValueError("Invalid color format") - case _: - raise ValueError(f"Unsupported type: {var_type}") - - -def process_effect(instr: dict): - # Extract stroke_id and project_id from instructions - stroke_id = instr.get("stroke_id", False) - project_id = instr.get("project_id", False) - - if not stroke_id or not project_id: - raise ValueError("stroke_id and project_id must be provided in the instructions.") - - project_path = app_path / f"project/{project_id}" - - # Get effect_id and load requirements - effect_id = instr.get("effect_id") - - effect_path = app_path / f"effect/{effect_id}" - req_path = effect_path / f"{effect_id}_requirements.json" - - with open(req_path, 'r') as req_file: - req = json.load(req_file) - - # Check dependencies with version control - for dependency, version in req.get("dependencies", {}).items(): - try: - module = importlib.import_module(dependency) - #TODO: Check that the version is correct - - except ImportError as e: - raise ImportError(f"Failed to load dependency {dependency}: {e}") - - # Process image - image_path = project_path / f"stroke/{stroke_id}_input.png" - - if not image_path.is_file(): - raise FileNotFoundError(f"Image file not found at {image_path}") - - with Image.open(image_path) as img: - req["stroke_input"]["image_rgba"] = np.array(img.convert("RGBA")) # Ensure the image is in RGBA format - - - # Process user_input and stroke_input - for key in req["user_input"]: - if key not in instr["user_input"]: - raise KeyError(f"Key '{key}' not found in user_input field of stroke instructions.") - - req["user_input"][key] = process_variable(req["user_input"][key]["type"], instr["user_input"][key]) - - for key in req["stroke_input"]: - if key == "image_rgba": - continue # Skip image_rgba as it's already processed - - if key not in instr["stroke_input"]: - raise KeyError(f"Key '{key}' not found in stroke_input of stroke instructions.") - - req["stroke_input"][key] = process_variable(req["stroke_input"][key], instr["stroke_input"][key]) - - # I need to rotate clicks and paths into (y,x) format - if ( key == "clicks" or key == "path" ): - req["stroke_input"][key] = req["stroke_input"][key][..., ::-1] - - - # Process any other flags - - if req["flags"].get("smooth_path", False): - req["stroke_input"]["path"] = interpolate_pixels(req["stroke_input"]["path"], numpy=True) - - if req["flags"].get("use_hls", False): - req["stroke_input"]["path"] = interpolate_pixels(req["stroke_input"]["path"], numpy=True) - - # Add a few flags needed to apply the effects - req["effect_id"] = effect_id - req["effect_script_path"] = effect_path / f"{effect_id}.py" - req["stroke_output_path"] = project_path / f"stroke/{stroke_id}_output.png" - - return req - -def apply_effect(req: dict): - # Save the input image to apply mask - input_image = copy(req["stroke_input"]["image_rgba"]) - - # Load and execute the effect - spec = importlib.util.spec_from_file_location(req["effect_id"], req["effect_script_path"]) - effect_module = importlib.util.module_from_spec(spec) - sys.modules[req["effect_id"]] = effect_module - spec.loader.exec_module(effect_module) - - new_image = effect_module.run(req) - - # Merge the new image with the original image - mask = np.all(new_image == input_image, axis=-1) - new_image[mask] = [0, 0, 0, 0] # Set differing pixels to [0, 0, 0, 0] - - output_path = req["stroke_output_path"] - output_path.parent.mkdir(parents=True, exist_ok=True) # Ensure the directory exists - Image.fromarray(new_image.astype(np.uint8)).save(output_path, format="PNG") - - return True - -def record_error(error): - log_file = app_path / "log/error.log" - log_file.parent.mkdir(parents=True, exist_ok=True) # Ensure log directory exists - - error_message = traceback.format_exc() - - with open(log_file, "a") as log: - log.write(error_message) - - print(error_message) - -def dump_json(data, file_path): - # Make sure the directory exists - Path(file_path).parent.mkdir(parents=True, exist_ok=True) - - # Use a safer approach for atomic file operations - temp_path = f"{file_path}.tmp" - try: - with open(temp_path, "w") as f: - json.dump(data, f) - - # On Windows, os.replace might fail if the destination exists - if os.path.exists(file_path): - os.remove(file_path) - os.rename(temp_path, file_path) - except Exception as e: - # If atomic operation fails, try direct write as fallback - print(f"Warning: Atomic write failed ({str(e)}), using direct write") - with open(file_path, "w") as f: - json.dump(data, f) - -class Tee: - def __init__(self, *files): - self.files = files - def write(self, obj): - for f in self.files: - f.write(obj) - f.flush() - def flush(self): - for f in self.files: - f.flush() - - -if __name__ == "__main__": - - log_output_file = app_path / "log/console_output.log" - log_output_file.parent.mkdir(parents=True, exist_ok=True) - log_fh = open(log_output_file, "a") - - sys.stdout = Tee(sys.stdout, log_fh) - sys.stderr = Tee(sys.stderr, log_fh) - - # Parse command line arguments - parser = argparse.ArgumentParser(description="Apply an effect to a stroke in a project.") - parser.add_argument("stroke_path", type=str, help="The ID of the stroke.") - args = parser.parse_args() - - success = False - instructions = {} - - try: - if not Path(args.stroke_path).is_file(): - raise FileNotFoundError(f"Stroke file not found at {args.stroke_path}") - - #Read the stroke instructions from the provided path - with open(args.stroke_path, 'r') as stroke_file: - instructions = json.load(stroke_file) - - instructions["effect_received"] = True - dump_json(instructions, args.stroke_path) - - try: - #Process the effect - data = process_effect(instructions) - - instructions["effect_processed"] = True - dump_json(instructions, args.stroke_path) - - #Apply the effect - success = apply_effect(data) - - instructions["effect_success"] = success - dump_json(instructions, args.stroke_path) - - except Exception as e: - record_error(e) - instructions["effect_success"] = False - dump_json(instructions, args.stroke_path) - success = False - - except FileNotFoundError as e: - record_error(e) - if instructions: - instructions["effect_received"] = False - dump_json(instructions, args.stroke_path) - success = False - except Exception as e: - record_error(e) - if instructions: - instructions["effect_success"] = False - dump_json(instructions, args.stroke_path) - success = False - # Redirect stdout and stderr to a log file - - - if success: - print("Effect applied successfully.") - sys.exit(0) - else: - print("Failed to apply effect.") - sys.exit(1) diff --git a/effect/chemical/__init__.py b/effect/chemical/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/effect/chemical/chemical.py b/effect/chemical/chemical.py deleted file mode 100644 index fcc50a9..0000000 --- a/effect/chemical/chemical.py +++ /dev/null @@ -1,206 +0,0 @@ -""" -Chemical Brush Effect Module. - -The `Chemical` brush uses intermediate steps of the Variational Quantum -Eigensolver (VQE) algorithm from quantum chemistry to locally modify the -colors of a canvas. In this way, the brush encodes not only the physical -process related to the ground state of molecules but also the behavior of -the variational algorithm itself. - -Authors: - Jui-Ting Lu & Henrique Ennes -""" - -import numpy as np -from qiskit import qpy -from qiskit import QuantumCircuit -from qiskit.quantum_info import Pauli, SparsePauliOp -import importlib.util -from scipy.stats import circmean -import json - -spec = importlib.util.spec_from_file_location("utils", "effect/utils.py") -utils = importlib.util.module_from_spec(spec) -spec.loader.exec_module(utils) - -def resize_list_repeat(values, new_length): - """ - Resize a list by repeating or skipping elements uniformly. - - Args: - values (list): Original list of elements to resize. - new_length (int): Desired length of the output list. Must be non-negative. - - Returns: - list: A new list of length `new_length`. - """ - - if new_length <= 0: - return [] - - old_length = len(values) - if old_length == 0: - return [] - if old_length == 1: - return [values[0]] * new_length - if old_length == new_length: - return values.copy() - - # Compute the new indices uniformly - idx = np.linspace(0, old_length - 1, new_length) - idx = np.round(idx).astype(int) - - return [values[i] for i in idx] - - -def chemistry(initial_angles, circuit, params_to_apply, num_repeat): - """ - Run Chemical model simulation on quantum hardware simulator. - - Args: - initial_angles (list): List of initial angles (phi, theta) for each drop - circuit: The quantum circuit in parametric form. - params_to_apply (list): List of parameters to apply to the circuit. - - - Returns: - Final angles after application of circuits. - """ - num_angles = len(initial_angles) - print(f"{len(initial_angles)} initial angles: {initial_angles}") - - num_qubits = circuit.num_qubits - num_circuits = num_angles // num_qubits - leftover_qubits = num_angles % num_qubits # number of leftover qubits - # repeat the parameters if user wants to apply each circuits on more than 1 times - adjusted_params_to_apply = [x for x in params_to_apply for _ in range(num_repeat)] - # adjust the number of parameters of subcircuits to match the expected number of subcircuits - if num_angles > len(adjusted_params_to_apply): - adjusted_params_to_apply = resize_list_repeat(params_to_apply, num_circuits) - - # Use mutliple circuits to get the output angles - x_expectations = np.zeros(num_qubits * num_circuits) - y_expectations = np.zeros(num_qubits * num_circuits) - z_expectations = np.zeros(num_angles * num_circuits) - for index_subcircuit in range(num_circuits): - qc = QuantumCircuit(num_qubits+1) - start_index = index_subcircuit * num_qubits - end_index = start_index + num_qubits - # Prepare each qubit in the state defined by (theta, phi) - qc.x(num_qubits) - for i, (phi, theta) in enumerate(initial_angles[leftover_qubits+start_index:leftover_qubits+end_index]): - qc.ry(theta, i) - qc.rz(phi, i) - - qc.compose(circuit.assign_parameters({ - '_t_0_' : adjusted_params_to_apply[index_subcircuit][0], - '_t_1_' : adjusted_params_to_apply[index_subcircuit][1], - '_t_2_' : adjusted_params_to_apply[index_subcircuit][2]}), qubits= range(num_qubits), inplace=True) - - # measure expectations - ops = [SparsePauliOp(Pauli('I'*(num_qubits-i) + p + 'I'*i)) for p in ['X','Y','Z'] for i in range(num_qubits)] - obs = utils.run_estimator(qc,ops) - # Store the expectations - x_expectations[start_index:end_index] = obs[:num_qubits].mean() - y_expectations[start_index:end_index] = obs[num_qubits:2*num_qubits].mean() - z_expectations[start_index:end_index] = obs[2*num_qubits:].mean() - - # phi = arctan2(Y, X) - phi_expectations = [np.arctan2(y,x) % (2 * np.pi) for x, y in zip(x_expectations, y_expectations)] - # theta = arccos(Z) - theta_expectations = [np.arctan2(np.sqrt(x**2 + y**2),z) for x, y, z in zip(x_expectations, y_expectations, z_expectations)] - - final_angles = list(zip(phi_expectations, theta_expectations)) - - return initial_angles[:leftover_qubits]+final_angles - - - -# The main function using Chemical model -def run(params): - """ - Executes the effect pipeline based on the provided parameters. - - Args: - parameters (dict): A dictionary containing all the relevant data. - - Returns: - Image: the new numpy array of RGBA values or None if the effect failed - """ - - - # Extract image parameters - image = params["stroke_input"]["image_rgba"] - assert image.shape[-1] == 4, "Image must be RGBA format" - - height = image.shape[0] - width = image.shape[1] - - # Extract user-defined parameters - molecule = "H2" - with open('effect/chemical/data/' + molecule.lower() + '_parameters.json', "r") as f: - circuit_params = json.load(f) - with open('effect/chemical/data/' + molecule.lower() + '_circuit.qpy', "rb") as f: - circuit = qpy.load(f)[0] - - distance = params["user_input"]["Bond Distance"] - assert 2.5 >= distance >= 0.735, "Distance must be greater than between 0.735 and 2.5 Angstroms" - distances = [float (d) for d in circuit_params.keys()] - distance = min(distances, key=lambda x:abs(x-distance)) - print(f"Selected distance for simulation: {distance} Angstroms") - - radius = params["user_input"]["Radius"] - assert radius > 0, "Radius must be greater than 0" - num_repeat = params["user_input"]["Number of Repeats"] - assert num_repeat >= 1, "Number of Repeats must be at least 1" - - # Extract stroke parameters - path = params["stroke_input"]["path"] - - path_length = len(path) - - # Split path to have the same number of pixels as circuits available - params_to_apply = circuit_params[str(distance)] - print(f"Using distance: {distance} and the number of available circuits: {len(params_to_apply)}") - num_discretization = len(params_to_apply) * circuit.num_qubits # number of available circuits * qubits - split_size = max(1, path_length // num_discretization) - split_paths = [path[i * split_size : (i + 1) * split_size] for i in range(num_discretization - 1)] - split_paths.append(path[(num_discretization - 1) * split_size :]) - - initial_angles = [] #(Theta,phi) - pixels = [] - for lines in split_paths: - - region, distance = utils.points_within_radius(lines, radius, border = (height, width), return_distance=True) - - selection = image[region[:, 0], region[:, 1]] - selection = selection.astype(np.float32) / 255.0 - selection_hls = utils.rgb_to_hls(selection) - - phi = circmean(2 * np.pi * selection_hls[..., 0]) - theta = np.pi * np.mean(selection_hls[..., 1], axis=0) - - initial_angles.append((phi,theta)) - pixels.append((region, distance, selection_hls)) - - final_angles = chemistry(initial_angles, circuit, params_to_apply, num_repeat) - print("final angles", final_angles) - - for i,(region, distance, selection_hls) in enumerate(pixels): - new_phi, new_theta = final_angles[i] - old_phi, old_theta = initial_angles[i] - - offset_h = (new_phi - old_phi) / (2 * np.pi) - offset_l = (new_theta - old_theta) / np.pi - - selection_hls[...,0] = (selection_hls[...,0] + offset_h) % 1 - selection_hls[...,1] += offset_l - - selection_hls = np.clip(selection_hls, 0, 1) - - selection_rgb = utils.hls_to_rgb(selection_hls) - selection_rgb = (selection_rgb * 254).astype(np.uint8) - - image[region[:, 0], region[:, 1]] = selection_rgb - - return image \ No newline at end of file diff --git a/effect/chemical/chemical_requirements.json b/effect/chemical/chemical_requirements.json deleted file mode 100644 index 053774a..0000000 --- a/effect/chemical/chemical_requirements.json +++ /dev/null @@ -1,43 +0,0 @@ -{ - "name": "Chemical", - "id": "chemical", - "author": "Luminists (Ali & Henrique & Jui-Ting)", - "version": "1.0.0", - "long_description": "The brush uses the Variational Quantum Eigensolver (VQE) to simulate simple molecules (e.g., H2) and drives changes on the canvas based on the resulting quantum states.\nThis is achieved by applying a preprocessed family of VQE circuits to different pixels of the canvas. The resulting quantum states are then mapped to color values, creating a dynamic and interactive painting experience that reflects the underlying quantum chemistry simulations.\nBy adjusting parameters such as bond distance and basis set, users can explore the visual effects produced by the brush.\nAvailable parameters include:\n- Radius: controls the size of the brush\n- Bond Distance: sets the interatomic distance for the simulated molecule.\n- Number of Repeats: Repetitions of each circuit before switching\n", - "description": "Chemical uses the Variational Quantum Eigensolver (VQE) to drive changes on the underlying canvas.\n\nThe effect is controlled by several parameters:\nπŸ”Ή Radius β†’ determines the size of the brush\nπŸ”Ή Bond Distance β†’ determines the interatomic distance to simulate\nπŸ”Ή Number of Repeats β†’ how many times each circuit is applied before moving to the next one.\n\nUsage:\nπŸ”Έ Click and drag on the canvas to apply the effect.", - "dependencies": { - "numpy": ">=2.1.0", - "colorsys": "", - "json": "", - "scipy": "", - "qiskit": ">=2.1.0" - }, - "user_input": { - "Radius": { - "type": "int", - "min": 0, - "max": 100, - "default": 20 - }, - "Bond Distance": { - "type": "float", - "min": 0.735, - "max": 2.5, - "default": 0.735 - }, - "Number of Repeats": { - "type": "int", - "min": 1, - "max": 100, - "default": 1 - } - }, - "stroke_input": { - "image_rgba": "array", - "path": "array", - "clicks": "array" - }, - "flags": { - "smooth_path": true - } -} diff --git a/effect/chemical/data/h2_circuit.qpy b/effect/chemical/data/h2_circuit.qpy deleted file mode 100644 index 004a69824bd62066566156c9dafdfe481c4349f4..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 17949 zcmeHPONbps6z%sWlPHQwR#8M3LfjZh{Xe*fUz{KTH7-Piv8$?U7zoLXnUP>jKo@@F z!cF|_+?nVq8#h80(S?ZMQbEOq=vF~+5hPZ1clGOeOsA@YlQ>B?%LV~U(~CMEB8Y#{a1e+Ke6n) zY{^EW<+5S&5pMNl{4rCV>g&A=?xGy6?zins>-X~V$$a(D;$trzIkdX6c;xWB=7lr{ zGb@oG2Cse>-X~V=rOY} zud!nWnOrNRhy_9vxki!zg@6H!n!rw=;_nQi@Ykg{ChP#;=8rY(WLYVA*W4yk_NzY* zKAx`>mFQz#=hC~jsAk!v*3k@|Dkh^bKul_pD^9SKiWP`3tq~!lpp;+dV%k~@tW$l@ zrYoh<-zW=Y+XmGdY4k`#wsuQ@gXf`(kEfq&_$VquqdRMY!Eaw4+qxy&_eXWLbn@=y zb6;-T|J!Tmo@Z&^I(2yskuASVOKUgO|zuX(cBPr_pLi}S95O#?5>}nO94rk($mjJQS@j`Dr-!t zi@}2vlWO{2Bl9~ym|ty8$qMKZ8Q0pSykTi?i?S zyyt~qc6{YxH(V3_FWa$yd3amjvjIu)}DJ#W zO1M8Pk#uu}!Rbn;bAg|`JrhI}5)x!xodDS!<(x{ zRmgbx^CX#j6%xOGz;^D-e|LxHt(B-8R|Uf$koXN7vajL%cO`Gx(uZHa@#nYCKX}JS zThClLbnnfN_DwBM-=EFC_x;JAKa~f5IQ99S_qV@t`X5)9Kx--+m+#;z8`CsP3LVYu z%Er2cI~eLw*=Q-i3oWj(-YTw>*GU=aSVq>HS1%t*8a0;StSUB1q;w<+Sf$j1f5bie z$~JVw>27?X(kp5Mtf^(MCHDAX);T7n(5$F_zT8Hr0Wg9^#x>SbfER51h7ARbST?x= zj3n2MWn4X}QCeXwmX)jkWwtWR&Kg}a6`0g&@58-3sK>JeO>{9hNg@sj$6A;E)GvQ9%nyQ@ZBBFIX_5-p`kvJwetr9Tx@Q*NVfZ4EAAwBj}@eQyL-??%KRYtxqD4! z0tfNXu}PN$gS)4z`2V;ZNOH{B7KmzgurVIg@rF)pu;xwh_=>0LI?ndG*|7(U_B%R$ z#vG2RmwsaZ?!(I^D~01f%39G(_%{KaZ}UUfwFeLJ*N!7xtp8SFPcGuGKSj7$e+R(& G%KsOVV!q-4 diff --git a/effect/chemical/data/h2_parameters.json b/effect/chemical/data/h2_parameters.json deleted file mode 100644 index 37fbb04..0000000 --- a/effect/chemical/data/h2_parameters.json +++ /dev/null @@ -1,366522 +0,0 @@ -{ - 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"qiskit": "" - }, - "user_input": { - "Strength": { - "type": "float", - "min": 0.0, - "max": 1.0, - "default": 0.33 - } - }, - "stroke_input": { - "image_rgba": "array", - "clicks": "array", - "path": "array" - }, - "flags": {} -} \ No newline at end of file diff --git a/effect/damping/__init__.py b/effect/damping/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/effect/damping/damping.py b/effect/damping/damping.py deleted file mode 100644 index 2d7ebc7..0000000 --- a/effect/damping/damping.py +++ /dev/null @@ -1,148 +0,0 @@ -#Add any dependencies but don't forget to list them in the requirements if they need to be pip installed -import numpy as np -import colorsys -from qiskit import QuantumCircuit -from qiskit.quantum_info import Pauli, SparsePauliOp, Statevector -import importlib.util -from scipy.stats import circmean - -spec = importlib.util.spec_from_file_location("utils", "effect/utils.py") -utils = importlib.util.module_from_spec(spec) -spec.loader.exec_module(utils) - - -def damping(initial_angles, strength,invert = False): - num_qubits = len(initial_angles) - print("initial angles",initial_angles) - - # We ned first to align the target angle to to z axis - - qc = QuantumCircuit(num_qubits + 1) - rotation = 2*np.arccos(1-strength) - - # Prepare each qubit in the state defined by (theta, phi) - for i, (phi, theta) in enumerate(initial_angles): - qc.ry(theta, i) - qc.rz(phi, i) - - if invert: - qc.x(i) - - qc.cry(rotation,target_qubit = num_qubits,control_qubit = i) - qc.cx(target_qubit = i,control_qubit = num_qubits) - - if invert: - qc.x(i) - - ops = [SparsePauliOp(Pauli('I'*(num_qubits-i) + p + 'I'*i)) for p in ['X','Y','Z'] for i in range(num_qubits) ] - obs = utils.run_estimator(qc,ops) - - x_expectations = obs[:num_qubits] - y_expectations = obs[num_qubits:2*num_qubits] - z_expectations = obs[2*num_qubits:] - - # phi = arctan2(Y, X) - phi_expectations = [np.arctan2(y,x) % (2 * np.pi) for x, y in zip(x_expectations, y_expectations)] - # theta = arccos(Z) - theta_expectations = [np.arctan2(np.sqrt(x**2 + y**2),z) for x, y, z in zip(x_expectations, y_expectations, z_expectations)] - - final_angles = list(zip(phi_expectations, theta_expectations)) - return final_angles - - - - - - - -# The only thing that you need to change is this function -def run(params): - """ - Executes the effect pipeline based on the provided parameters. - - Args: - parameters (dict): A dictionary containing all the relevant data. - - Returns: - Image: the new numpy array of RGBA values or None if the effect failed - """ - - - # Extract image to work from - image = params["stroke_input"]["image_rgba"] - # It's a good practice to check any of the request variables - assert image.shape[-1] == 4, "Image must be RGBA format" - - height = image.shape[0] - width = image.shape[1] - - path = params["stroke_input"]["path"] - clicks = params["stroke_input"]["clicks"] - assert len(clicks) < 20, "There can be no more than 20 clicks in a stroke" - - n_drops = len(clicks) - - split_paths = [] - # Split path into subpaths, each starting with a click - click_indices = [] - c = 0 - for i, p in enumerate(path): - if np.all(p == clicks[c]): - click_indices.append(i) - c += 1 - if c >= n_drops: - break - - for idx, start in enumerate(click_indices): - end = click_indices[idx + 1] if idx + 1 < len(click_indices) else len(path) - interp_path = utils.interpolate_pixels(path[start:end]) - split_paths.append(interp_path) - - # Get the radius of the drop - radius = params["user_input"]["Radius"] - assert radius > 0, "Radius must be greater than 0" - - invert = params["user_input"]["Invert Luminosity"] - if invert: - print("Inverting luminosity") - - initial_angles = [] #(Theta,phi) - pixels = [] - for lines in split_paths: - - region = utils.points_within_radius(lines, radius, border = (height, width)) - - selection = image[region[:, 0], region[:, 1]] - selection = selection.astype(np.float32) / 255.0 - selection_hls = utils.rgb_to_hls(selection) - - phi = circmean(2 * np.pi * selection_hls[..., 0]) - theta = np.pi * np.mean(selection_hls[..., 1], axis=0) - - initial_angles.append((phi,theta)) - pixels.append((region, selection_hls)) - - strength = params["user_input"]["Strength"] - assert strength >= 0 and strength <= 1, "Strength must be between 0 and 1" - - final_angles = damping(initial_angles, strength,invert) - - for i,(region,selection_hls) in enumerate(pixels): - new_phi, new_theta = final_angles[i] - old_phi, old_theta = initial_angles[i] - - offset_h = (new_phi - old_phi) / (2 * np.pi) - offset_l = (new_theta - old_theta) / np.pi - - selection_hls[...,0] = (selection_hls[...,0] + offset_h) % 1 - selection_hls[...,1] += offset_l - - #Need to change the luminosity - selection_hls = np.clip(selection_hls, 0, 1) - selection_rgb = utils.hls_to_rgb(selection_hls) - selection_rgb = (selection_rgb * 254).astype(np.uint8) - - image[region[:, 0], region[:, 1]] = selection_rgb - - - return image diff --git a/effect/damping/damping_requirements.json b/effect/damping/damping_requirements.json deleted file mode 100644 index 4498d29..0000000 --- a/effect/damping/damping_requirements.json +++ /dev/null @@ -1,38 +0,0 @@ -{ - "name": "Smudge", - "id": "damping", - "author": "Joao", - "version": "1.0.0", - "description": "The smudge brush allows the user to paint over different parts of the canvas and mix colors based on pumping/damping quantum channels.\n\nThe quality of the effect is controlled by several parameters:\n πŸ”Ή Radius β†’ determines the size of the brush\n πŸ”Ή Strength β†’ controls how strong the effect will be\n πŸ”Ή Invert Luminosity β†’ ON = first color light, OFF = first color dark\n\nUsage:\n πŸ”Έ Click and drag multiple times over the canvas to create multiple strokes.\n πŸ”Έ Each stroke has a new color.\n\n ⚠️ Warning: the number of strokes is limited to 20.", - "dependencies": { - "numpy": ">=2.1.0", - "colorsys": "", - "qiskit": "" - }, - "user_input": { - "Radius": { - "type": "int", - "min": 0, - "max": 100, - "default": 20 - }, - "Strength": { - "type": "float", - "min": 0.0, - "max": 1.0, - "default": 1.0 - }, - "Invert Luminosity": { - "type": "bool", - "default": false - } - }, - "stroke_input": { - "image_rgba": "array", - "path": "array", - "clicks": "array" - }, - "flags": { - "smooth_path": false - } -} \ No newline at end of file diff --git a/effect/heisenbrush/__init__.py b/effect/heisenbrush/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/effect/heisenbrush/heisenbrush.py b/effect/heisenbrush/heisenbrush.py deleted file mode 100644 index 8ef9389..0000000 --- a/effect/heisenbrush/heisenbrush.py +++ /dev/null @@ -1,177 +0,0 @@ -import numpy as np -import colorsys -from qiskit import QuantumCircuit, QuantumRegister, generate_preset_pass_manager -from qiskit.quantum_info import SparsePauliOp -import importlib.util - -spec = importlib.util.spec_from_file_location("utils", "effect/utils.py") -utils = importlib.util.module_from_spec(spec) -spec.loader.exec_module(utils) - - -def scale_to_range(x, in_min=1, in_max=100, out_min=2, out_max=10): - """ - Linearly scale x from [in_min, in_max] to [out_min, out_max]. - """ - if not (in_min <= x <= in_max): - raise ValueError(f"Input {x} is out of range [{in_min}, {in_max}]") - return int(round(out_min + (x - in_min) * (out_max - out_min) / (in_max - in_min))) if in_max<100 else 10 - - -def get_mean_magnetization(n_qubits:int): - z_pauli = [] - for site in range(n_qubits): - z_op = ['I'] * n_qubits - z_op[site] = 'Z' - z_pauli.append(''.join(z_op)) - return SparsePauliOp(z_pauli)/n_qubits - -def time_evolution_Heisenberg(n_qubits: int, J_list: list, hz_list: list, hx_list: list, dt: float) -> QuantumCircuit: - """Time evolution circuit for the Heisenberg model with periodic boundary conditions - Args: - n_qubits: number of qubits - J_list: interacting couplings for each nearest neighbor - hz_list: local Z field for each qubit - hx_list: local X field for each qubit - dt: time step - Returns: - circ_dt: QuantumCircuit of the time evolution - """ - - if not isinstance(dt, (int, float)): - dt = 0.1 - if dt <= 0: - raise ValueError("dt must be a positive number.") - - q = QuantumRegister(n_qubits) - circ_dt = QuantumCircuit(q) - - for n in range(n_qubits): - J = J_list[n] - ## exp(-it * J * (X_n X_{n+1} + Y_n Y_{n+1} + Z_n Z_{n+1})) - circ_dt.rxx(2*J*dt, q[n], q[(n+1)%n_qubits]) - circ_dt.ryy(2*J*dt, q[n], q[(n+1)%n_qubits]) - circ_dt.rzz(2*J*dt, q[n], q[(n+1)%n_qubits]) - - for n in range(n_qubits): - ## exp(-it * hx[n] * X_n) exp(-it * hz[n] * Z_n) - circ_dt.rz(2*dt*hz_list[n], q[n]) - circ_dt.rx(2*dt*hx_list[n], q[n]) - - return circ_dt - -def run_heisenberg_hardware(dt_list, radius, phi, theta): - """ - Run Heisenberg model simulation on quantum hardware simulator. - - Args: - dt_list: List of time steps for evolution - - Returns: - List of RGB color tuples - """ - try: - - nsteps = len(dt_list) - n_qubits = scale_to_range(radius) - - J_list =[-0.5]*n_qubits - hz_list =[0.5]*n_qubits - hx_list =[0.5]*n_qubits - - circuits=[] - circ = QuantumCircuit(n_qubits) - #Create initial state with rotations of phi,theta for each qubit - initial_angles = [(phi, theta)] * n_qubits # All qubits start with the same angles - for i, (phi, theta) in enumerate(initial_angles): - circ.ry(theta, i) - circ.rz(phi, i) - - - ### start time evolution - for step,dt in zip(range(nsteps),dt_list): - print(f"J_list: {J_list}, hz_list: {hz_list}, hx_list: {hx_list}, dt: {dt}") - circ_dt = time_evolution_Heisenberg(n_qubits, J_list, hz_list, hx_list, dt) - circ = circ.compose(circ_dt) - circuits.append(circ.copy()) - - - observables = get_mean_magnetization(n_qubits) - - # Run the estimator - values=utils.run_estimator(circuits, observables, backend=None) - - values=np.array([val[0] for val in values]) - - print(f"Values: {values}") - return values - - - except Exception as e: - print(f"Quantum simulation failed: {e}") - - return - - -# The main function using Heisenberg model -def run(params): - """ - Executes the Heisenberg quantum effect pipeline based on the provided parameters. - - Args: - parameters (dict): A dictionary containing all the relevant data. - - Returns: - Image: the new numpy array of RGBA values or None if the effect failed - """ - - # Extract image to work from - image = params["stroke_input"]["image_rgba"].copy() - assert image.shape[-1] == 4, "Image must be RGBA format" - - height = image.shape[0] - width = image.shape[1] - - path = params["stroke_input"]["path"] - - # Get the radius of the effect - radius = params["user_input"]["Radius"] - assert radius > 0, "Radius must be greater than 0" - - color = params["user_input"]["Color"] - h,l,s = colorsys.rgb_to_hls(color[0]/255, color[1]/255, color[2]/255) - print(f"Using color: {color}") - - phi, theta, _ = utils.color_to_spherical(color) - print(f"Using angles: phi={phi}, theta={theta}") - - strength = params["user_input"]["Strength"] - assert strength > 0, "Strength must be greater than 0" - - - normalized_distances = [0.1] * int(max(2,min(len(path)/radius/4, 10))) #dt*path_length - - # Run Heisenberg simulation to get colors - color_shifts = run_heisenberg_hardware(normalized_distances, radius, phi, theta) - - new_hls = np.array([[(h + shift) % 1.0, (l + shift) % 1, (s + shift) % 1.0] for shift in color_shifts]) - new_hls = np.array([(1 - strength) * np.array([h,l,s]) + strength * new for new in new_hls]) - heisenberg_colors = utils.hls_to_rgb(new_hls) - - - split_size = max(1, len(path) // len(heisenberg_colors)) - split_paths = [path[i * split_size : (i + 1) * split_size] for i in range(len(heisenberg_colors) - 1)] - split_paths.append(path[(len(heisenberg_colors) - 1) * split_size :]) - - - for i,path in enumerate(split_paths): - # Get the region around this point - region = utils.points_within_radius(path, radius, border=(height, width)) - - new_patch = image[region[:, 0], region[:, 1]].astype(np.float32)/255 - new_patch[...,:3] = heisenberg_colors[i] - - image[region[:, 0], region[:, 1]] = utils.apply_patch_to_image(image[region[:, 0], region[:, 1]], new_patch) - - print("Heisenberg effect applied successfully") - return image \ No newline at end of file diff --git a/effect/heisenbrush/heisenbrush_requirements.json b/effect/heisenbrush/heisenbrush_requirements.json deleted file mode 100644 index 58d94c6..0000000 --- a/effect/heisenbrush/heisenbrush_requirements.json +++ /dev/null @@ -1,40 +0,0 @@ -{ - "name": "Heisenbrush (continuous)", - "id": "heisenbrush", - "author": "Arianna", - "version": "1.0.0", - "long_description": "This brush blends artistic expression with quantum physics by simulating how quantum spins evolve in the Heisenberg model. When you paint a stroke, your selected color is converted into quantum angles, and each point on the path becomes part of a simulated quantum system.\n\nAs the brush moves, a quantum circuit models the magnetization of this system over timeβ€”how the spins of quantum particles align or shift. This magnetization data is then used to gradually modify your original color’s Hue, Lightness, and Saturation, producing a smooth, evolving color effect along the stroke.\n\nThe Strength setting controls how much the quantum-evolved colors influence your base color. At low strength, the original color dominates; at high strength, the quantum behavior takes over, leading to unexpected color transformations.\n\n -The stroke path and brush radius determine how many qubits are simulated. \n -The Heisenberg model evolves these qubits over multiple time steps. \n -The mean magnetization is measured and mapped back into visual color changes.", - "description": "The Heisenbrush simulates color shifts through the Heisenberg spin model. Each stroke is split into segments, and each segment evolves a quantum state that transforms Hue, Lightness, and Saturation.\n\nThe quality of the effect is controlled by several parameters:\n πŸ”Ή Radius β†’ determines the size of the brush and the number of qubits in the simulation\n πŸ”Ή Strength β†’ blends between the base color and quantum-generated colors\n πŸ”Ή Color β†’ defines the initial state of the quantum evolution\n\nUsage:\n πŸ”Έ Click and drag on the canvas in a single motion to apply the effect.", - "dependencies": { - "numpy": ">=2.1.0", - "colorsys": "", - "qiskit": ">=1.0.0", - "qiskit_ibm_runtime": ">=0.20.0", - "qiskit_aer": ">=0.17.0" - }, - "user_input": { - "Radius": { - "type": "int", - "min": 1, - "max": 100, - "default": 5 - }, - "Strength": { - "type": "float", - "min": 0.0, - "max": 1.0, - "default": 0.5 - }, - "Color": { - "type": "color", - "default": "#FF0000" - } - }, - "stroke_input": { - "image_rgba": "array", - "path": "array" - }, - "flags": { - "smooth_path": true - } -} \ No newline at end of file diff --git a/effect/heisenbrush2/__init__.py b/effect/heisenbrush2/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/effect/heisenbrush2/heisenbrush2.py b/effect/heisenbrush2/heisenbrush2.py deleted file mode 100644 index 226d8e3..0000000 --- a/effect/heisenbrush2/heisenbrush2.py +++ /dev/null @@ -1,176 +0,0 @@ -import numpy as np -import colorsys -from qiskit import QuantumCircuit, QuantumRegister, generate_preset_pass_manager -from qiskit.quantum_info import SparsePauliOp -import importlib.util - -spec = importlib.util.spec_from_file_location("utils", "effect/utils.py") -utils = importlib.util.module_from_spec(spec) -spec.loader.exec_module(utils) - - -def scale_to_range(x, in_min=1, in_max=100, out_min=2, out_max=10): - """ - Linearly scale x from [in_min, in_max] to [out_min, out_max]. - """ - if not (in_min <= x <= in_max): - raise ValueError(f"Input {x} is out of range [{in_min}, {in_max}]") - return int(round(out_min + (x - in_min) * (out_max - out_min) / (in_max - in_min))) if in_max<100 else 10 - - -def get_mean_magnetization(n_qubits:int): - z_pauli = [] - for site in range(n_qubits): - z_op = ['I'] * n_qubits - z_op[site] = 'Z' - z_pauli.append(''.join(z_op)) - return SparsePauliOp(z_pauli)/n_qubits - -def time_evolution_Heisenberg(n_qubits: int, J_list: list, hz_list: list, hx_list: list, dt: float) -> QuantumCircuit: - """Time evolution circuit for the Heisenberg model with periodic boundary conditions - Args: - n_qubits: number of qubits - J_list: interacting couplings for each nearest neighbor - hz_list: local Z field for each qubit - hx_list: local X field for each qubit - dt: time step - Returns: - circ_dt: QuantumCircuit of the time evolution - """ - - if not isinstance(dt, (int, float)): - dt = 0.1 - if dt <= 0: - raise ValueError("dt must be a positive number.") - - q = QuantumRegister(n_qubits) - circ_dt = QuantumCircuit(q) - - for n in range(n_qubits): - J = J_list[n] - ## exp(-it * J * (X_n X_{n+1} + Y_n Y_{n+1} + Z_n Z_{n+1})) - circ_dt.rxx(2*J*dt, q[n], q[(n+1)%n_qubits]) - circ_dt.ryy(2*J*dt, q[n], q[(n+1)%n_qubits]) - circ_dt.rzz(2*J*dt, q[n], q[(n+1)%n_qubits]) - - for n in range(n_qubits): - ## exp(-it * hx[n] * X_n) exp(-it * hz[n] * Z_n) - circ_dt.rz(2*dt*hz_list[n], q[n]) - circ_dt.rx(2*dt*hx_list[n], q[n]) - - return circ_dt - -def run_heisenberg_hardware(dt_list, radius, phi, theta): - """ - Run Heisenberg model simulation on quantum hardware simulator. - - Args: - dt_list: List of time steps for evolution - - Returns: - List of RGB color tuples - """ - try: - - nsteps = len(dt_list) - n_qubits = scale_to_range(radius) - - J_list =[-0.5]*n_qubits - hz_list =[0.5]*n_qubits - hx_list =[0.5]*n_qubits - - circuits=[] - circ = QuantumCircuit(n_qubits) - #Create initial state with rotations of phi,theta for each qubit - initial_angles = [(phi, theta)] * n_qubits # All qubits start with the same angles - for i, (phi, theta) in enumerate(initial_angles): - circ.ry(theta, i) - circ.rz(phi, i) - - - ### start time evolution - for step,dt in zip(range(nsteps),dt_list): - print(f"J_list: {J_list}, hz_list: {hz_list}, hx_list: {hx_list}, dt: {dt}") - circ_dt = time_evolution_Heisenberg(n_qubits, J_list, hz_list, hx_list, dt) - circ = circ.compose(circ_dt) - circuits.append(circ.copy()) - - - observables = get_mean_magnetization(n_qubits) - - # Run the estimator - values=utils.run_estimator(circuits, observables, backend=None) - - values=np.array([val[0] for val in values]) - - print(f"Values: {values}") - return values - - - except Exception as e: - print(f"Quantum simulation failed: {e}") - - return - - -# The main function using Heisenberg model -def run(params): - """ - Executes the Heisenberg quantum effect pipeline based on the provided parameters. - - Args: - parameters (dict): A dictionary containing all the relevant data. - - Returns: - Image: the new numpy array of RGBA values or None if the effect failed - """ - - # Extract image to work from - image = params["stroke_input"]["image_rgba"].copy() - assert image.shape[-1] == 4, "Image must be RGBA format" - - height = image.shape[0] - width = image.shape[1] - - path = params["stroke_input"]["path"] - - # Get the radius of the effect - radius = params["user_input"]["Radius"] - assert radius > 0, "Radius must be greater than 0" - - color = params["user_input"]["Color"] - h,l,s = colorsys.rgb_to_hls(color[0]/255, color[1]/255, color[2]/255) - print(f"Using color: {color}") - - phi, theta, _ = utils.color_to_spherical(color) - print(f"Using angles: phi={phi}, theta={theta}") - - strength = params["user_input"]["Strength"] - assert strength > 0, "Strength must be greater than 0" - - clicks = params["stroke_input"]["clicks"] - assert len(clicks) < 11, "There can be no more than 10 clicks in a stroke" - - split_paths = utils.split_path_from_clicks(path,clicks) - - normalized_distances = [0.1] * len(split_paths) #dt*path_length - - # Run Heisenberg simulation to get colors - color_shifts = run_heisenberg_hardware(normalized_distances, radius, phi, theta) - - new_hls = np.array([[(h + shift) % 1.0, (l + shift) % 1, (s + shift) % 1.0] for shift in color_shifts]) - new_hls = np.array([(1 - strength) * np.array([h,l,s]) + strength * new for new in new_hls]) - heisenberg_colors = utils.hls_to_rgb(new_hls) - - - for i,path in enumerate(split_paths): - # Get the region around this point - region = utils.points_within_radius(path, radius, border=(height, width)) - - new_patch = image[region[:, 0], region[:, 1]].astype(np.float32)/255 - new_patch[...,:3] = heisenberg_colors[i] - - image[region[:, 0], region[:, 1]] = utils.apply_patch_to_image(image[region[:, 0], region[:, 1]], new_patch) - - print("Heisenberg effect applied successfully") - return image \ No newline at end of file diff --git a/effect/heisenbrush2/heisenbrush2_requirements.json b/effect/heisenbrush2/heisenbrush2_requirements.json deleted file mode 100644 index 6e808ff..0000000 --- a/effect/heisenbrush2/heisenbrush2_requirements.json +++ /dev/null @@ -1,41 +0,0 @@ -{ - "name": "Heisenbrush (discrete)", - "id": "heisenbrush2", - "author": "Arianna", - "version": "1.0.0", - "long_description": "This brush simulates a quantum system to generate color effects based on the Heisenberg spin model. Each stroke is composed of discrete segments (defined by user clicks), and each segment drives a quantum time evolution that computes the system’s mean magnetization. This magnetization is used to shift the original color’s Hue, Lightness, and Saturation, creating unique color changes for each stroke segment.\n\nThe quantum algorithm models interactions between spins in a closed loop of qubits. Your base color is translated into a quantum state using angular coordinates, then evolves over time steps determined by stroke geometry. Each segment produces a magnetization value, which is mapped back into HSL color space.\n\nThe Strength setting controls how much influence the quantum-generated colors have on the final result. A low strength blends more of your original color, while high strength allows the quantum behavior to fully shape the effect.\n\nEach segment is rendered with its own color derived from quantum simulation, giving your brushwork a discrete, physics-inspired variation along the stroke.\n\n To use this effect, click and drag on the canvas to create up to 10 strokes.", - "description": "The Heisenbrush simulates color shifts through the Heisenberg spin model. Each stroke is split into segments, and each segment evolves a quantum state that transforms Hue, Lightness, and Saturation.\n\nThe quality of the effect is controlled by several parameters:\n πŸ”Ή Radius β†’ determines the size of the brush and the number of qubits in the simulation\n πŸ”Ή Strength β†’ blends between the base color and quantum-generated colors\n πŸ”Ή Color β†’ defines the initial state of the quantum evolution\n\nUsage:\n πŸ”Έ Click and drag multiple times over the canvas to create multiple strokes.\n πŸ”Έ Each stroke has a new color.\n\n ⚠️ Warning: the number of strokes is limited to 10.", - "dependencies": { - "numpy": ">=2.1.0", - "colorsys": "", - "qiskit": ">=1.0.0", - "qiskit_ibm_runtime": ">=0.20.0", - "qiskit_aer": ">=0.17.0" - }, - "user_input": { - "Radius": { - "type": "int", - "min": 1, - "max": 100, - "default": 5 - }, - "Strength": { - "type": "float", - "min": 0.0, - "max": 1.0, - "default": 0.5 - }, - "Color": { - "type": "color", - "default": "#FF0000" - } - }, - "stroke_input": { - "image_rgba": "array", - "path": "array", - "clicks": "array" - }, - "flags": { - "smooth_path": false - } -} \ No newline at end of file diff --git a/effect/pointillism/__init__.py b/effect/pointillism/__init__.py deleted file mode 100644 index eafbf51..0000000 --- a/effect/pointillism/__init__.py +++ /dev/null @@ -1,3 +0,0 @@ -# effect/pointillism/__init__.py -from .pointillism import run - diff --git a/effect/pointillism/docs/PointlisimBrush.ipynb b/effect/pointillism/docs/PointlisimBrush.ipynb deleted file mode 100644 index 9b9445a..0000000 --- a/effect/pointillism/docs/PointlisimBrush.ipynb +++ /dev/null @@ -1,721 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "a46300b1-1614-4931-8bfb-c4e4d36e72a3", - "metadata": {}, - "source": [ - "# Developing the Quantum Circuit and Time evolution of Pointilisim Brush\n", - "- Building adjaceny matrix J_ij from distance (`DONE`)\n", - "- Encode into Ising Hamiltonian\n", - "- Evolve with exp(-i*H*t)\n", - "- Measure Expectations \n", - "- Map normalised values to RGB\n", - "\n", - "Inputs to general function: dot_positions, coupling_strength, evolution_time" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "e568a3c3-e303-4135-81fe-0aa99e078122", - "metadata": {}, - "outputs": [], - "source": [ - "#!pip install qutip\n", - "#!pip install qiskit-dynamics" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "dcb59ff6-c7f2-4373-974a-933194aec121", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "from IPython.display import Image\n", - "# set a parameter to see animations in line\n", - "from matplotlib import rc\n", - "rc('animation', html='jshtml')\n", - "\n", - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "f922d8bd-2e9f-4378-bf11-ed3c28986396", - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit import QuantumCircuit,ClassicalRegister, QuantumRegister, transpile\n", - "from qiskit.quantum_info import Pauli, SparsePauliOp, Statevector\n", - "from qiskit.visualization import plot_histogram, plot_bloch_multivector\n", - "from qiskit_aer import AerSimulator\n", - "from qiskit.circuit import Parameter, ParameterVector\n", - "import qiskit.qasm3\n", - "from qiskit_ibm_runtime.fake_provider import FakeVigoV2\n", - "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", - "from qiskit_ibm_runtime import SamplerV2 as Sampler, EstimatorV2 as Estimator, QiskitRuntimeService\n", - "from qiskit.circuit.library import PauliEvolutionGate\n", - "from qiskit.synthesis.evolution import SuzukiTrotter" - ] - }, - { - "cell_type": "markdown", - "id": "4dd30b7f-b3a0-4306-a59b-34ac7ced4500", - "metadata": {}, - "source": [ - "### Build $J_{ij}$ matrix\n", - "- Find the distance between points in 2D system.\n", - "\n", - "#### Assumptions\n", - "- Assumes all points will be equ-distance from each other to complete check that these are neighbouring qubits." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "89ce3beb-36b1-4c08-8053-4997ab1d668b", - "metadata": {}, - "outputs": [], - "source": [ - "#import qiskit\n", - "#qiskit.__version__" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "32040ab5-c1f5-4fa2-b9ce-85d806727c0e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 2.]\n", - " [2. 0.]]\n" - ] - } - ], - "source": [ - "dot_positions = np.array([\n", - " (0.0, 0.0),\n", - " (1.0, 0.0),\n", - "])\n", - "def J_matrix(dot_pos,coupling_constant,tol = 1.5):\n", - " '''\n", - " Generates the coupling matrix for the system. As a place holder\n", - " the system currently just has a simple multipication between the \n", - " coupling constant and distance between dots.\n", - " Function takes a tolerance to identify if dots are neighbouring\n", - " otherwise discards the value\n", - " Input:\n", - " - dot_pos = Positions of dots in x-y plane[array]\n", - " - coupling_constant = J coupling constant[float]\n", - " - tol = tolerance for identifying neighbouring dots set at 1.5[float]\n", - "\n", - " Output\n", - " - matrix = J matrix[array]\n", - " '''\n", - " #Generate empty matrix\n", - " N = len(dot_pos)\n", - " matrix = np.zeros((N,N))\n", - " \n", - " #Loop over all positions\n", - " for i in range(N):\n", - " for j in range(i+1,N):\n", - " #Find Difference in positions\n", - " dij = dot_pos[i] - dot_pos[j]\n", - " \n", - " #Checks to see if these are neighbouring states\n", - " if (abs(dij[0]) < tol and dij[1] == 0) or (dij[0] ==0 and abs(dij[1]) < tol):\n", - " d = np.sqrt(dij[0]**2+dij[1]**2)\n", - " \n", - " #Add to matrix\n", - " matrix[i,j]=matrix[j,i]=coupling_constant*d\n", - " return matrix\n", - "\n", - "Jmatrix = J_matrix(dot_positions,2)\n", - "print(Jmatrix)\n" - ] - }, - { - "cell_type": "markdown", - "id": "fac5a771-ac20-48ac-8320-496ebe66515a", - "metadata": {}, - "source": [ - "### Building Hamiltonian $\\hat{H~}$\n", - "Classical Hamiltonian\n", - "$$\n", - "H(\\sigma) = - \\sum_{\\left}J_{ij}\\sigma_i\\sigma_{j}\n", - "$$\n", - "\n", - "Hamiltonian of Quantum Ising Model [4].\n", - "\n", - "$$\n", - "\\hat{H} = - \\sum_{\\left< ij \\right>} J_{ij}\\hat{\\sigma}^\\mathcal{Z}_i \\hat{\\sigma}^\\mathcal{Z}_j\n", - "$$\n", - "$\\hat{\\sigma}^{\\mathcal{X},\\mathcal{Z}}$ are the Pauli Matrices. $J$ is the exchange constant which varies on the qubits interacting and varies based on distance. The matrix containing the possible values for $J$ was produced above. For now we will just work with just the entanging of the states. We will then add the element which introduces the bias introduced by the colour of the image at the point of the dot. \n", - "\n", - "### Aim\n", - "$J$ will be a matrix (first introduce it as a constant as between neighbouring dots its constant), $t$ will be the time evolution of the circuit. To begin lets just consider the interaction between 2 neighbouring dots such that we can only consider the following term.\n", - "\n", - "Qiskit β†’ Trotterized time evolution OR VQE algorithm package\n", - "AerSimulator β†’ Optimization + tranpilation are crucial." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "46cf0a59-f9d6-4452-99b4-22df755e91a9", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.display import Image # needed to embed an image\n", - "Image(filename='2 qubit Ising System.png', embed=True) # image downloadable from Moodle" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "66161076-03b7-4c28-9d67-9c9795222f79", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 0.7]\n", - " [0.7 0. ]]\n" - ] - } - ], - "source": [ - "dot_positions = np.array([\n", - " (0.0, 0.0),\n", - " (1.0, 0.0)\n", - "])\n", - "J_C =0.7\n", - "Jmatrix = J_matrix(dot_positions,0.7)\n", - "print(Jmatrix)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "7229c249-e672-418b-9d84-760b9433b0d5", - "metadata": {}, - "outputs": [], - "source": [ - "def Ising_Quantum_Circuit_1D(J,t):\n", - " '''\n", - " Function that generates the Quantum Circuit for a 1D \n", - " Ising model system. \n", - " Input:\n", - " - J = Coupling Interaction Matrix[array]\n", - " - t = Time Evolution[float]\n", - "\n", - " Output:\n", - " - qc = Quantum Circuit[obj]\n", - " '''\n", - " N = len(J)\n", - " theta = []\n", - " for i in range(N-1):\n", - " theta_ij = -2*J[i,i+1]*t\n", - " theta.append(theta_ij)\n", - "\n", - " q = QuantumRegister(N,'q')\n", - " qc = QuantumCircuit(q)\n", - " \n", - " for n in range(N-1):\n", - " qc.rzz(theta[n],n,n+1)\n", - " return qc\n" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "cb0c44ce-e0cd-44bf-9c75-70adc25b3b47", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
    " - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc = Ising_Quantum_Circuit_1D(Jmatrix,1)\n", - "\n", - "qc.draw(\"mpl\") " - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "61d41760-cc69-446d-913d-81c14821ed89", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$$(0.7648421873 + 0.6442176872 i) |00\\rangle$$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Find Vector\n", - "v = Statevector(qc)\n", - "display(v.draw(\"latex\"))" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "dda04add-3831-42bf-99bf-39a0da521770", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'00': 1024}\n" - ] - } - ], - "source": [ - "qc.measure_all()\n", - "\n", - "#Transpile Circuit using AerSimulator backend\n", - "pm = generate_preset_pass_manager(backend=AerSimulator(),optimization_level=3)\n", - "tc = pm.run(qc)\n", - "\n", - "#Initialise 'Sampler' Primitive with 'AerSimulator' backend\n", - "sampler = Sampler(mode=AerSimulator())\n", - "\n", - "#Runs Sampler\n", - "sj=sampler.run([tc])\n", - "\n", - "#Measures Count\n", - "result = sj.result()\n", - "print(result[0].data.meas.get_counts())#Only one state so all in state" - ] - }, - { - "cell_type": "markdown", - "id": "e48c7c6a-669e-4258-a020-49a9fb09e8c6", - "metadata": {}, - "source": [ - "### Consider 2D Case\n" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "60ae04ab-749f-463b-9a64-1cdd828b7cfd", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "Image(filename='2D Case.png', embed=True)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "5357073d-89d5-4748-baa9-810f59f9e435", - "metadata": {}, - "outputs": [], - "source": [ - "def Ising_Quantum_Circuit_2D(J,t):\n", - " '''\n", - " Function that generates the Quantum Circuit for a 2D \n", - " Ising model system. \n", - " Input:\n", - " - J = Coupling Interaction Matrix[array]\n", - " - t = Time Evolution[float]\n", - "\n", - " Output:\n", - " - qc = Quantum Circuit[obj]\n", - " '''\n", - " N = len(J)\n", - " q = QuantumRegister(N,'q')\n", - " qc = QuantumCircuit(q)\n", - " for i in range(N):\n", - " for j in range(i+1,N):\n", - " if J[i,j] !=0:\n", - " theta_ij = -2*J[i,j]*t\n", - " qc.rzz(theta_ij,i,j)\n", - " return qc\n" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "2f34d215-8d26-429c-84d0-18827b99e283", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 0.7 0.7 0. ]\n", - " [0.7 0. 0. 0.7]\n", - " [0.7 0. 0. 0.7]\n", - " [0. 0.7 0.7 0. ]]\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
    " - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dot_positions = np.array([\n", - " (0.0, 0.0),\n", - " (1.0, 0.0),\n", - " (0.0, 1.0),\n", - " (1.0, 1.0),\n", - "])\n", - "Jmatrix = J_matrix(dot_positions,0.7)\n", - "qc = Ising_Quantum_Circuit_2D(Jmatrix,1)\n", - "print(Jmatrix)\n", - "qc.draw(\"mpl\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "f31575aa-e76e-4615-b254-18a459f68297", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$$(-0.9422223407 + 0.3349881502 i) |0000\\rangle$$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Find Vector\n", - "v = Statevector(qc)\n", - "display(v.draw(\"latex\"))" - ] - }, - { - "cell_type": "markdown", - "id": "d95f5a00-7405-4a38-98be-6bb302c460cf", - "metadata": {}, - "source": [ - "### 2D Case with 3 rows" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "a3dd64d0-18ef-4021-8de0-239806df8369", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", - "text/plain": [ - "
    " - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dot_positions = np.array([\n", - " (0.0, 0.0),\n", - " (1.0, 0.0),\n", - " (0.0, 1.0),\n", - " (1.0, 1.0),\n", - " (0.0, 2.0),\n", - " (1.0, 2.0),\n", - "])\n", - "Jmatrix = J_matrix(dot_positions,0.7)\n", - "qc = Ising_Quantum_Circuit_2D(Jmatrix,1) #Expect 2 qubits to have 3 interactions\n", - "qc.draw(\"mpl\") " - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "345b6798-a79b-4574-85c7-2f32993876ee", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$$(0.1865123694 - 0.9824526126 i) |000000\\rangle$$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Find Vector\n", - "v = Statevector(qc)\n", - "display(v.draw(\"latex\"))" - ] - }, - { - "cell_type": "markdown", - "id": "8be168e9-bfeb-449e-856e-fcf5f7fa12d6", - "metadata": {}, - "source": [ - "# 3 x 3 Case\n" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "bba67933-507d-4374-a6b6-a3ff69d9ac17", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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ID/KMHgQD3/PzLw5ZD8ydGEk6cKhZ9dNmK5NxlNnzjtyOI+YWnCSrdJgSp56uRMLW7g0rVVPNA3VBRQ/yhx4EC1nPn7hkPTB3YiSpprpK997+FUmSXX2quYxByJ3nvbd/JbJhjgp6kD/0IFjIev7EJeuBuhOTc9acq7Vl23Y5B3fLaWk0l3GC7Mpa2SPq9TcTxumtlc+aywgoejC06EFwkfWhFaesB+pOTM6C+bdIkhLDR0mJAnMZJyJRkD1HSQu//lVzFQFGD4YQPQg0sj6EYpb1QA4xV825WJ+fNVOuZStRM8ZcxglI1IyRa9n6/KyZumrOxeYyAoweDB16EGxkfejELeuBfDtJkt7b9b6mXXWjmloOy2neK6dpj7kFx2EPP1V2VZ2GV1Zow3PPaMKY0eYWBBw9GDx6EA5kffDimPVA3omRpAljRuvpBxdKkuyqOlmpanMLjsFKVcuuqpMkPf3gwliEOYroweDQg/Ag64MT16wnFixYsMB8MShOHzdGw8rLtHr9JiXKq+S2H5YyaXMbDFZRqQpOPV2S9OB3vq5/uPJz5haECD04OfQgfMj6yYlz1gN7JyZn/pe+qJuuuVKupMTI8ZId+D+yv2xbiZHj5Uq66ZorNf9LXzR3IITowQmiB6FF1k9QzLMe2GdiTJ+9/sta99pmuW3Nyux7z1xGn8TICbLKq3Th+ZP1u6U/N5cRcvTg46EH4UfWP564Zz00Q8z23Q2adtWNOtjcwkNfHyH3UNeIqkpteO4Zja/P/pgdooMeHB89iAayfnxkPQRvJ+WMrx+lp3/0wUNfdkWNuSXW7IqaDx7q+tHCWIY5DujBsdGD6CDrx0bWswL9YK/p9HFjVJEq16p1G2WVVUiOI7er3dwWO3blKbJr6iVJD931T/r7K//O3IIIoQcfjh5ED1n/cGT9A6EaYiRpyjlnKVVWqtXrN8kqHSZJcjvbzG2xYVfXye77dMYffXt+7B7qiit6MBA9iC6yPhBZHyh0Q4wkTZ18tupqR+i3r6yTVZKS7EQs//ZTe8To/tuJjy+6S7fecI25BRFGD7LoQfSR9Syy/tdC82Dvh1n6/Iu68RvflSS57YeVObBT6o3BZwoUJJWoGZu9vSrpmR8v0vVXXGbuQkzQA3oQF2SdrJtCPcRI0qp1G/Xl79ynhv0HZGXS6t2/I9ITulU6TAWnjJObSGrUKTX6+QP36tILp5rbEDOr1m3Uzd9eqD2NB+kBIo2sk/WjhX6IkaS9jQd1y93f1wtr1kuSnKYGOc37zG2hZ1eN7H8v9PKZ0/XE4ntUVzvC3IaYogeIC7KOnFA+E2NKlZXquivmqCed1quv/0lW6TBZpRVSulvq7TG3h45VklJi5ATZw4ZLku68ZZ6efOBepcpKza2IMXqAuCDryInEnZij/eZ3a3XXgz/VX97dLklyDjfKaWqQHMfcGny2LXv4KNkVtZKkSaeN0wPf+po+99kZ5k5gAHqAuCDr8Ra5ISbnew//TPc/9lT2PzK9cloa5bTsl9wQBNuys58DUFkrJQokSXfdepMWzv+quRM4JnqAuCDr8RTZIUaSNr/1F9390KN66dU/SJIs11GmeV822EGc0u1skBNVI+Va2Q9TvuSCT2vxN2/T5DM/ae4GPhZ6gLgg6/ET6SEmZ+XaDXpkyVKtXr9JygX7SJPctkOB+NAkq6RcVnm1EsOG9wd51vQpumPe9Zo9Y5q5HTgp9ABxQdbjIxZDTM7q9Zv0yJKlWrl2Q/9rbk+n3NZDctua5aa7B+zPJytZJKu8SlaqWlZhSf/rs2dM0x3zrtes6VMG7AeGCj1AXJD16IvVEJPz5patWrZ8pZYtX6Hde/f3v+6mu+V2tsrtaJXb2SplhvBDlBJJWSUpWaWp7L+TRf1Lo0fW6tq5c3TdFXN09qSJA34ZkC/0AHFB1qMrlkPM0Za/vFbLlq/QKxtf04FDzQMXe3vk9nRlp/WeLrnpLimTkdyMXCeTfY/VyUh2QrJtWXai7+uErGSxVFgsK1ksq7BIKigc8FvXVFfpoqnn69q5czT3Yp48h7/oAeKCrEdL7IeYo73x57f1yqbXtWbT61r7xzfU2TV0txpLios041PnauaU83TRlPN07llnmFuAQKAHiAuyHn4MMcewfXeDtmzboa3bd2rLezu0bedutba3q7WtQ61t7dmv2zuUKitVqqxMqfIypcqzX582tl6TJozTxPFjNem0cRpfn/3URSBs6AHigqyHD0MMAAAIpezPdgEAAIQMQwwAAAglhhgAABBKDDEAACCUGGIAAEAoMcQAAIBQYogBAAChxBADAABCiSEGAACEEkMMAAAIJYYYAAAQSgwxAAAglBhihlDtvEWqnbfIfBmIHLKOuCDrwcYQAwAAQokhBgAAhBJDDAAACCWGGAAAEEoMMQAAIJQYYgAAQCgxxAAAgFBiiAEAAKHEEAMAAEKJIQYAAIQSQwwAAAglhhgAABBKDDEAACCUGGIAAEAoMcQAAIBQYogBAAChxBADAABCiSEGAACEEkMMAAAIJYYYAAAQSgwxAAAglBhiAABAKDHEAACAUGKIAQAAocQQAwAAQokhBgAAhBJDDAAACCWGGAAAEEoMMQAAIJQYYgAAQCgxxAAAgFBiiAEAAKHEEAMAAEKJIQYAAIQSQwwAAAglhhgAABBKDDEAACCUGGIAAEAoMcQAAIBQYogBAAChZLmu65ov4uT8Ys1mSdINMyebS0CkkHXEBVkPNoYYAAAQSrydBAAAQokhBgAAhBJDDAAACCWGGAAAEEoMMQAAIJQYYgAAQCgxxAAAgFBiiAEAAKHEEAMAAEKJIQYAAIQSQwwAAAglhhgAABBK/AWQx7B9d4O2bNuhrdt3ast7O7Rt5261trerta1DrW3t2a/bO5QqK1WqrEyp8jKlyrNfnza2XpMmjNPE8WM16bRxGl8/yvztgVCgB4gLsh4+DDFHeePPb+uVTa9rzabXtfaPb6izq9vcctJKios041PnauaU83TRlPN07llnmFuAQKAHiAuyHn6xH2KWv7xWy5av0CsbX9OBQ80DF3t75PZ0yU13Sz1dctNdkpORnIxcJyM5Tva/7YRk27LshGQlpERCVrJYKiyWlSySVVgsFRQO+K1rqqt00dTzde3cOZp78YwBa4DX6AHigqxHSyyHmDe3bNW/Pb9Cy5av0Pv7Gvtfd9Pdcjtb5Xa0yu1slTLpAb9uUBJJWSUpWaWp7L+TRf1L9XWn6Nq5c3Tt3Nk6e9LEAb8MyBd6gLgg69EVqyFm9fpNemTJUq1cu6H/NbenU27rIbltzdnp2yNWskhWeZWsVLWswpL+12fPmKY75l2vWdOnDNgPDBV6gLgg69EXiyFm5doNemTJUq1ev0mSZLmOMkea5LYdktvZZm73nFVSLqu8Wolhw+Va2R8YmzV9iu6Yd71mz5hmbgdOCj1AXJD1+Ij0ELP5rb/o7oce1Uuv/kGSZMtV76G9clr2Z9/bDBrbll15ihJVI/uDfckFn9bib96myWd+0twNfCz0AHFB1uMnskPM9x7+me5/7Knsf2R65bQ0ZoPsBjDIJisbbLuyVkoUSJLuuvUmLZz/VXMncEz0AHFB1uMpckPMb363Vnc/9Kjefuc9SZJzuFFOU0Mwp/DjsW3Zw0fJrqiVJJ1x+gQt/uZt+txnebIdx0YPEBdkPd4iNcTc8+PH9MMnlkiS3K52OU0N2SfOQ84qSckePkpWcZkk6c5b5un737jV3AZI9AAxQtYRiSFmb+NB3XL39/XCmvWSJKepQU7zPnNb6NlVI2UPz34K5OUzp+uJxfeornaEuQ0xRQ8QF2QdOaEfYlat26iv3LVI7+9rlO30Kr1vu9yOI+a2yLBKhyk5crwcu0CjR9bqn+//ri69cKq5DTGzat1Gffk796lh/wF6gEgj62T9aKEeYpY+/6Ju/MZ3JUlu+2FlDuyUeofww4qCqiCpRM1YWWUVkqRnfrxI119xmbkLMUEP6EFckHWybkosWLBggfliGDy57D9087fvkyQ5LfvlNO4I54NcJ8Nx5LYdkuyErOJy/eeqV1RXO0Ln8iN5sUMP6EFckHWy/mFCOcT85Kl/0fxFD0qSnEN75DTtMbfEQu4WqlWS0m9fWadUWammTj7b3IaIogdZ9CD6yHoWWf9roRtiHlmyVP/7gZ9IkpyD70fyYa4T4Xa2SY4jq3SYVq/fpIpUuaacc5a5DRFDDwaiB9FF1gci6wOF6pmYF9e8qituvkOS5BzYJefwAXNLbNkVNbJrxkiSnn/yEV028wJzCyKCHnw0ehAtZP2jkfWs0Awx23c3aNpVN+pgc4uc5r2xvZ14LPbwU2VX1WlEVaU2PPeMxtdnfzQP0UEPjo8eRANZPz6yLmX/soYQuOnOhTrY3CK3rZkwfwSnaY/ctmYdbG7RTXcuNJcRAfTg+OhBNJD14yPrIRlibrlnsda9tllKdynTuMNcxlEyjTukdJfWvbZZt9yz2FxGiNGDj48ehBtZ//jinvXAP9j78NP/qh8+sUSWpMyed6TeHnMLjua6crvalaio0eb/3qJh5WWack68n16PAnpwguhBaJH1ExTzrAf6mZgX1qzX52+eL0nK7N8ut/WQuQUfwUpVK3HKeEnSr598WJfPnG5uQUjQg5NHD8KFrJ+8uGY9sEPMe7ve17SrblRTy2Ee6jpJuYe+hldWaMNzz2jCmNHmFgQcPRg8ehAOZH3w4pj1wD4T860fPKymlsM81DUIuYe+mloO61s/eNhcRgjQg8GjB+FA1gcvjlkP5BDz3IqX9evVa2S5jjIHdpnLOAGZA7tkuY5+vXqNnlvxsrmMAKMHQ4ceBBtZHzpxy3og3046a87V2rJtu5yDu+W0NJrLOEF2Za3sEfX6mwnj9NbKZ81lBBQ9GFr0ILjI+tCKU9YDdyfm/see0pZt2+V2tRPmIeK0NMrtatf/vLdD9z/2lLmMAKIHQ48eBBNZH3pxynqg7sQcONSs+mmzlck4yux5p/8vu8LgWaXDlDj1dCUStnZvWKma6ipzCwKCHuQPPQgWsp4/ccl6oO7EPP7LXymTceS2txDmIeZ2HJHb3qJMxtHjv/yVuYwAoQf5Qw+ChaznT1yyHpg7MT3ptEZNuVQtR1qVadgqt7PV3IJBskpSSoyaqMphKTVsWqXCZNLcAp919/Ro9NTZ9CCP6EEw8D0//+KQ9cDciXn8l79Sy5FWuZ3ZfzD0cmfbcqQ10pN5mNGD/KMHwUDW8y8OWQ/MEPPTZ5ZJfQ8kIX9y55s7bwTLo7/4d4ke5B098B/f870R9awHYoh5/qXfa9eevXK7O+S2t5jLGEJue4vc7g7t2rNXy19eay7DR/TAO/TAX2TdO1HPeiCGmOdefEmS5LY1m0vIg9w5P/vCanMJPqIH3qIH/iHr3opy1n1/sLezq1sjJs9UTzqtzM635Ka7zS0YYlaySImxZ6owmdTBzWtUUlxkboHH6IH36IE/yLr3opx13+/EPPviS+pJp7MPIBFmT7jpbrmdrepJp/Vs3/8RwV/0wHv0wB9k3XtRzrrvQwy3Ff2RO+/c+cNf9MAf9MB7ZN0fUc2670PMmk2vS5IcHu7yVO68c+cPf9EDf9AD75F1f0Q1674OMRs3v6n2zk65PZ1Sb9pcRj71puX2dKq9s1MbN79prsJD9MBH9MBTZN1HEc26r0PMutc2S5LczjZzCR7InXvuOsAf9MBf9MA7ZN1fUcw6Q0yMRTHQYUQP/EUPvEPW/RXFrPs6xKx/7U+SJLeLj5z2Q+7cc9cB/qAH/qIH3iHr/opi1n0bYnY27FVbR0f2fVHeG/VH39m3dXRoZ8NecxUeoAcBQA88QdYDIIJZ922IeWfHLkmSm+4yl+Ch3Pnnrge8RQ+CgR7kH1kPhqhl3bch5t3+QPNhR37KnX/uesBb9CAY6EH+kfVgiFrWfRtitm7vO8AepnJf9Z1///WAp+hBQNCDvCPrARGxrPs2xLy7k6k8CPqn8r7rAW/Rg2CgB/lH1oMhaln3bYg51HIk+0WGB7x81Xf+/dcDnqIHAUEP8o6sB0TEsu7bENPW0ZH9wnHMJXip7/z7rwc8RQ8Cgh7kHVkPiIhl3b8hpj17gK6TMZfgIdfNnn/uesBb9CAY6EH+kfVgiFrWfR9i5DKV+yo3lUck0GFDDwKCHuQdWQ+IiGXdtyGmNXeATOX+6jv//usBT9GDgKAHeUfWAyJiWfdtiAEAABgMy3Vd13zRCyPPv1hNLYfVu/3/kzK95jK8kihQwfj/W8MrK7TvtZfN1RNWO2+R+VLovfmT+RpZmTJfHhL0ICBOogdk/cSQ9YA4iawHmW93YsrLSrNfWL79EaAPzr//esBT9CAg6EHekfWAiFjWfbsT87d/d43+e+s2ZXa9Lben01yGR6zCEiXGnKH/a+Jp+tNv/91cRp7Rg2CgB/lH1oMhaln3bSQuL+2bAm3f/gjQB+fffz3gKXoQEPQg78h6QEQs676lqbpyWPaLRNJcgpf6zr//esBT9CAg6EHekfWAiFjWfRtiPjF2jCTJShaZS/BQ7vxz1wPeogfBQA/yj6wHQ9Sy7tsQM3F83wEWFptL8FLf+fdfD3iKHgQEPcg7sh4QEcu6b0PMJ8YxlQdB/1Tedz3gLXoQDPQg/8h6MEQt674NMaf3B5qp3E+5889dD3iLHgQDPcg/sh4MUcu6b0PM2FF12aejC5LZf+C9vrMvLy3V2FF15io8QA8CgB54gqwHQASz7tsQI0nTz/9bSZJVnJ9PiMSx5c49dx3gD3rgL3rgHbLuryhm3dch5sLzJ0uSrJJycwkeyJ177jrAH/TAX/TAO2TdX1HMOkNMjEUx0GFED/xFD7xD1v0Vxaz7OsRMnXy2ykpKZBWW8B6p1wqSsgpLVFZSoqmTzzZX4SF64CN64Cmy7qOIZt3XIUaSZk45T5Jkl1WaS8ij3Hnnzh/+ogf+oAfeI+v+iGrWfR9irrrsEkmSVV5lLiGPcuedO3/4ix74gx54j6z7I6pZ9+1vsc7p7OrW8HM+o3RvrzI735Kb7ja3YIhZySIlxp6pZEGBmv7r9yop5sOn/EYPvEcP/EHWvRflrPt+J6akuEhXXz5LYjL3TO6cr758VqTCHGb0wHv0wB9k3XtRzrrvQ4wkfYFAeyqqtxXDjh54ix74h6x7K8pZD8QQM/fiGRpzap2solJZPOyVV1ZZpayiUtXXjdQVl3zGXIaP6IF36IG/yLp3op71QAwxknT7jddKkuzKWnMJQyh3vl/7x+vMJQTAbTdcI9GDvKMH/uN7vjeinnXfH+zN6UmnNWrKpWo50qpMw1a5na3mFgySVZJSYtREVaTKtecPq1WY5HMagqa7p0ejp86mB3lED4KB7/n5F4esB+ZOTGEyqdtuYDLPp9y53n7jdZEMcxQUFRbSgzyjB8HA9/z8i0PWA3MnRpIOHGpW/bTZymQcZfa8I7fjiLkFJ8kqHabEqacrkbC1e8NK1VTzQF1Q0YP8oQfBQtbzJy5ZD8ydGEmqqa7Svbd/RZJkV59qLmMQcud57+1fiWyYo4Ie5A89CBaynj9xyXqg7sTknDXnam3Ztl3Owd1yWhrNZZwgu7JW9oh6/c2EcXpr5bPmMgKKHgwtehBcZH1oxSnrgboTk7Ng/i2SpMTwUVKiwFzGiUgUZM9R0sKvf9VcRYDRgyFEDwKNrA+hmGU9kEPMVXMu1udnzZRr2UrUjDGXcQISNWPkWrY+P2umrppzsbmMAKMHQ4ceBBtZHzpxy3og306SpPd2va9pV92oppbDcpr3ymnaY27BcdjDT5VdVafhlRXa8NwzmjBmtLkFAUcPBo8ehANZH7w4Zj2Qd2IkacKY0Xr6wYWSJLuqTlaq2tyCY7BS1bKr6iRJTz+4MBZhjiJ6MDj0IDzI+uDENeuJBQsWLDBfDIrTx43RsPIyrV6/SYnyKrnth6VM2twGg1VUqoJTT5ckPfidr+sfrvycuQUhQg9ODj0IH7J+cuKc9cDeicmZ/6Uv6qZrrpQrKTFyvGQH/o/sL9tWYuR4uZJuuuZKzf/SF80dCCF6cILoQWiR9RMU86wH9pkY02ev/7LWvbZZbluzMvveM5fRJzFygqzyKl14/mT9bunPzWWEHD34eOhB+JH1jyfuWQ/NELN9d4OmXXWjDja38NDXR8g91DWiqlIbnntG4+uzP2aH6KAHx0cPooGsHx9ZD8HbSTnj60fp6R998NCXXVFjbok1u6Lmg4e6frQwlmGOA3pwbPQgOsj6sZH1rEA/2Gs6fdwYVaTKtWrdRlllFZLjyO1qN7fFjl15iuyaeknSQ3f9k/7+yr8ztyBC6MGHowfRQ9Y/HFn/QKiGGEmacs5ZSpWVavX6TbJKh0mS3M42c1ts2NV1svs+nfFH354fu4e64ooeDEQPoousD0TWBwrdECNJUyefrbraEfrtK+tklaQkOxHLv/3UHjG6/3bi44vu0q03XGNuQYTRgyx6EH1kPYus/7XQPNj7YZY+/6Ju/MZ3JUlu+2FlDuyUemPwmQIFSSVqxmZvr0p65seLdP0Vl5m7EBP0gB7EBVkn66ZQDzGStGrdRn35O/epYf8BWZm0evfviPSEbpUOU8Ep4+Qmkhp1So1+/sC9uvTCqeY2xMyqdRt187cXak/jQXqASCPrZP1ooR9iJGlv40Hdcvf39cKa9ZIkp6lBTvM+c1vo2VUj+98LvXzmdD2x+B7V1Y4wtyGm6AHigqwjJ5TPxJhSZaW67oo56kmn9errf5JVOkxWaYWU7pZ6e8ztoWOVpJQYOUH2sOGSpDtvmacnH7hXqbJScytijB4gLsg6ciJxJ+Zov/ndWt314E/1l3e3S5Kcw41ymhokxzG3Bp9tyx4+SnZFrSRp0mnj9MC3vqbPfXaGuRMYgB4gLsh6vEVuiMn53sM/0/2PPZX9j0yvnJZGOS37JTcEwbbs7OcAVNZKiQJJ0l233qSF879q7gSOiR4gLsh6PEV2iJGkzW/9RXc/9KheevUPkiTLdZRp3pcNdhCndDsb5ETVSLlW9sOUL7ng01r8zds0+cxPmruBj4UeIC7IevxEeojJWbl2gx5ZslSr12+ScsE+0iS37VAgPjTJKimXVV6txLDh/UGeNX2K7ph3vWbPmGZuB04KPUBckPX4iMUQk7N6/SY9smSpVq7d0P+a29Mpt/WQ3LZmuenuAfvzyUoWySqvkpWqllVY0v/67BnTdMe86zVr+pQB+4GhQg8QF2Q9+mI1xOS8uWWrli1fqWXLV2j33v39r7vpbrmdrXI7WuV2tkqZIfwQpURSVklKVmkq++9kUf/S6JG1unbuHF13xRydPWnigF8G5As9QFyQ9eiK5RBztOUvr9Wy5Sv0ysbXdOBQ88DF3h65PV3Zab2nS266S8pkJDcj18lk32N1MpKdkGxblp3o+zohK1ksFRZnp+/CYqmgcMBvXVNdpYumnq9r587R3It58hz+ogeIC7IeLbEfYo72xp/f1iubXteaTa9r7R/fUGfX0N1qLCku0oxPnauZU87TRVPO07lnnWFuAQKBHiAuyHr4McQcw/bdDdqybYe2bt+pLe/t0Ladu9Xa3q7Wtg61trVnv27vUKqsVKmyMqXKy5Qqz3592th6TZowThPHj9Wk08ZpfH32UxeBsKEHiAuyHj4MMQAAIJSyP9sFAAAQMgwxAAAglBhiAABAKDHEAACAUGKIAQAAocQQAwAAQokhBgAAhBJDzBCqnbdItfMWmS8DkUPWERdkPdgYYgAAQCgxxAAAgFBiiAEAAKHEEAMAAEKJIQYAAIQSQwwAAAglhhgAABBKDDEAACCUGGIAAEAoMcQAAIBQYogBAAChxBADAABCiSEGAACEEkMMAAAIJYYYAAAQSgwxAAAglBhiAABAKDHEAACAUGKIAQAAocQQAwAAQokhBgAAhBJDDAAACCWGGAAAEEoMMQAAIJQYYgAAQCgxxAAAgFBiiAEAAKHEEAMAAEKJIQYAAIQSQwwAAAglhhgAABBKDDEAACCUGGIAAEAoMcQAAIBQYogBAAChxBADAABCiSEGAACEEkMMAAAIJYYYAAAQSgwxAAAglCzXdV3zRZycX6zZLEm6YeZkcwmIFLKOuCDrwcYQAwAAQom3kwAAQCgxxAAAgFBiiAEAAKHEEAMAAEKJIQYAAIQSQwwAAAglhhgAABBKDDEAACCUGGIAAEAoMcQAAIBQYogBAAChxBADAABCiSEGAACEEkMMAAAIJYYYAAAQSgwxAAAglBhiAABAKFmu67rmi8javrtBW7bt0NbtO7XlvR3atnO3Wtvb1drWoda29uzX7R1KlZUqVVamVHmZUuXZr08bW69JE8Zp4vixmnTaOI2vH2X+9kAo0APEBVkPH4aYo7zx57f1yqbXtWbT61r7xzfU2dVtbjlpJcVFmvGpczVzynm6aMp5OvesM8wtQCDQA8QFWQ+/2A8xy19eq2XLV+iVja/pwKHmgYu9PXJ7uuSmu6WeLrnpLsnJSE5GrpORHCf733ZCsm1ZdkKyElIiIStZLBUWy0oWySoslgoKB/zWNdVVumjq+bp27hzNvXjGgDXAa/QAcUHWoyWWQ8ybW7bq355foWXLV+j9fY39r7vpbrmdrXI7WuV2tkqZ9IBfNyiJpKySlKzSVPbfyaL+pfq6U3Tt3Dm6du5snT1p4oBfBuQLPUBckPXoitUQs3r9Jj2yZKlWrt3wwYvpLjlHmuS2NWenb49YySJZ5VWyhw2XksX9r8+eMU13zLtes6ZPGbAfGCr0AHFB1qMvFkPMyrUb9MiSpVq9fpMkyZar3sMH5bYdktvZZm73nFVSLqu8Wolhw+Va2R8YmzV9iu6Yd71mz5hmbgdOCj1AXJD1+Ij0ELP5rb/o7oce1Uuv/kHKBfnQXjkt+7PvbQaNbcuuPEUF1XVyZEmSLrng01r8zds0+cxPmruBj4UeIC7IevxEdoj53sM/0/2PPSVJspyMMs37s0F2Axhkk5UNtl1ZKyUKJEl33XqTFs7/qrkTOCZ6gLgg6/EUuSHmN79bq7sfelRvv/OeJMk53CinqSGYU/jx2Lbs4aNkV9RKks44fYIWf/M2fe6zPNmOY6MHiAuyHm+RGmLu+fFj+uETSyRJble7nKaG7BPnIWeVpGQPHyWruEySdOct8/T9b9xqbgMkeoAYIeuIxBCzt/Ggbrn7+3phzXpJktPUIKd5n7kt9OyqkbKHZz8F8vKZ0/XE4ntUVzvC3IaYogeIC7KOnNAPMavWbdRX7lqk9/c1ynZ6ld63XW7HEXNbZFilw5QcOV6OXaDRI2v1z/d/V5deONXchphZtW6jvvyd+9Sw/wA9QKSRdbJ+tFAPMUuff1E3fuO7kiS3/bAyB3ZKvUP4YUVBVZBUomasrLIKSdIzP16k66+4zNyFmKAH9CAuyDpZNyUWLFiwwHwxDJ5c9h+6+dv3SZKclv1yGneE80Guk+E4ctsOSXZCVnG5/nPVK6qrHaFz+ZG82KEH9CAuyDpZ/zChHGJ+8tS/aP6iByVJzqE9cpr2mFtiIXcL1SpJ6bevrFOqrFRTJ59tbkNE0YMsehB9ZD2LrP+10A0xjyxZqv/9wE8kSc7B9yP5MNeJcDvbJMeRVTpMq9dvUkWqXFPOOcvchoihBwPRg+gi6wOR9YFC9UzMi2te1RU33yFJcg7sknP4gLkltuyKGtk1YyRJzz/5iC6beYG5BRFBDz4aPYgWsv7RyHpWaIaY7bsbdMEX/lEHDjXLad4b29uJx2IPP1V2VZ1qqqv06rP/R+Prsz+ah+igB8dHD6KBrB8fWZeyf/NUCNx050IdONQst62ZMH8Ep2mP3LZmHTjUrJvuXGguIwLowfHRg2gg68dH1kMyxNxyz2Kte22zrN5uZRp3mMs4SqZxh6zebq17bbNuuWexuYwQowcfHz0IN7L+8cU964F/sPfhp/9VP3xiiSxJvQ3vSL095hYczXXldrYpUVGjzf+9RcPKyzTlnHg/vR4F9OAE0YPQIusnKOZZD/QzMS+sWa/P3zxfkpTZv11u6yFzCz6ClapW4pTxkqRfP/mwLp853dyCkKAHJ48ehAtZP3lxzXpgh5j3dr2vC77wjzrY3MJDXScp99DXiKpKvfrs/9GEMaPNLQg4ejB49CAcyPrgxTHrgX0m5ls/eFgHm1t4qGsQcg99HWxu0bd+8LC5jBCgB4NHD8KBrA9eHLMeyCHmuRUv69er18iWq8yBXeYyTkDmwC7ZcvXr1Wv03IqXzWUEGD0YOvQg2Mj60Ilb1gP5dtJZc67Wlm3b5RzcLael0VzGCbIra2WPqNek08brzyv+X3MZAUUPhhY9CC6yPrTilPXA3Ym5/7GntGXbdqm7gzAPEaelUW5Xu7Zs2677H3vKXEYA0YOhRw+CiawPvThlPVB3Yg4calb9tNnKZBxl9rzT/5ddYfCs0mFKnHq6EglbuzesVE11lbkFAUEP8oceBAtZz5+4ZD1Qd2Ie/+WvlMk4cttbCPMQczuOyG1vUSbj6PFf/spcRoDQg/yhB8FC1vMnLlkPzJ2YnnRao6ZcqpYjrco0bJXb2WpuwSBZJSklRk1U5bCUGjatUmEyaW6Bz7p7ejR66mx6kEf0IBj4np9/cch6YO7EPP7LX6nlSKvczuw/GHq5s2050hrpyTzM6EH+0YNgIOv5F4esB2aI+ekzy6S+B5KQP7nzzZ03guXRX/y7RA/yjh74j+/53oh61gMxxDz/0u+1a89eud0dcttbzGUMIbe9RW53h3bt2avlL681l+EjeuAdeuAvsu6dqGc9EEPMcy++JEly25rNJeRB7pyffWG1uQQf0QNv0QP/kHVvRTnrvj/Y29nVrRGTZ6onnVZm51ty093mFgwxK1mkxNgzVZhM6uDmNSopLjK3wGP0wHv0wB9k3XtRzrrvd2KeffEl9aTT2QeQCLMn3HS33M5W9aTTerbv/4jgL3rgPXrgD7LuvShn3fchhtuK/sidd+784S964A964D2y7o+oZt33IWbNptclSQ4Pd3kqd96584e/6IE/6IH3yLo/opp1X4eYjZvfVHtnp9yeTqk3bS4jn3rTcns61d7ZqY2b3zRX4SF64CN64Cmy7qOIZt3XIWbda5slSW5nm7kED+TOPXcd4A964C964B2y7q8oZp0hJsaiGOgwogf+ogfeIev+imLWfR1i1r/2J0mS28VHTvshd+656wB/0AN/0QPvkHV/RTHrvg0xOxv2qq2jI/u+KO+N+qPv7Ns6OrSzYa+5Cg/QgwCgB54g6wEQwaz7NsS8s2OXJMlNd5lL8FDu/HPXA96iB8FAD/KPrAdD1LLu2xDzbn+g+bAjP+XOP3c94C16EAz0IP/IejBELeu+DTFbt/cdYA9Tua/6zr//esBT9CAg6EHekfWAiFjWfRti3t3JVB4E/VN53/WAt+hBMNCD/CPrwRC1rPs2xBxqOZL9IsMDXr7qO//+6wFP0YOAoAd5R9YDImJZ922IaevoyH7hOOYSvNR3/v3XA56iBwFBD/KOrAdExLJuua7rmi964RMz52pnw1717viz1NtjLsMryUIVjD1LY0fV6d01y83VE1Y7b5H5Uui9+ZP5GlmZMl8eEvQgIE6iB2T9xJD1gDiJrAeZf3di2vumQJep3Fe5qTx3PeApehAQ9CDvyHpARCzrvt2JKTtjqnrSafVu2yz580eAJFmWCk6brMJkUu1vbzRXkWf0ICDoQd6R9YCIWNZ9uxMDAAAwGL4NMamy0uwXdsJcgpf6zr//esBT9CAg6EHekfWAiFjWfRtiynMHaPn2R4A+OP/+6wFP0YOAoAd5R9YDImJZ9y1NuQO0mMp9lTv/qAQ6bOhBMNCD/CPrwRC1rPs3xJTmbi369keAPjj//usBT9GDgKAHeUfWAyJiWfctTdWVw7JfJJLmErzUd/791wOeogcBQQ/yjqwHRMSy7tsQ84mxYyRJVrLIXIKHcuefux7wFj0IBnqQf2Q9GKKWdd+GmInj+w6wsNhcgpf6zr//esBT9CAg6EHekfWAiFjWfRtiPjGOqTwI+qfyvusBb9GDYKAH+UfWgyFqWfdtiDm9P9BM5X7KnX/uesBb9CAY6EH+kfVgiFrWfRtixo6qyz4dXZDM/gPv9Z19eWmpxo6qM1fhAXoQAPTAE2Q9ACKYdd+GGEmafv7fSpKs4vz8rak4tty5564D/EEP/EUPvEPW/RXFrPs6xFx4/mRJklVSbi7BA7lzz10H+IMe+IseeIes+yuKWWeIibEoBjqM6IG/6IF3yLq/oph1X4eYqZPPVllJiazCEt4j9VpBUlZhicpKSjR18tnmKjxED3xEDzxF1n0U0az7OsRI0swp50mS7LJKcwl5lDvv3PnDX/TAH/TAe2TdH1HNuu9DzFWXXSJJssqrzCXkUe68c+cPf9EDf9AD75F1f0Q165bruq75opc6u7o1/JzPKN3bq8zOt+Smu80tGGJWskiJsWcqWVCgpv/6vUqK+fApv9ED79EDf5B170U5677fiSkpLtLVl8+SmMw9kzvnqy+fFakwhxk98B498AdZ916Us+77ECNJXyDQnorqbcWwowfeogf+IeveinLWAzHEzL14hurrRsoqKpXFw155ZZVVyioqVX3dSF1xyWfMZfiIHniHHviLrHsn6lkPxBAjSV/7x+skSXZlrbmEIZQ739x5I1huv/FaiR7kHT3wH9/zvRH1rPv+YG9OTzqtUVMuVcuRVmUatsrtbDW3YJCskpQSoyaqIlWuPX9YrcIkn9MQNN09PRo9dTY9yCN6EAx8z8+/OGQ9MHdiCpNJ3XYD/xeaT7lzvf3G6yIZ5igoKiykB3lGD4KB7/n5F4esB+ZOjCQdONSs+mmzlck4yux5R27HEXMLTpJVOkyJU09XImFr94aVqqnmgbqgogf5Qw+ChaznT1yyHpg7MZJUU12le2//iiTJrj7VXMYg5M7z3tu/EtkwRwU9yB96ECxkPX/ikvVA3YnJOXP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- "text/plain": [ - "
    " - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dot_positions = np.array([\n", - " (0.0, 0.0),\n", - " (1.0, 0.0),\n", - " (2.0, 0.0),\n", - " (0.0, 1.0),\n", - " (1.0, 1.0),\n", - " (2.0, 1.0),\n", - " (0.0, 2.0),\n", - " (1.0, 2.0),\n", - " (2.0, 2.0)\n", - "])\n", - "\n", - "Jmatrix = J_matrix(dot_positions,0.7)\n", - "qc = Ising_Quantum_Circuit_2D(Jmatrix,1) #Expect 1 qubit to have 4 interactions \n", - "print(Jmatrix)\n", - "qc.draw(\"mpl\") " - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "408cc2a9-be2e-4afe-aae7-987e4245c352", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$$(-0.5192886541 + 0.8545989081 i) |000000000\\rangle$$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Find Vector\n", - "v = Statevector(qc)\n", - "display(v.draw(\"latex\"))" - ] - }, - { - "cell_type": "markdown", - "id": "aaca166b-a495-4fdb-a99c-6b82aacbb569", - "metadata": {}, - "source": [ - "# Results\n", - "Generated a circuit that can entangle neighbouring qubits together using the Ising model. It was first proven for two adjacent dots and then built up to a $3\\times 3$ grid of dots. As it has been achieved for a $3\\times 3$ grid it can be achieved for a $n \\times n$ grid." - ] - }, - { - "cell_type": "markdown", - "id": "b47f7f5b-9d90-420d-be7a-dddb1d681bb2", - "metadata": {}, - "source": [ - "# References \n", - "[1]https://rajeshrinet.github.io/blog/2014/ising-model/\n", - "\n", - "[2]https://en.wikipedia.org/wiki/Ising_model\n", - "\n", - "[3]https://quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.circuit.library.RZZGate\n", - "\n", - "[4]Sachdev, S. (2011) Quantum Phase Transitions. Second edition. Vol. 9780521514682. [Online]. Cambridge: Cambridge University Press.\n", - "\n", - "[5]https://quantum.cloud.ibm.com/docs/en/api/qiskit/0.46 qiskit.algorithms.minimum_eigensolvers.VQE\n", - "\n", - "[6]https://qiskit-community.github.io/qiskit-algorithms/tutorials/13_trotterQRTE.html\n", - "\n", - "[7]https://quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.circuit.library.PauliEvolutionGate\n", - "\n", - "[8]https://quantumcomputing.stackexchange.com/questions/39020/what-is-the-use-of-sparsepauliop-in-qiskit-and-how-to-use-it\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3883724e-70c4-4391-82f0-5c8d0818982f", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "34830d0a-8f72-4cf6-a1ef-3bab72ae846f", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python [conda env:qediwrk]", - "language": "python", - "name": "conda-env-qediwrk-py" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.13" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/effect/pointillism/docs/USAGE_GUIDE.md b/effect/pointillism/docs/USAGE_GUIDE.md deleted file mode 100644 index 11f81f1..0000000 --- a/effect/pointillism/docs/USAGE_GUIDE.md +++ /dev/null @@ -1,175 +0,0 @@ -# How to Use the Quantum Pointillism Brush - -A simple guide to painting with quantum-connected dots. - ---- - -## What Does This Brush Do? - -It turns your brush strokes into colorful dots - like the famous pointillism art style (think Georges Seurat). But instead of random dots, these dots "talk" to each other through quantum physics, creating unique color patterns you can't get any other way. - ---- - -## How to Use It - -### Step 1: Draw Your Stroke - -Just **click and drag** on your image - anywhere you want dots to appear. - -![Drawing paths on canvas](images/stroke_example.png) - -The brush follows your path, so: -- **Curved strokes** = dots follow the curve -- **Long strokes** = more dots spread along the line -- **Short strokes** = concentrated dot clusters - -You can see the orange paths drawn on the canvas (left) and the parameter panel (right). - -### Step 2: The Brush Does Its Magic - -After you release, the brush: -1. Places dots along your path -2. Figures out which dots are neighbors -3. Runs quantum physics to make neighbor colors interact -4. Paints the final dots on your canvas - -![Colorful quantum dots applied](images/dots_applied.png) - -The dots pick up colors from your image underneath, but then quantum physics blends and shifts them based on your settings. - ---- - -## The Controls That Actually Matter - -You'll see a parameter panel with sliders. Here's what they do in plain English: - -### **Dot Count** (10-200) -How many dots you want. -- **Low (10-30)**: Sparse, artistic, fast -- **High (100-200)**: Dense, detailed, slower - -### **Coupling Strength** (-1.0 to 1.0) -This is the "quantum conversation" knob: -- **Positive (0.5 to 1.0)**: Dots blend together β†’ smooth gradients, harmonious colors -- **Negative (-1.0 to -0.5)**: Dots push apart β†’ contrasting colors, vibrant chaos -- **Zero (0)**: Dots ignore each other β†’ random colors - -![Negative coupling example](images/negative_coupling_example.png) - -*Above: Negative coupling (-0.67) - notice the wild color variety and contrast!* - -![Positive coupling example](images/positive_coupling_example.png) - -*Above: Positive coupling (1.0) - see how dots have similar, harmonious colors* - -### **Dot Size** (1-20) -How big each dot is. Pretty self-explanatory. -- Small dots = fine detail -- Big dots = bold, visible from far away - -### **Evolution Time** (0.1-10.0) -How long the quantum "conversation" runs. -- **Short time (0.5-1.0)**: Colors stay closer to original image -- **Long time (5.0-10.0)**: More mixing, more quantum weirdness - -### **Color Variance** (0-1.0) -Adds randomness so dots don't look identical. -- **0**: All dots in a region look the same (boring) -- **0.35** (default): Nice organic variety -- **1.0**: Maximum chaos - -### **Target Color** -A color "magnet" that pulls all dots slightly toward it. Usually you can ignore this unless you want a specific color bias. - ---- - -## Tips for Best Results - -### Start Simple -Begin with these settings and adjust from there: -- Dot Count: **50** -- Coupling: **0.5** (positive for smooth, or **-0.7** for wild) -- Evolution Time: **2.0** -- Dot Size: **8** - -### Experiment with Coupling -This is the most dramatic control: -- **Sunsets/Smooth gradients**: Use positive coupling (0.5-0.8) -- **Abstract/Psychedelic**: Use negative coupling (-0.5 to -1.0) -- **Pointillist portraits**: Use slightly positive (0.2-0.4) - -### More Dots = Slower -- Under 30 dots: Nearly instant -- 30-100 dots: A few seconds wait -- Over 100 dots: Could take 10-30 seconds (be patient!) - -### Work in Layers -- Apply multiple small strokes instead of one giant stroke -- Build up your effect gradually -- Each stroke is independent - ---- - -## What "Brush Path" Means - -This confused some people, so here's the deal: - -**"Brush path" = the line you draw when you click and drag** - -That's it. The dots aren't scattered randomly across your whole canvas - they follow your mouse/stylus movement. You have full control over where the dots appear. - -Think of it like: -- You draw an invisible guideline -- The brush sprinkles dots along and around that guideline -- Quantum physics decides the colors - ---- - -## Common Issues - -### "Nothing is happening" -- Make sure you actually drag (not just click) -- Check if your dot count is too low -- Try making the dot size bigger - -### "It's taking forever" -- You probably set dot count too high (>100) -- Wait it out, or click "Delete" and try with fewer dots -- The app should show "Status: completed" when done - -### "The colors look wrong" -- Play with the coupling strength - it dramatically changes colors -- Try different evolution times -- Adjust color variance - -### "I accidentally clicked the canvas while moving the window" -- Yeah, this is a known issue with QuantumBrush itself (not specific to this brush) -- Workaround: Use the title bar to move windows, not the canvas area -- If you get an accidental dot, just undo or paint over it - ---- - -## Quick Example Workflow - -1. Open an image in QuantumBrush (File β†’ Open) -2. Select "Quantum Pointillism" from the effects menu -3. Set Dot Count to **50**, Coupling to **0.6**, Dot Size to **10** -4. Draw a curved stroke across your image -5. Wait a few seconds -6. Click "Apply to Canvas" to finalize it -7. Repeat with different strokes to build up your artwork - ---- - -## That's It! - -It's really just: -1. Draw where you want dots -2. Adjust the quantum physics knobs -3. Let the magic happen - -The quantum stuff is happening behind the scenes - you don't need to understand Ising models or Bloch spheres to make cool art. Just play with the sliders and see what happens! - ---- - -**Pro tip**: Save your favorite parameter combinations. 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