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Generative Adversarial Networks for Resource State Generation

Shahbaz Shaik, Sourav Chatterjee, Sayantan Pramanik, Indranil Chakrabarty

TL;DR

A physics-informed Generative Adversarial Network framework that recasts quantum resource-state generation as an inverse-design task and embeds task-specific utility functions into training, establishing adversarial learning as a lightweight yet effective method for constraint-driven quantum-state discovery.

Abstract

We introduce a physics-informed Generative Adversarial Network framework that recasts quantum resource-state generation as an inverse-design task. By embedding task-specific utility functions into training, the model learns to generate valid two-qubit states optimized for teleportation and entanglement broadcasting. Comparing decomposition-based and direct-generation architectures reveals that structural enforcement of Hermiticity, trace-one, and positivity yields higher fidelity and training stability than loss-only approaches. The framework reproduces theoretical resource boundaries for Werner-like and Bell-diagonal states with fidelities exceeding ~98%, establishing adversarial learning as a lightweight yet effective method for constraint-driven quantum-state discovery. This approach provides a scalable foundation for automated design of tailored quantum resources for information-processing applications, exemplified with teleportation and broadcasting of entanglement, and it opens up the possibility of using such states in efficient quantum network design.

Generative Adversarial Networks for Resource State Generation

TL;DR

A physics-informed Generative Adversarial Network framework that recasts quantum resource-state generation as an inverse-design task and embeds task-specific utility functions into training, establishing adversarial learning as a lightweight yet effective method for constraint-driven quantum-state discovery.

Abstract

We introduce a physics-informed Generative Adversarial Network framework that recasts quantum resource-state generation as an inverse-design task. By embedding task-specific utility functions into training, the model learns to generate valid two-qubit states optimized for teleportation and entanglement broadcasting. Comparing decomposition-based and direct-generation architectures reveals that structural enforcement of Hermiticity, trace-one, and positivity yields higher fidelity and training stability than loss-only approaches. The framework reproduces theoretical resource boundaries for Werner-like and Bell-diagonal states with fidelities exceeding ~98%, establishing adversarial learning as a lightweight yet effective method for constraint-driven quantum-state discovery. This approach provides a scalable foundation for automated design of tailored quantum resources for information-processing applications, exemplified with teleportation and broadcasting of entanglement, and it opens up the possibility of using such states in efficient quantum network design.
Paper Structure (42 sections, 33 equations, 7 figures, 7 tables)

This paper contains 42 sections, 33 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Quantum Resource States
  3. Resource States for Broadcasting
  4. Local Cloning.
  5. Nonlocal Cloning.
  6. Entanglement Detection.
  7. Resource States for Teleportation
  8. Overview of GAN
  9. Conditional GANs and Quantum Constraints
  10. Generator Architectures
  11. Adversarial Training
  12. Loss Functions and Evaluation Metrics
  13. Loss Functions:
  14. Evaluation Metrics:
  15. Generation of Resource States through CGAN
  16. ...and 27 more sections

Figures (7)

  • Figure 1: Physics-informed CGAN framework used in this work. (a) Training: the generator $G$ maps latent noise $z$ to $\rho_{\text{gen}}$. The discriminator $D$ compares $\rho_{\text{gen}}$ with training samples $\rho_{\text{train}}$, producing the adversarial term $L_{\text{adv}}$. In parallel, a physics module computes constraint and utility terms (trace-one, PSD, and task utility), yielding the weighted objective in Eq. \ref{['eq:generator_loss']}. The discriminator and generator are updated alternately. (b) Inference: after training, samples $z$ are mapped by the trained generator $G^*$ to $\rho_{\text{resource}}$, producing candidate quantum resource states.
  • Figure 2: Accuracy comparison across generator architectures (training size = 500). (1) Bell-diagonal states; (2) Werner-like states. Subplots: (a) local broadcasting, (b) non-local broadcasting, (c) teleportation.
  • Figure 3: Average cross-set fidelity between generated and training states (training size $=1000$). (1) Bell-diagonal states; (2) Werner-like states. Subplots: (a) local broadcasting, (b) non-local broadcasting, (c) teleportation. The dashed red line indicates the ideal benchmark—the average fidelity of the training data with itself.
  • Figure 4: Fréchet Inception Distance (FID) between generated and training state distributions (training size = 2000). (1) Bell-diagonal states; (2) Werner-like states. Subplots: (a) local broadcasting, (b) non-local broadcasting, (c) teleportation. Lower FID indicates closer distributional match.
  • Figure 5: Generated Bell-diagonal states plotted in the parameter space $(c_1, c_2, c_3)$. Subplots: (1) local broadcasting, (2) non-local broadcasting, (3) teleportation. The brown wireframe outlines the octahedron of inseparable (entangled) Bell-diagonal states, contained within the larger tetrahedron of all valid Bell-diagonal states. The teal shaded subregions indicate the theoretical parameter ranges where states are useful for each task. Green dots represent generated states meeting the resource criterion; red dots represent states not meeting it. All generated states are from models trained with dataset size 2000.
  • ...and 2 more figures