Quantum GANs – Generative Adversarial Networks: Quantum Approaches to Data Generation

Table of Contents

1. Introduction
2. Classical GANs: A Brief Overview
3. Motivation for Quantum GANs
4. Structure of a Quantum GAN (QGAN)
5. Quantum Generator: Circuit-Based Design
6. Quantum Discriminator Options
7. Hybrid Classical-Quantum Architectures
8. Objective Functions and Training
9. Training QGANs on NISQ Devices
10. Gradient Estimation in QGANs
11. QGAN with Real-Valued Data
12. QGANs for Image and State Generation
13. QGANs vs Classical GANs
14. Implementation with PennyLane
15. Implementation with Qiskit
16. Quantum Wasserstein GANs (QWGAN)
17. Challenges in QGAN Training
18. Experimental Realizations and Research
19. Applications of QGANs
20. Conclusion

1. Introduction

Quantum Generative Adversarial Networks (QGANs) are quantum analogs of classical GANs, designed to generate synthetic data through a competitive training process between two models: a generator and a discriminator.

2. Classical GANs: A Brief Overview

• Generator creates fake samples
• Discriminator classifies real vs fake
• Minimax training:

3. Motivation for Quantum GANs

• Leverage high-dimensional quantum state spaces for generative modeling
• Potential speedups in learning complex distributions
• Natural fit for quantum data generation and simulation

4. Structure of a Quantum GAN (QGAN)

• Quantum Generator: Variational quantum circuit
• Discriminator: Classical or quantum model
• Output: Distribution of quantum or classical samples

5. Quantum Generator: Circuit-Based Design

• Input: random noise vector \( z \)
• Output: quantum state or measured bitstring
• Parameterized quantum gates (e.g., RY, RX, entangling gates)

6. Quantum Discriminator Options

• Classical: Neural network acting on measurement outcomes
• Quantum: Circuit with learnable gates and projective measurements

7. Hybrid Classical-Quantum Architectures

• Classical noise sampled → encoded into quantum state → generator circuit → measured → classical discriminator
• Gradient flows through hybrid backpropagation

8. Objective Functions and Training

• Cross-entropy or Wasserstein loss
• Optimize using classical optimizers (Adam, COBYLA)
• Training alternates between generator and discriminator

9. Training QGANs on NISQ Devices

• Keep circuit depth minimal
• Use measurement error mitigation
• Batch training with low-shot fidelity

10. Gradient Estimation in QGANs

• Use parameter-shift rule:
  \[
  rac{\partial}{\partial heta} \langle O
  angle = rac{f( heta + \pi/2) – f( heta – \pi/2)}{2}
  \]

11. QGAN with Real-Valued Data

• Encode real values into quantum rotations
• Decode via expectation value mapping

12. QGANs for Image and State Generation

• Low-resolution image generation (e.g., 4×4)
• Quantum state preparation for simulation

13. QGANs vs Classical GANs

14. Implementation with PennyLane

import pennylane as qml
@qml.qnode(dev)
def generator_circuit(z, weights):
    qml.AngleEmbedding(z, wires=[0, 1])
    qml.StronglyEntanglingLayers(weights, wires=[0, 1])
    return qml.expval(qml.PauliZ(0))

15. Implementation with Qiskit

• Use Aer simulator or real backend
• Construct generator and discriminator using QuantumCircuit
• Optimize with qiskit.algorithms.optimizers

16. Quantum Wasserstein GANs (QWGAN)

• Use Wasserstein loss:

• Lipschitz regularization required (e.g., gradient penalty)

17. Challenges in QGAN Training

• Barren plateaus in generator circuit
• Quantum noise and decoherence
• Mode collapse and instability

18. Experimental Realizations and Research

• IBM: Experimental QGAN in 2018
• Numerous simulations in PennyLane and Cirq
• Active area in QML research

19. Applications of QGANs

• Synthetic data generation
• Quantum chemistry state synthesis
• Quantum data compression
• Image enhancement in medical or quantum imaging

20. Conclusion

Quantum GANs bring the power of adversarial learning into the quantum domain. While limited by current hardware, they demonstrate how quantum circuits can learn and synthesize complex distributions, laying the foundation for quantum-native generative AI.