Optimal Tuning of Quantum Generative Adversarial Networks for Multivariate Distribution Loading
Abstract
:1. Introduction
2. Encoding and Loading Classical Information in Quantum Registers: Overcoming the Challenges of the NISQ Era
2.1. Techniques for Exact Data Loading and Their Limitations
2.2. Approximate Data Loading with qGANs
3. From GANs to qGANs
3.1. The Generative Interpretation of qGANs
3.2. The Data-Compression Interpretation of qGANs
4. Results
4.1. Design of the Generative Quantum Circuit Network
4.2. Design of the Classical Discriminative Deep Neural Network
4.3. Optimization of the qGAN Accuracy and Comparison with Benchmarks
4.4. Trade-Off between Accuracy and Training Time: The Effect of the Optimizer and of Other Hyper-Parameters
4.5. Isolation of the Best Runs
5. Methods
5.1. Testing Conditions
5.2. Run Evaluation
5.3. Objective Function and Optimizers
5.4. Estimating Complexity
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Tuning a qGAN
Appendix A.1. Summary of Choices and Tunable Degrees of Freedom
Appendix A.2. The Testing Campaign
Test Set | n | k | Generator Optimizer | Discriminator Optimizer | Max Epochs | Shots | ||
---|---|---|---|---|---|---|---|---|
A | 3 | 1 | 8 | 16 | Adam, lr = *, = 0.7, = 0.99 | Adam, lr = *, = 0.7, = 0.99 | 2000 | 2000 |
B | 3 | 1 | * | * | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 2000 | 2000 |
C | 3 | 1 | * | * | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 2000 | 2000 |
D | 3 | 1 | * | * | Adam, lr = , = 0.9, = 0.99 | Adam, lr = , = 0.9, = 0.99 | 2000 | 2000 |
E | 3 | 1 | 8 | 8 | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 2000 | * |
F | 3 | 1 | 8 | 8 | SPSA, lr = *, perturb = * | Adam, lr = , = 0.7, = 0.99 | 10000 | 2000 |
G | 3 | 1 | 8 | 8 | SPSA, lr = , perturb = | Adam, lr = , = 0.7, = 0.99 | 10,000 | * |
H | 3 | 1 | 8 | 8 | Adam, lr = , = 0.7, = 0.99 | SPSA, lr = *, perturb = * | 10,000 | 2000 |
I | 3 | 1 | 8 | 8 | Adam, lr = , = 0.7, = 0.99 | SPSA, lr = , perturb = | 10,000 | * |
J | 4 | 1 | * | * | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 2000 | 2000 |
K | 4 | 1 | 32 | 16 | Adam, lr = *, = 0.7, = 0.99 | Adam, lr = *, = 0.7, = 0.99 | 2000 | 2000 |
L | 4 | 1 | 32 | 16 | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 2000 | * |
Case | Originating Test Set |
---|---|
a. Baseline | B with |
b. Big discriminator size | B with |
c. Low generator learning rate | C with |
d. Many shots | E with shots = 8000 |
e. SPSA in generator | F with lr = and ratio = |
Run | Originating Test Set |
---|---|
(a) Divergent | B with |
(b) Oscillatory | B with |
(c) Poor solution quality | B with |
(d) Good solution quality | B with |
Appendix B. Additional Remarks on the Isolation of the Best Run
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Encoding | Form | Number of Qubits | Data Type of Each Item | Algorithms |
---|---|---|---|---|
Multi-register | Any binary string of length m (including integer, fixed point, and floating point numbers). In literature, a common choice for numbers is fixed point. | Quantum arithmetic (adder, multiplier, max,…) | ||
Digital | Any binary string of length m (including integer, fixed point, and floating point numbers). In literature, a common choice for numbers is fixed point. | Grover | ||
Analog | n | Complex numbers satisfying the constraint . | Quantum Fourier Transform (QFT), HHL |
Case | n | k | Generator | Discriminator | Shots | ||
---|---|---|---|---|---|---|---|
a. Baseline | 3 | 1 | 8 | 8 | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 2000 |
b. Big discriminator size | 3 | 1 | 128 | 128 | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 2000 |
c. Low generator learning rate | 3 | 1 | 8 | 8 | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 2000 |
d. Many shots | 3 | 1 | 8 | 8 | Adam, lr = , = 0.7, = 0.99 | Adam, lr = , = 0.7, = 0.99 | 8000 |
e. SPSA in generator | 3 | 1 | 8 | 8 | SPSA, lr = , perturbation = | Adam, lr = , = 0.7, = 0.99 | 2000 |
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Agliardi, G.; Prati, E. Optimal Tuning of Quantum Generative Adversarial Networks for Multivariate Distribution Loading. Quantum Rep. 2022, 4, 75-105. https://doi.org/10.3390/quantum4010006
Agliardi G, Prati E. Optimal Tuning of Quantum Generative Adversarial Networks for Multivariate Distribution Loading. Quantum Reports. 2022; 4(1):75-105. https://doi.org/10.3390/quantum4010006
Chicago/Turabian StyleAgliardi, Gabriele, and Enrico Prati. 2022. "Optimal Tuning of Quantum Generative Adversarial Networks for Multivariate Distribution Loading" Quantum Reports 4, no. 1: 75-105. https://doi.org/10.3390/quantum4010006