pygridsynth

pygridsynth is a Python library for approximating arbitrary Z-rotations using the Clifford+T gate set, based on a given angle θ and tolerance ε. It is particularly useful for addressing approximate gate synthesis problems in quantum computing and algorithm research.

Features

• Inspired by Established Work: This library is based on P. Selinger's gridsynth program (newsynth), adapted for Python with additional functionality.
• High Precision: Utilizes the mpmath library to support high-precision calculations.
• Customizable: Allows adjustment of calculation precision (dps) and verbosity of output.
• Graph Visualization: Provides an option to visualize decomposition results as a graph.

Installation

You can install pygridsynth via pip:

pip install pygridsynth

Or, to install from source:

pip install git+https://github.com/quantum-programming/pygridsynth.git

Usage

pygridsynth can be used as a command-line tool.

Command-Line Example

python -m pygridsynth <theta> <epsilon> [options]

Arguments

• theta (required): The rotation angle to decompose, specified in radians (e.g., 0.5).
• epsilon (required): The allowable error tolerance (e.g., 1e-10).

Options

• --dps: Sets the calculation precision (default: 128).
• --dtimeout, -dt: Sets the timeout for solving diophantine equations in milliseconds (default: 200).
• --ftimeout, -ft: Sets the timeout for factorization in milliseconds (default: 50).
• --verbose, -v: Enables detailed output.
• --time, -t: Measures the execution time.
• --showgraph, -g: Displays the decomposition result as a graph.

Example Execution

python -m pygridsynth 0.5 1e-50 --dps 256 --verbose --time

This command will:

1. Compute the Clifford+T gate decomposition of a Z-rotation gate with $\theta = 0.5$ and $\epsilon = 0.01$.
2. Set the calculation precision to 256 decimal places.
3. Display detailed output and measure the execution time.

Using as a Library

You can also use pygridsynth directly in your scripts:

from pygridsynth.gridsynth import gridsynth_gates
import mpmath

mpmath.mp.dps = 128
theta = mpmath.mpmathify("0.5")
epsilon = mpmath.mpmathify("1e-10")

gates = gridsynth_gates(theta=theta, epsilon=epsilon)
print(gates)

Contributing

Bug reports and feature requests are welcome. Please submit them via the GitHub repository Issues section. Contributions must comply with the GNU General Public License v3 or later.

License

This project is licensed under the GNU General Public License v3 or later.

References

• Brett Giles and Peter Selinger. Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators, 2019.
• Ken Matsumoto and Kazuyuki Amano. Representation of Quantum Circuits with Clifford and π/8 Gates, 2008.
• Neil J. Ross and Peter Selinger. Optimal ancilla-free Clifford+T approximation of z-rotations, 2016.
• Peter Selinger. Efficient Clifford+T approximation of single-qubit operators, 2014.
• Peter Selinger and Neil J. Ross. Exact and approximate synthesis of quantum circuits. https://www.mathstat.dal.ca/~selinger/newsynth/, 2018.
• Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates, 2013.