Quantum Portfolio Optimization

(for exploring part 3 of step1-5.py)

This project demonstrates a quantum approach to portfolio optimization using Variational Quantum Eigensolver (VQE) with QAOA ansatz and PennyLane. The implementation achieves competitive performance with classical methods while demonstrating constraint satisfaction capabilities. This is a Hackathon for Wiser's Project 2: Quantum for Portfolio Optimization.

Team Information

Team Name: Team Super(Position)
Clyde Villacrusis: gst-RGv39A8K2CxnOWG
Sanskriti Shindadkar: gst-WbZV2NEGnMyfSje

Overview

The goal of this project is to solve a Quadratic Unconstrained Binary Optimization (QUBO) problem for portfolio optimization. The problem is mapped to a quantum Hamiltonian, and the ground state of the Hamiltonian represents the optimal portfolio.

Key Results

Real Data Example 1 (3 QAOA layers deep)

Constraint Analysis of 20 bonds, basket size 6 (Some constraints because we made the characteristic ranges from 1.6 to 2.0 but quantum still wins) [There's graphs for this in the folder called v_quantum_analysis]

In the next run, we will make the characteristic range realistic now, just experimenting with it

Basket Size: min(8, max(5, n // 3)), where n is the actual number of bonds loaded -- So if we have 20 bonds --> min (8, max(5, 6)) --> min(8,6) --> 6 basket size

Solution	Basket Size	Cash Flow	Characteristic	Total Violation	Cost
Quantum	6	0.0663	0.2698	1.3365	-42359
Classical	6	0.0766	0.2633	2.3533	-42351

Real V Data Example 2 (3 QAOA layers deep)

Constraint Analysis of 20 bonds, basket size 6 (Characteristic ranges from 0.4 to 0.8 but quantum still wins) [There's graphs for this in the folder called v_quantum_analysis-1]

Basket Size: min(8, max(5, n // 3)), where n is the actual number of bonds loaded -- So if we have 20 bonds --> min (8, max(5, 6)) --> min(8,6) --> 6 basket size

Solution	Basket Size	Cash Flow	Characteristic	Total Violation	Cost
Quantum	6	0.0624	0.2698	0.1326	-42100
Classical	6	0.0785	0.2792	1.1392	-42102

Real V Data Example 3

Constraint Analysis of 15 bonds, basket size 5 (3 QAOA layers deep)

Basket Size: min(8, max(5, n // 3)), where n is the actual number of bonds loaded -- So if we have 15 bonds --> min (8, max(5, 5)) --> min(8,5) --> 5 basket size

Solution	Basket Size	Cash Flow	Characteristic	Total Violation	Cost
Quantum	5	0.0546	0.2276	0.1724	-30089
Classical	5	0.0653	0.2623	1.1430	-30098

Real V Data Example 4

Constraint Analysis of 15 bonds, basket size 5 (15 QAOA layers deep) (Graphs under v_quantum_analysis-3 folder)

Basket Size: min(8, max(5, n // 3)), where n is the actual number of bonds loaded -- So if we have 15 bonds --> min (8, max(5, 5)) --> min(8,5) --> 5 basket size

Solution	Basket Size	Cash Flow	Characteristic	Total Violation	Cost
Quantum	5	0.0555	0.2254	0.1746	-30088
Classical	5	0.0633	0.2394	1.1639	-30092

Real V Data Example 5

Constraint Analysis of 24 bonds, basket size 8 (2 QAOA layers deep) (Graphs under v_quantum_analysis-4 folder)

Basket Size: min(8, max(5, n // 3)), where n is the actual number of bonds loaded -- So if we have 24 bonds --> min (8, max(5, 8)) --> min(8,8) --> 8 basket size

Solution	Basket Size	Cash Flow	Characteristic	Total Violation	Cost
Quantum	8	0.0900	0.3478	0.0822	-72117
Classical	9/8	0.0955	0.3793	1.0562	-72122

Enhanced VQE Implementation

Circuit Architecture: QAOA ansatz with 4 layers for optimal expressivity; Also utilizing LIGHTNING.QUBIT instead of DEFAULT.QUBIT (Using lightning.GPU in one of the examples and 3 ansatz layers and 100 batch size)
Multiple Restarts: 4 restarts × 200 iterations each for robust optimization (6 restarts * 150 iterations with lightning.GPU)
Adative Learning Rate: Use adaptive learning rate of 0.05 during optimization
Adaptive Penalties: Dynamic constraint weight adjustment during optimization
Sampling Strategy: 50,000 shots for high-precision measurements
Post-Processing: Greedy feasibility correction for quantum solutions

Scalability Analysis

Current Implementation:
- 16 qubits (20-25 qubits for lightning.GPU): Substantial classical simulation requirements
- 65,536+ possible solutions: Classical enumeration becomes challenging
- Complexity: Exponential classical search space vs polynomial VQE optimization
Scaling Potential:
- Real-world portfolios: 50-500+ assets (using v data now!)
- Quantum advantage: Expected at 20+ qubits where classical optimization becomes intractable
- Hybrid approaches: Quantum sampling with classical post-processing proves effective (You can see more of this in the part 3 py file)

Task 1 (Mathematical Review):

Identified binary decision variables, linear constraints, and quadratic objective
Understanding of the portfolio optimization formulation from the challenge image

Task 2 (Quantum Formulation):

Converted constrained problem to unconstrained using penalty methods
Proper QUBO formulation with all constraints included

Task 3 (Quantum Program):

Implemented VQE with QAOA ansatz (4 layers) and adaptive penalties
Hamiltonian construction and optimization

Task 4 (Solve with Quantum):

Optimized and found quantum solutions (see above section for enhanced VQE)
Proper sampling and result interpretation

Task 5 (Classical Comparison):

Implemented classical brute-force benchmark with simulated annealing with basin hopping algorithm
Performance comparison with releveant metrics (see examples below)

How to Run

Install dependencies:
```
pip install pennylane matplotlib scipy
```
Run the script:
```
python "exploring part 3 of step1-5.py"
```
Review the output:
- The script prints the best quantum and classical solutions, along with their costs and constraint violations.
- Top 10 quantum solutions with frequency and feasibility analysis
- Comprehensive constraint satisfaction metrics

Real Data Example 1 output for exploring part 3 of steps1-5.py (WITH Lightning.GPU (20 qubits))

=== Hardware-Optimized Quantum Portfolio Optimization ===

=== Loading Real V Portfolio Data ===

Loading V V bond portfolio data...
Successfully loaded 2629 bond positions from V portfolio
Dataset dimensions: 2629 assets x 278 features
Filtered to 2618 bond positions
Selected top 20 holdings by market value for optimization
  Returns calculated from OAS (credit spreads): 90 bps average
  Risk calculated from duration (avg: 5.85 years) and credit spreads
  Correlation matrix estimated from sector/credit clustering (avg: 0.303)
  Weights calculated from market values (largest: 0.134)

Portfolio Analysis Summary:
  Fund: V ($2,665,535,685)
  Average Duration: 5.85 years
  Average Credit Spread: 90 basis points
  Expected Returns: [0.049, 0.074]
  Risk Measures: [0.044, 0.070]
  Sector Distribution: ['Financial', 'Industrial', 'Treasury Bond Portfolio']

=== Real Portfolio Characteristics ===
Fund: V
Portfolio size: 20 bonds (quantum optimized)
Average duration: 5.85 years
Average credit spread: 90 basis points
Returns range: [0.049, 0.074]
Risk range: [0.044, 0.070]
Sample bonds: ['US91282CLN91', 'US87264ABF12', 'US06051GLH01']

=== Quantum Optimization Problem Setup ===
Real V bonds: 20, Target portfolio: 6
Data source: v_real
Fund: V ($2,665,535,685)

Real Market Parameters:
  Expected returns (m): [4.91, 7.35]%
  Return bounds (M): [5.89, 8.82]%
  Risk measures (i_c): [0.444, 0.699]
  Position weights (x_c): [1.475, 5.360]

Portfolio Constraints:
  Target basket size: 6 bonds
  Yield range: [3.0%, 6.0%]
  Duration target: 0.058
  Risk aversion: 2.0

Sample Real Bonds:
  US91282CLN91: Return=0.049, Risk=0.045
  US87264ABF12: Return=0.057, Risk=0.048
  US06051GLH01: Return=0.061, Risk=0.065
  US00287YBX67: Return=0.054, Risk=0.045
  US716973AE24: Return=0.059, Risk=0.068

Optimization ready: 20 real V bonds → 6 quantum portfolio

=== Building QUBO with Real Bond Data ===
Covariance matrix built from real bond correlations: (20, 20)
QUBO matrix Q shape: (20, 20)

=== Initializing Optimized Components ===
Hardware Config:
  CPUs: 16, Memory: 7.3GB
  Recommended: {'qaoa_layers': 3, 'shots': 36681, 'restarts': 6, 'processes': 4, 'batch_size': 100}
Main device: lightning.gpu
Circuit Analysis:
  Significant gates: 210
  Estimated memory: 16.01 MB

QAOA layers: 3, Restarts: 6

--- Restart 1/6 ---
  Iter   0: 3387.1966 | Cache: 1/500 entries, 0.0% hit rate
  Iter  50: 712.5424 | Cache: 51/500 entries, 0.0% hit rate
  Iter 100: -315.2314 | Cache: 101/500 entries, 0.0% hit rate
  Iter 150:  72.2990 | Cache: 151/500 entries, 0.0% hit rate
New best: 2410.7104

--- Restart 2/6 ---
  Iter   0: 2063.2704 | Cache: 201/500 entries, 0.0% hit rate
  Iter  50: -467.8108 | Cache: 251/500 entries, 0.0% hit rate
  Iter 100: -2610.6298 | Cache: 301/500 entries, 0.0% hit rate
  Iter 150: -1290.3852 | Cache: 351/500 entries, 0.0% hit rate
New best: -316.0350

--- Restart 3/6 ---
  Iter   0: -174.9646 | Cache: 401/500 entries, 0.0% hit rate
  Iter  50: -818.6676 | Cache: 451/500 entries, 0.0% hit rate
  Iter 100: 454.9084 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -310.2751 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 4/6 ---
  Iter   0: -838.9887 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -260.3688 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: 526.8209 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -559.2327 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 5/6 ---
  Iter   0: 317.6500 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -116.8064 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -96.2636 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: 2406.7156 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 6/6 ---
  Iter   0: -119.8970 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -153.6804 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -217.6202 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -315.2520 | Cache: 500/500 entries, 0.0% hit rate

=== Optimized Sampling ===
Sampling: 36681 shots in 0.29s

Top quantum solutions:
   1. Cost: -42357.21, Freq:   46
   2. Cost: -42357.21, Freq:   39
   3. Cost: -42359.65, Freq:   37
   4. Cost: -42340.07, Freq:   36
   5. Cost: -42315.32, Freq:   36
   6. Cost: -42359.65, Freq:   32
   7. Cost: -42357.21, Freq:   32
   8. Cost: -42357.21, Freq:   31
   9. Cost: -42359.65, Freq:   29
  10. Cost: -42340.98, Freq:   28

Classical benchmark...

=== Hardware-Optimized Performance Summary ===
Backend: lightning.gpu
Circuit gates: 210 (optimized)
Memory usage: 16.01 MB

Timing:
  Training: 1612.60s
  Sampling: 0.29s
  Classical: 0.12s
  Total quantum: 1612.90s

Results:
  Best quantum cost: -42359.6522
  Best classical cost: -42351.2775
  Quantum advantage: 1.000x

System Performance:
  Peak CPU: 0.0%
  Peak Memory: 3517.1 MB
  Duration: 1618.9s

Optimization Stats:
  Cache: 500/500 entries, 0.0% hit rate
  Best quantum cost: -42359.6522

Quantum Solution Analysis:
  Selected 6 bonds (target: 6):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US06051GMA49: Return=0.062, Risk=0.070
    3. US46647PDR47: Return=0.061, Risk=0.066
    4. US95000U3F88: Return=0.062, Risk=0.067
    5. US06051GLU12: Return=0.062, Risk=0.068
    6. US95000U3B74: Return=0.057, Risk=0.067
  Portfolio metrics:
    Cash flow: 0.0663 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2698 (target: [1.6 - 2.0])
    Average return: 0.061 (6.1%)
    Average risk: 0.067
    Total constraint violation: 1.3365

Classical Solution Analysis:
  Selected 7 bonds (target: 6):
    1. US06051GMA49: Return=0.062, Risk=0.070
    2. US06051GKY43: Return=0.060, Risk=0.062
    3. US097023CY98: Return=0.062, Risk=0.046
    4. US95000U3F88: Return=0.062, Risk=0.067
    5. US031162DR88: Return=0.060, Risk=0.066
    6. US172967MP39: Return=0.059, Risk=0.047
    7. US95000U3D31: Return=0.062, Risk=0.066
  Portfolio metrics:
    Cash flow: 0.0766 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2633 (target: [1.6 - 2.0])
    Average return: 0.061 (6.1%)
    Average risk: 0.061
    Total constraint violation: 2.3533

=== Final Assessment ===
QUANTUM ADVANTAGE: Better constraint satisfaction

Final Quantum Solution Analysis:
  Selected 6 bonds (target: 6):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US06051GMA49: Return=0.062, Risk=0.070
    3. US46647PDR47: Return=0.061, Risk=0.066
    4. US95000U3F88: Return=0.062, Risk=0.067
    5. US06051GLU12: Return=0.062, Risk=0.068
    6. US95000U3B74: Return=0.057, Risk=0.067
  Portfolio metrics:
    Cash flow: 0.0663 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2698 (target: [1.6 - 2.0])
    Average return: 0.061 (6.1%)
    Average risk: 0.067
    Total constraint violation: 1.3365

=== Real Data Integration Impact ===
Data source: v_real (V)
Real portfolio: $2,665,535,685 market value
Authentic bonds: 20 from 20 total positions
Real correlations: Avg 0.303
Actual risk-return: Duration 5.8y, Spread 90bp

=== Hardware Optimization Impact ===
Backend: lightning.gpu (hardware-optimized)
Circuit gates: 210 (memory-optimized)
Caching: Cache: 500/500 entries, 0.0% hit rate
Monitoring: Peak 3517MB
Configuration: 3 layers, 6 restarts

Top 10 Quantum Solutions Data for Plotting:
Solution 1: Cost = -36428.23, Frequency = 46
Solution 2: Cost = -30471.71, Frequency = 39
Solution 3: Cost = -583.66, Frequency = 37
Solution 4: Cost = -30434.15, Frequency = 36
Solution 5: Cost = -40363.69, Frequency = 36
Solution 6: Cost = -12563.88, Frequency = 32
Solution 7: Cost = -36451.70, Frequency = 32
Solution 8: Cost = -36446.99, Frequency = 31
Solution 9: Cost = -22540.13, Frequency = 29
Solution 10: Cost = -30455.63, Frequency = 28

Real Data Example 2 output for exploring part 3 of steps1-5.py (WITH Lightning.GPU (20 qubits))

== Hardware-Optimized Quantum Portfolio Optimization ===

=== Loading Real V Portfolio Data ===
Loading V V bond portfolio data...
Successfully loaded 2629 bond positions from V portfolio
Dataset dimensions: 2629 assets x 278 features
Filtered to 2618 bond positions
Selected top 20 holdings by market value for optimization
  Returns calculated from OAS (credit spreads): 90 bps average
  Risk calculated from duration (avg: 5.85 years) and credit spreads
  Correlation matrix estimated from sector/credit clustering (avg: 0.303)
  Weights calculated from market values (largest: 0.134)

Portfolio Analysis Summary:
  Fund: V ($2,665,535,685)
  Average Duration: 5.85 years
  Average Credit Spread: 90 basis points
  Expected Returns: [0.049, 0.074]
  Risk Measures: [0.044, 0.070]
  Sector Distribution: ['Financial', 'Industrial', 'Treasury Bond Portfolio']

=== Real Portfolio Characteristics ===
Fund: V
Portfolio size: 20 bonds (quantum optimized)
Average duration: 5.85 years
Average credit spread: 90 basis points
Returns range: [0.049, 0.074]
Risk range: [0.044, 0.070]
Sample bonds: ['US91282CLN91', 'US87264ABF12', 'US06051GLH01']

=== Quantum Optimization Problem Setup ===
Real V bonds: 20, Target portfolio: 6
Data source: v_real
Fund: V ($2,665,535,685)

Real Market Parameters:
  Expected returns (m): [4.91, 7.35]%
  Return bounds (M): [5.89, 8.82]%
  Risk measures (i_c): [0.444, 0.699]
  Position weights (x_c): [1.475, 5.360]

Portfolio Constraints:
  Target basket size: 6 bonds
  Yield range: [3.0%, 6.0%]
  Duration target: 0.058
  Risk aversion: 2.0

Sample Real Bonds:
  US91282CLN91: Return=0.049, Risk=0.045
  US87264ABF12: Return=0.057, Risk=0.048
  US06051GLH01: Return=0.061, Risk=0.065
  US00287YBX67: Return=0.054, Risk=0.045
  US716973AE24: Return=0.059, Risk=0.068

Optimization ready: 20 real V bonds → 6 quantum portfolio

=== Building QUBO with Real Bond Data ===
Covariance matrix built from real bond correlations: (20, 20)
QUBO matrix Q shape: (20, 20)

=== Initializing Optimized Components ===
Hardware Config:
  CPUs: 16, Memory: 7.3GB
  Recommended: {'qaoa_layers': 3, 'shots': 36681, 'restarts': 6, 'processes': 4, 'batch_size': 100}
Main device: lightning.gpu
Circuit Analysis:
  Significant gates: 210
  Estimated memory: 16.01 MB

=== Starting Optimized Training ===
QAOA layers: 3, Restarts: 6

--- Restart 1/6 ---
  Iter   0: -8617.0178 | Cache: 1/500 entries, 0.0% hit rate
  Iter  50: 1317.2524 | Cache: 51/500 entries, 0.0% hit rate
  Iter 100: 1304.5634 | Cache: 101/500 entries, 0.0% hit rate
  Iter 150: 1716.1425 | Cache: 151/500 entries, 0.0% hit rate
New best: -3464.7871

--- Restart 2/6 ---
  Iter   0: -1069.8705 | Cache: 201/500 entries, 0.0% hit rate
  Iter  50: -439.2024 | Cache: 251/500 entries, 0.0% hit rate
  Iter 100: 331.4856 | Cache: 301/500 entries, 0.0% hit rate
  Iter 150: 261.3003 | Cache: 351/500 entries, 0.0% hit rate

--- Restart 3/6 ---
  Iter   0: 393.2238 | Cache: 401/500 entries, 0.0% hit rate
  Iter  50: -1240.2969 | Cache: 451/500 entries, 0.0% hit rate
  Iter 100: -249.7027 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -464.9459 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 4/6 ---
  Iter   0: 141.7047 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: 126.1367 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -323.2413 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: 529.7106 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 5/6 ---
  Iter   0:  27.0196 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: 462.4843 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -46.0504 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -140.0843 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 6/6 ---
  Iter   0: -801.4223 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: 508.8128 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -144.8660 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -481.7243 | Cache: 500/500 entries, 0.0% hit rate

=== Optimized Sampling ===
Sampling: 36681 shots in 0.27s

Top quantum solutions:
   1. Cost: -42100.10, Freq:   34
   2. Cost: -42100.79, Freq:   33
   3. Cost: -42100.68, Freq:   33
   4. Cost: -42100.79, Freq:   30
   5. Cost: -42100.68, Freq:   27
   6. Cost: -42100.05, Freq:   25
   7. Cost: -42100.10, Freq:   22
   8. Cost: -42100.68, Freq:   21
   9. Cost: -42100.10, Freq:   19
  10. Cost: -42100.68, Freq:   19

Classical benchmark...

=== Hardware-Optimized Performance Summary ===
Backend: lightning.gpu
Circuit gates: 210 (optimized)
Memory usage: 16.01 MB

Timing:
  Training: 1604.53s
  Sampling: 0.27s
  Classical: 0.12s
  Total quantum: 1604.80s

Results:
  Best quantum cost: -42100.7901
  Best classical cost: -42102.4849
  Quantum advantage: 1.000x

System Performance:
  Peak CPU: 0.0%
  Peak Memory: 3575.3 MB
  Duration: 1609.7s

Optimization Stats:
  Cache: 500/500 entries, 0.0% hit rate
  Best quantum cost: -42100.7901

Quantum Solution Analysis:
  Selected 6 bonds (target: 6):
    1. US06051GMA49: Return=0.062, Risk=0.070
    2. US46647PDR47: Return=0.061, Risk=0.066
    3. US95000U3F88: Return=0.062, Risk=0.067
    4. US031162DR88: Return=0.060, Risk=0.066
    5. US95000U3B74: Return=0.057, Risk=0.067
    6. US95000U3D31: Return=0.062, Risk=0.066
  Portfolio metrics:
    Cash flow: 0.0624 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2698 (target: [0.4, 0.8])
    Average return: 0.060 (6.0%)
    Average risk: 0.067 (6.7%)
    Total constraint violation: 0.1326

Classical Solution Analysis:
  Selected 7 bonds (target: 6):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US716973AE24: Return=0.059, Risk=0.068
    3. US097023CY98: Return=0.062, Risk=0.046
    4. US46647PDH64: Return=0.059, Risk=0.062
    5. US95000U3F88: Return=0.062, Risk=0.067
    6. US06051GLU12: Return=0.062, Risk=0.068
    7. US17327CAR43: Return=0.064, Risk=0.064
  Portfolio metrics:
    Cash flow: 0.0785 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2792 (target: [0.4, 0.8])
    Average return: 0.061 (6.1%)
    Average risk: 0.063 (6.3%)
    Total constraint violation: 1.1392

=== Final Assessment ===
QUANTUM ADVANTAGE: Better constraint satisfaction

Final Quantum Solution Analysis:
  Selected 6 bonds (target: 6):
    1. US06051GMA49: Return=0.062, Risk=0.070
    2. US46647PDR47: Return=0.061, Risk=0.066
    3. US95000U3F88: Return=0.062, Risk=0.067
    4. US031162DR88: Return=0.060, Risk=0.066
    5. US95000U3B74: Return=0.057, Risk=0.067
    6. US95000U3D31: Return=0.062, Risk=0.066
  Portfolio metrics:
    Cash flow: 0.0624 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2698 (target: [0.4, 0.8])
    Average return: 0.060 (6.0%)
    Average risk: 0.067 (6.7%)
    Total constraint violation: 0.1326

=== Real Data Integration Impact ===
Data source: v_real (V)
Real portfolio: $2,665,535,685 market value
Authentic bonds: 20 from 20 total positions
Real correlations: Avg 0.303
Actual risk-return: Duration 5.8y, Spread 90bp

=== Hardware Optimization Impact ===
Backend: lightning.gpu (hardware-optimized)
Circuit gates: 210 (memory-optimized)
Caching: Cache: 500/500 entries, 0.0% hit rate
Monitoring: Peak 3575MB
Configuration: 3 layers, 6 restarts

Top 10 Quantum Solutions Data for Plotting:
Solution 1: Cost = 29872.48, Frequency = 34
Solution 2: Cost = -12122.31, Frequency = 33
Solution 3: Cost = 13873.46, Frequency = 33
Solution 4: Cost = -123.77, Frequency = 30
Solution 5: Cost = 13872.26, Frequency = 27
Solution 6: Cost = -12119.02, Frequency = 25
Solution 7: Cost = 29872.02, Frequency = 22
Solution 8: Cost = 13873.14, Frequency = 21
Solution 9: Cost = 29872.75, Frequency = 19
Solution 10: Cost = 29872.96, Frequency = 19

Real Data Example 3 output for exploring part 3 of steps1-5.py (With Lightning.GPU (15 qubits))

== Hardware-Optimized Quantum Portfolio Optimization ===

=== Loading Real V Portfolio Data ===
Loading V bond portfolio data...
Successfully loaded 2629 bond positions from V portfolio
Dataset dimensions: 2629 assets x 278 features
Filtered to 2618 bond positions
Selected top 15 holdings by market value for optimization
  Returns calculated from OAS (credit spreads): 91 bps average
  Risk calculated from duration (avg: 5.89 years) and credit spreads
  Correlation matrix estimated from sector/credit clustering (avg: 0.303)
  Weights calculated from market values (largest: 0.166)

Portfolio Analysis Summary:
  Fund: V ($2,153,890,208)
  Average Duration: 5.89 years
  Average Credit Spread: 91 basis points
  Expected Returns: [0.049, 0.074]
  Risk Measures: [0.045, 0.070]
  Sector Distribution: ['Financial', 'Industrial', 'Treasury Bond Portfolio']

=== Real Portfolio Characteristics ===
Fund: V
Portfolio size: 15 bonds (quantum optimized)
Average duration: 5.89 years
Average credit spread: 91 basis points
Returns range: [0.049, 0.074]
Risk range: [0.045, 0.070]
Sample bonds: ['US91282CLN91', 'US87264ABF12', 'US06051GLH01']

=== Quantum Optimization Problem Setup ===
Real V bonds: 15, Target portfolio: 5
Data source: v_real
Fund: V ($2,153,890,208)

Real Market Parameters:
  Expected returns (m): [4.91, 7.35]%
  Return bounds (M): [5.89, 8.82]%
  Risk measures (i_c): [0.447, 0.699]
  Position weights (x_c): [1.525, 4.975]

Portfolio Constraints:
  Target basket size: 5 bonds
  Yield range: [3.0%, 6.0%]
  Duration target: 0.059
  Risk aversion: 2.0

Sample Real Bonds:
  US91282CLN91: Return=0.049, Risk=0.045
  US87264ABF12: Return=0.057, Risk=0.048
  US06051GLH01: Return=0.061, Risk=0.065
  US00287YBX67: Return=0.054, Risk=0.045
  US716973AE24: Return=0.059, Risk=0.068

Optimization ready: 15 real V bonds → 5 quantum portfolio

=== Building QUBO with Real Bond Data ===
Covariance matrix built from real bond correlations: (15, 15)
QUBO matrix Q shape: (15, 15)

=== Initializing Optimized Components ===
Hardware Config:
  CPUs: 16, Memory: 7.3GB
  Recommended: {'qaoa_layers': 3, 'shots': 36681, 'restarts': 5, 'processes': 4, 'batch_size': 312}
Main device: lightning.gpu
Circuit Analysis:
  Significant gates: 120
  Estimated memory: 0.51 MB

=== Starting Optimized Training ===
QAOA layers: 3, Restarts: 5

--- Restart 1/5 ---
  Iter   0: 2235.7510 | Cache: 1/500 entries, 0.0% hit rate
  Iter  50: 646.2934 | Cache: 51/500 entries, 0.0% hit rate
  Iter 100: 284.5512 | Cache: 101/500 entries, 0.0% hit rate
  Iter 150: 1421.9041 | Cache: 151/500 entries, 0.0% hit rate
New best: -147.8232

--- Restart 2/5 ---
  Iter   0: 333.5096 | Cache: 201/500 entries, 0.0% hit rate
  Iter  50: -214.2464 | Cache: 251/500 entries, 0.0% hit rate
  Iter 100: 116.7286 | Cache: 301/500 entries, 0.0% hit rate
  Iter 150: -207.4894 | Cache: 351/500 entries, 0.0% hit rate
New best: -1609.3758

--- Restart 3/5 ---
  Iter   0: 617.4431 | Cache: 401/500 entries, 0.0% hit rate
  Iter  50: -404.4405 | Cache: 451/500 entries, 0.0% hit rate
  Iter 100: -641.2667 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150:  80.8913 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 4/5 ---
  Iter   0: -397.5769 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -208.9377 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -544.1584 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -323.2236 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 5/5 ---
  Iter   0: -190.2146 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -2295.5743 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -42.8319 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: 173.8719 | Cache: 500/500 entries, 0.0% hit rate

=== Optimized Sampling ===
Sampling: 36681 shots in 0.13s

Top quantum solutions:
   1. Cost: -30087.48, Freq:  196
   2. Cost: -30087.57, Freq:  191
   3. Cost: -30087.57, Freq:  150
   4. Cost: -30082.17, Freq:  123
   5. Cost: -30088.93, Freq:  122
   6. Cost: -30082.30, Freq:  110
   7. Cost: -30089.25, Freq:  108
   8. Cost: -30081.91, Freq:  105
   9. Cost: -30072.90, Freq:  101
  10. Cost: -30077.22, Freq:   98

Classical benchmark...

=== Hardware-Optimized Performance Summary ===
Backend: lightning.gpu
Circuit gates: 120 (optimized)
Memory usage: 0.51 MB

Timing:
  Training: 408.27s
  Sampling: 0.13s
  Classical: 0.10s
  Total quantum: 408.40s

Results:
  Best quantum cost: -30089.2520
  Best classical cost: -30098.7602
  Quantum advantage: 1.000x

System Performance:
  Peak CPU: 0.0%
  Peak Memory: 2300.1 MB
  Duration: 415.7s

Optimization Stats:
  Cache: 500/500 entries, 0.0% hit rate
  Best quantum cost: -30089.2520

Quantum Solution Analysis:
  Selected 5 bonds (target: 5):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US716973AE24: Return=0.059, Risk=0.068
    3. US06051GMA49: Return=0.062, Risk=0.070
    4. US95000U3F88: Return=0.062, Risk=0.067
    5. US06051GLU12: Return=0.062, Risk=0.068
  Portfolio metrics:
    Cash flow: 0.0546 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2276 (target: [0.4, 0.8])
    Average return: 0.061 (6.1%)
    Average risk: 0.067 (6.7%)
    Total constraint violation: 0.1724

Classical Solution Analysis:
  Selected 6 bonds (target: 5):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US06051GMA49: Return=0.062, Risk=0.070
    3. US46647PDR47: Return=0.061, Risk=0.066
    4. US55903VBC63: Return=0.074, Risk=0.062
    5. US95000U3F88: Return=0.062, Risk=0.067
    6. US031162DR88: Return=0.060, Risk=0.066
  Portfolio metrics:
    Cash flow: 0.0653 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2623 (target: [0.4, 0.8])
    Average return: 0.063 (6.3%)
    Average risk: 0.066 (6.6%)
    Total constraint violation: 1.1430

=== Final Assessment ===
QUANTUM ADVANTAGE: Better constraint satisfaction

Final Quantum Solution Analysis:
  Selected 5 bonds (target: 5):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US716973AE24: Return=0.059, Risk=0.068
    3. US06051GMA49: Return=0.062, Risk=0.070
    4. US95000U3F88: Return=0.062, Risk=0.067
    5. US06051GLU12: Return=0.062, Risk=0.068
  Portfolio metrics:
    Cash flow: 0.0546 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2276 (target: [0.4, 0.8])
    Average return: 0.061 (6.1%)
    Average risk: 0.067 (6.7%)
    Total constraint violation: 0.1724

=== Real Data Integration Impact ===
Data source: v_real (V)
Real portfolio: $2,153,890,208 market value
Authentic bonds: 15 from 15 total positions
Real correlations: Avg 0.303
Actual risk-return: Duration 5.9y, Spread 91bp

=== Hardware Optimization Impact ===
Backend: lightning.gpu (hardware-optimized)
Circuit gates: 120 (memory-optimized)
Caching: Cache: 500/500 entries, 0.0% hit rate
Monitoring: Peak 2300MB
Configuration: 3 layers, 5 restarts

Top 10 Quantum Solutions Data for Plotting:
Solution 1: Cost = -10116.73, Frequency = 196
Solution 2: Cost = -24107.83, Frequency = 191
Solution 3: Cost = -18115.20, Frequency = 150
Solution 4: Cost = -28065.98, Frequency = 123
Solution 5: Cost = -24108.95, Frequency = 122
Solution 6: Cost = -28092.91, Frequency = 110
Solution 7: Cost = -10122.46, Frequency = 108
Solution 8: Cost = -28092.67, Frequency = 105
Solution 9: Cost = -30072.90, Frequency = 101
Solution 10: Cost = -30083.41, Frequency = 98

Real Data Example 4 output for exploring part 3 of steps1-5.py (With Lightning.GPU (15 qubits) but this time we tried increasing the QAOA Layers to 15 deep)

=== Hardware-Optimized Quantum Portfolio Optimization ===

=== Loading Real V Portfolio Data ===
Loading V V bond portfolio data...
Successfully loaded 2629 bond positions from V portfolio
Dataset dimensions: 2629 assets x 278 features
Filtered to 2618 bond positions
Selected top 15 holdings by market value for optimization
  Returns calculated from OAS (credit spreads): 91 bps average
  Risk calculated from duration (avg: 5.89 years) and credit spreads
  Correlation matrix estimated from sector/credit clustering (avg: 0.303)
  Weights calculated from market values (largest: 0.166)

Portfolio Analysis Summary:
  Fund: V ($2,153,890,208)
  Average Duration: 5.89 years
  Average Credit Spread: 91 basis points
  Expected Returns: [0.049, 0.074]
  Risk Measures: [0.045, 0.070]
  Sector Distribution: ['Financial', 'Industrial', 'Treasury Bond Portfolio']

=== Real Portfolio Characteristics ===
Fund: V
Portfolio size: 15 bonds (quantum optimized)
Average duration: 5.89 years
Average credit spread: 91 basis points
Returns range: [0.049, 0.074]
Risk range: [0.045, 0.070]
Sample bonds: ['US91282CLN91', 'US87264ABF12', 'US06051GLH01']

=== Quantum Optimization Problem Setup ===
Real V bonds: 15, Target portfolio: 5
Data source: v_real
Fund: V ($2,153,890,208)

Real Market Parameters:
  Expected returns (m): [4.91, 7.35]%
  Return bounds (M): [5.89, 8.82]%
  Risk measures (i_c): [0.447, 0.699]
  Position weights (x_c): [1.525, 4.975]

Portfolio Constraints:
  Target basket size: 5 bonds
  Yield range: [3.0%, 6.0%]
  Duration target: 0.059
  Risk aversion: 2.0

Sample Real Bonds:
  US91282CLN91: Return=0.049, Risk=0.045
  US87264ABF12: Return=0.057, Risk=0.048
  US06051GLH01: Return=0.061, Risk=0.065
  US00287YBX67: Return=0.054, Risk=0.045
  US716973AE24: Return=0.059, Risk=0.068

Optimization ready: 15 real V bonds → 5 quantum portfolio

=== Building QUBO with Real Bond Data ===
Covariance matrix built from real bond correlations: (15, 15)
QUBO matrix Q shape: (15, 15)

=== Initializing Optimized Components ===
Hardware Config:
  CPUs: 16, Memory: 7.3GB
  Recommended: {'qaoa_layers': 15, 'shots': 36681, 'restarts': 5, 'processes': 4, 'batch_size': 312}
Main device: lightning.gpu
Circuit Analysis:
  Significant gates: 120
  Estimated memory: 0.51 MB

=== Starting Optimized Training ===
QAOA layers: 15, Restarts: 5

--- Restart 1/5 ---
  Iter   0:   7.7829 | Cache: 1/500 entries, 0.0% hit rate
  Iter  50: -49.8649 | Cache: 51/500 entries, 0.0% hit rate
  Iter 100:  26.9868 | Cache: 101/500 entries, 0.0% hit rate
  Iter 150: -165.9924 | Cache: 151/500 entries, 0.0% hit rate
New best: -83.5176

--- Restart 2/5 ---
  Iter   0:  78.2687 | Cache: 201/500 entries, 0.0% hit rate
  Iter  50: 221.9504 | Cache: 251/500 entries, 0.0% hit rate
  Iter 100:  19.3818 | Cache: 301/500 entries, 0.0% hit rate
  Iter 150:  -2.7413 | Cache: 351/500 entries, 0.0% hit rate

--- Restart 3/5 ---
  Iter   0: -17.6540 | Cache: 401/500 entries, 0.0% hit rate
  Iter  50: 144.3433 | Cache: 451/500 entries, 0.0% hit rate
  Iter 100: -148.7635 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150:  94.4706 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 4/5 ---
  Iter   0: -185.8001 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -55.0280 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: 139.2483 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150:   5.7107 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 5/5 ---
  Iter   0:  97.8533 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -91.7477 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: 133.6604 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -77.2422 | Cache: 500/500 entries, 0.0% hit rate

=== Optimized Sampling ===
Sampling: 36681 shots in 0.70s

Top quantum solutions:
   1. Cost: -30086.55, Freq:   15
   2. Cost: -30081.27, Freq:   14
   3. Cost: -30084.67, Freq:   14
   4. Cost: -30087.48, Freq:   14
   5. Cost: -30085.61, Freq:   14
   6. Cost: -30088.01, Freq:   13
   7. Cost: -30086.93, Freq:   13
   8. Cost: -30086.85, Freq:   13
   9. Cost: -30088.30, Freq:   13
  10. Cost: -30088.54, Freq:   13

Classical benchmark...

=== Hardware-Optimized Performance Summary ===
Backend: lightning.gpu
Circuit gates: 120 (optimized)
Memory usage: 0.51 MB

Timing:
  Training: 1713.42s
  Sampling: 0.70s
  Classical: 0.16s
  Total quantum: 1714.11s

Results:
  Best quantum cost: -30088.5432
  Best classical cost: -30092.5023
  Quantum advantage: 1.000x

System Performance:
  Peak CPU: 0.0%
  Peak Memory: 6588.5 MB
  Duration: 1720.8s

Optimization Stats:
  Cache: 500/500 entries, 0.0% hit rate
  Best quantum cost: -30088.5432

Quantum Solution Analysis:
  Selected 5 bonds (target: 5):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US716973AE24: Return=0.059, Risk=0.068
    3. US06051GMA49: Return=0.062, Risk=0.070
    4. US46647PDR47: Return=0.061, Risk=0.066
    5. US95000U3F88: Return=0.062, Risk=0.067
  Portfolio metrics:
    Cash flow: 0.0555 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2254 (target: [0.4, 0.8])
    Average return: 0.061 (6.1%)
    Average risk: 0.067 (6.7%)
    Total constraint violation: 0.1746

Classical Solution Analysis:
  Selected 6 bonds (target: 5):
    1. US00287YBX67: Return=0.054, Risk=0.045
    2. US716973AE24: Return=0.059, Risk=0.068
    3. US46647PDR47: Return=0.061, Risk=0.066
    4. US55903VBC63: Return=0.074, Risk=0.062
    5. US95000U3F88: Return=0.062, Risk=0.067
    6. US06051GLU12: Return=0.062, Risk=0.068
  Portfolio metrics:
    Cash flow: 0.0633 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2394 (target: [0.4, 0.8])
    Average return: 0.062 (6.2%)
    Average risk: 0.063 (6.3%)
    Total constraint violation: 1.1639

=== Final Assessment ===
QUANTUM ADVANTAGE: Better constraint satisfaction

Final Quantum Solution Analysis:
  Selected 5 bonds (target: 5):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US716973AE24: Return=0.059, Risk=0.068
    3. US06051GMA49: Return=0.062, Risk=0.070
    4. US46647PDR47: Return=0.061, Risk=0.066
    5. US95000U3F88: Return=0.062, Risk=0.067
  Portfolio metrics:
    Cash flow: 0.0555 (target: [3.0%, 6.0%])
    Risk characteristic: 0.2254 (target: [0.4, 0.8])
    Average return: 0.061 (6.1%)
    Average risk: 0.067 (6.7%)
    Total constraint violation: 0.1746

=== Real Data Integration Impact ===
Data source: v_real (V)
Real portfolio: $2,153,890,208 market value
Authentic bonds: 15 from 15 total positions
Real correlations: Avg 0.303
Actual risk-return: Duration 5.9y, Spread 91bp

=== Hardware Optimization Impact ===
Backend: lightning.gpu (hardware-optimized)
Circuit gates: 120 (memory-optimized)
Caching: Cache: 500/500 entries, 0.0% hit rate
Monitoring: Peak 6589MB
Configuration: 15 layers, 5 restarts

Top 10 Quantum Solutions Data for Plotting:
Solution 1: Cost = -10113.02, Frequency = 15
Solution 2: Cost = -28091.72, Frequency = 14
Solution 3: Cost = -18104.35, Frequency = 14
Solution 4: Cost = -18113.44, Frequency = 14
Solution 5: Cost = -24106.47, Frequency = 14
Solution 6: Cost = -18114.30, Frequency = 13
Solution 7: Cost = -28098.57, Frequency = 13
Solution 8: Cost = -24106.78, Frequency = 13
Solution 9: Cost = -124.98, Frequency = 13
Solution 10: Cost = -18110.81, Frequency = 13

Real Data Example 5 output for exploring part 3 of steps1-5.py (With Lightning.GPU (24 qubits), QAOA Layers of 2)

=== Hardware-Optimized Quantum Portfolio Optimization ===

=== Loading Real V Portfolio Data ===
Loading V V bond portfolio data...
Successfully loaded 2629 bond positions from V portfolio
Dataset dimensions: 2629 assets x 278 features
Filtered to 2618 bond positions
Selected top 24 holdings by market value for optimization
  Returns calculated from OAS (credit spreads): 90 bps average
  Risk calculated from duration (avg: 5.91 years) and credit spreads
  Correlation matrix estimated from sector/credit clustering (avg: 0.318)
  Weights calculated from market values (largest: 0.117)

Portfolio Analysis Summary:
  Fund: ($3,047,237,649)
  Average Duration: 5.91 years
  Average Credit Spread: 90 basis points
  Expected Returns: [0.049, 0.074]
  Risk Measures: [0.044, 0.070]
  Sector Distribution: ['Financial', 'Industrial', 'Treasury Bond Portfolio']

=== Real Portfolio Characteristics ===
Fund: V
Portfolio size: 24 bonds (memory-optimized)
Memory requirement: 0.25 GB
Note: For 31 qubits, you would need 32.0 GB RAM
Average duration: 5.91 years
Average credit spread: 90 basis points
Returns range: [0.049, 0.074]
Risk range: [0.044, 0.070]
Sample bonds: ['US91282CLN91', 'US87264ABF12', 'US06051GLH01']

=== Quantum Optimization Problem Setup ===
Real V bonds: 24, Target portfolio: 8
Data source: v_real
Fund: ($3,047,237,649)

Real Market Parameters:
  Expected returns (m): [4.91, 7.35]%
  Return bounds (M): [5.89, 8.82]%
  Risk measures (i_c): [0.444, 0.699]
  Position weights (x_c): [1.478, 5.627]

Portfolio Constraints:
  Target basket size: 8 bonds
  Yield range: [3.0%, 6.0%]
  Duration target: 0.059
  Risk aversion: 2.0

Sample Real Bonds:
  US91282CLN91: Return=0.049, Risk=0.045
  US87264ABF12: Return=0.057, Risk=0.048
  US06051GLH01: Return=0.061, Risk=0.065
  US00287YBX67: Return=0.054, Risk=0.045
  US716973AE24: Return=0.059, Risk=0.068

Optimization ready: 24 real V bonds → 8 quantum portfolio

=== Building QUBO with Real Bond Data ===
Covariance matrix built from real bond correlations: (24, 24)
QUBO matrix Q shape: (24, 24)

=== Initializing Optimized Components ===
Hardware Config for 24 qubits:
  CPUs: 16, Memory: 7.3GB
  State memory needed: 0.25GB
  Recommended: {'qaoa_layers': 2, 'shots': 14672, 'restarts': 6, 'processes': 2, 'batch_size': 100, 'state_memory_gb': 0.25}
Memory Analysis for 24 qubits:
  Required: 0.25 GB
  Available: 7.34 GB
Using GPU acceleration (Lightning GPU)
Selected backend: lightning.gpu for 24 qubits
Circuit Analysis:
  Significant gates: 300
  Estimated memory: 256.02 MB

=== Starting Memory-Aware Training ===
Problem size: 24 qubits
QAOA layers: 2, Restarts: 6
Expected memory: 0.25 GB
Initial memory: 653.5 MB, Available: 5.81 GB

--- Restart 1/6 ---
  Iter   0: 2662.2465 | Cache: 1/500 entries, 0.0% hit rate
  Iter  50: 1871.0666 | Cache: 51/500 entries, 0.0% hit rate
  Iter 100: 744.2100 | Cache: 101/500 entries, 0.0% hit rate
  Iter 150:  61.8382 | Cache: 151/500 entries, 0.0% hit rate
New best: 283.7757

--- Restart 2/6 ---
  Iter   0: 1454.8002 | Cache: 201/500 entries, 0.0% hit rate
  Iter  50: -94.2396 | Cache: 251/500 entries, 0.0% hit rate
  Iter 100: -616.9449 | Cache: 301/500 entries, 0.0% hit rate
  Iter 150: 1466.1301 | Cache: 351/500 entries, 0.0% hit rate
New best: -849.9316

--- Restart 3/6 ---
  Iter   0: -886.3320 | Cache: 401/500 entries, 0.0% hit rate
  Iter  50: -114.1793 | Cache: 451/500 entries, 0.0% hit rate
  Iter 100: -352.3910 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -578.7280 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 4/6 ---
  Iter   0: 3335.9176 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50:  17.4718 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100:  65.5230 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: 127.4739 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 5/6 ---
  Iter   0: 177.5902 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -579.7770 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -306.7492 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: -672.4514 | Cache: 500/500 entries, 0.0% hit rate

--- Restart 6/6 ---
  Iter   0: -230.0905 | Cache: 500/500 entries, 0.0% hit rate
  Iter  50: -672.4463 | Cache: 500/500 entries, 0.0% hit rate
  Iter 100: -1088.8363 | Cache: 500/500 entries, 0.0% hit rate
  Iter 150: 140.4235 | Cache: 500/500 entries, 0.0% hit rate

=== Optimized Sampling ===
Memory Analysis for 24 qubits:
  Required: 0.25 GB
  Available: 7.34 GB
Using GPU acceleration (Lightning GPU)
Sampling: 14672 shots in 3.27s

Top quantum solutions:
   1. Cost: -72114.44, Freq:    6
   2. Cost: -72116.75, Freq:    4
   3. Cost: -72108.89, Freq:    4
   4. Cost: -72117.12, Freq:    4
   5. Cost: -72108.98, Freq:    3
   6. Cost: -72116.13, Freq:    3
   7. Cost: -72115.29, Freq:    3
   8. Cost: -72116.22, Freq:    3
   9. Cost: -72114.58, Freq:    3
  10. Cost: -72105.34, Freq:    3

Classical benchmark...

=== Hardware-Optimized Performance Summary ===
Backend: lightning.gpu
Circuit gates: 300 (optimized)
Memory usage: 256.02 MB

Timing:
  Training: 23734.30s
  Sampling: 3.27s
  Classical: 0.15s
  Total quantum: 23737.57s

Results:
  Best quantum cost: -72117.1201
  Best classical cost: -72122.6228
  Quantum advantage: 1.000x

System Performance:
  Peak CPU: 0.0%
  Peak Memory: 3590.4 MB
  Duration: 23739.5s

Optimization Stats:
  Cache: 500/500 entries, 0.0% hit rate
  Best quantum cost: -72117.1201

Quantum Solution Analysis:
  Selected 8 bonds (target: 8):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US716973AE24: Return=0.059, Risk=0.068
    3. US06051GMA49: Return=0.062, Risk=0.070
    4. US031162DR88: Return=0.060, Risk=0.066
    5. US06051GLU12: Return=0.062, Risk=0.068
    6. US17327CAR43: Return=0.064, Risk=0.064
    7. US95000U3D31: Return=0.062, Risk=0.066
    8. US06051GKQ19: Return=0.060, Risk=0.060
  Portfolio metrics:
    Cash flow: 0.0900 (target: [3.0%, 6.0%])
    Risk characteristic: 0.3478 (target: [0.4, 0.8])
    Average return: 0.061 (6.1%)
    Average risk: 0.066 (6.6%)
    Total constraint violation: 0.0822

Classical Solution Analysis:
  Selected 9 bonds (target: 8):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US46647PDH64: Return=0.059, Risk=0.062
    3. US46647PDR47: Return=0.061, Risk=0.066
    4. US95000U3F88: Return=0.062, Risk=0.067
    5. US06051GLU12: Return=0.062, Risk=0.068
    6. US95000U3D31: Return=0.062, Risk=0.066
    7. US46647PDK93: Return=0.061, Risk=0.062
    8. US92343VGN82: Return=0.060, Risk=0.066
    9. US61747YEY77: Return=0.060, Risk=0.062
  Portfolio metrics:
    Cash flow: 0.0955 (target: [3.0%, 6.0%])
    Risk characteristic: 0.3793 (target: [0.4, 0.8])
    Average return: 0.061 (6.1%)
    Average risk: 0.065 (6.5%)
    Total constraint violation: 1.0562

=== Final Assessment ===
QUANTUM ADVANTAGE: Better constraint satisfaction

Final Quantum Solution Analysis:
  Selected 8 bonds (target: 8):
    1. US06051GLH01: Return=0.061, Risk=0.065
    2. US716973AE24: Return=0.059, Risk=0.068
    3. US06051GMA49: Return=0.062, Risk=0.070
    4. US031162DR88: Return=0.060, Risk=0.066
    5. US06051GLU12: Return=0.062, Risk=0.068
    6. US17327CAR43: Return=0.064, Risk=0.064
    7. US95000U3D31: Return=0.062, Risk=0.066
    8. US06051GKQ19: Return=0.060, Risk=0.060
  Portfolio metrics:
    Cash flow: 0.0900 (target: [3.0%, 6.0%])
    Risk characteristic: 0.3478 (target: [0.4, 0.8])
    Average return: 0.061 (6.1%)
    Average risk: 0.066 (6.6%)
    Total constraint violation: 0.0822

=== Real Data Integration Impact ===
Data source: v_real 
Real portfolio: $3,047,237,649 market value
Authentic bonds: 24 from 24 total positions
Real correlations: Avg 0.318
Actual risk-return: Duration 5.9y, Spread 90bp

=== Hardware Optimization Impact ===
Backend: lightning.gpu (hardware-optimized)
Circuit gates: 300 (memory-optimized)
Caching: Cache: 500/500 entries, 0.0% hit rate
Monitoring: Peak 3590MB
Configuration: 2 layers, 6 restarts

Top 10 Quantum Solutions Data for Plotting:
Solution 1: Cost = -60122.00, Frequency = 6
Solution 2: Cost = -60123.01, Frequency = 4
Solution 3: Cost = -66116.15, Frequency = 4
Solution 4: Cost = -52128.57, Frequency = 4
Solution 5: Cost = -70115.93, Frequency = 3
Solution 6: Cost = -70121.98, Frequency = 3
Solution 7: Cost = -52128.19, Frequency = 3
Solution 8: Cost = -30126.30, Frequency = 3
Solution 9: Cost = -60127.51, Frequency = 3
Solution 10: Cost = -70110.51, Frequency = 3

Key Features

Adaptive Penalty System

Dynamic constraint weight adjustment during optimization
Automatic penalty scaling based on violation severity
Improved convergence to feasible solutions

QAOA Implementation

Quantum Approximate Optimization Algorithm with 3 layers with lightning.gpu and shots are 36681 with 6 restarts, 4 processes, and batch size of 100
Optimized parameter initialization and learning rates
Robust multi-restart strategy for global optimization

Post-Processing Pipeline

Greedy feasibility correction for quantum solutions
Statistical analysis of solution frequency and quality
Constraint violation tracking

Performance Analysis

Detailed constraint satisfaction metrics
Classical benchmark comparison with simulated annealing
Cost ratio analysis and competitive assessment

Algorithm Performance:

Strengths:

VQE shows good convergence behavior
Quantum algorithm explores different solution regions
Handles multiple constraints simultaneously
Proper constraint violation analysis

Areas for Improvement:

Penalty parameter tuning needed for better constraint satisfaction
Larger problem sizes would better demonstrate quantum advantage, in theory, however it will be harder due to limited amount of qubits in the world

Technical Implementation

Quantum Framework: PennyLane with lightning.qubit and lightning.gpu simulators
Optimization: Adam optimizer with adaptive learning rate of 0.05 and 0.01
Sampling: 50,000 shots for high-precision measurements (36681 shots for lightning.gpu)
Classical Benchmark: Simulated annealing with basin hopping
Constraint Handling: Penalty method with adaptive scaling

Name		Name	Last commit message	Last commit date
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.vscode		.vscode
current_progress		current_progress
.gitignore		.gitignore
Dockerfile		Dockerfile
README.md		README.md
V_data_info.md		V_data_info.md
portfolio optimization PRESENTATION.pdf		portfolio optimization PRESENTATION.pdf
requirements.txt		requirements.txt
setup_environment.sh		setup_environment.sh
v_portfolio_analysis.ipynb		v_portfolio_analysis.ipynb

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