Source-linked AI summary
Quantum State Tomography with Conditional Generative Adversarial Networks
Shahnawaz Ahmed, Carlos Sánchez Muñoz, Franco Nori, Anton Frisk Kockum
TL;DR
Quantum state tomography must infer quantum states from noisy measurements, often with limited data. This paper adapts conditional generative adversarial networks with quantum-state-specific layers, achieving high-fidelity reconstruction faster and from fewer data points than iterative maximum likelihood, while enabling single-shot reconstruction after pre-training.
Problem
Quantum state tomography seeks to reconstruct quantum states from noisy measurement data while using as few measurements as possible.
Method
The QST-CGAN combines a conditional GAN with custom layers that represent physical density matrices and supports pre-training on simulated states.
Results
The QST-CGAN consistently reconstructs states with higher fidelity than iMLE using ∼100× fewer iterations and ∼10× fewer data points, while pre-training enables high-fidelity single-shot reconstruction.
Takeaways & Limitations
Pre-trained QST-CGANs can provide high-fidelity reconstructions rapidly for states similar to those represented in their training data.
Abstract
from arXiv · showhide
Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two duelling neural networks, a generator and a discriminator, learn multi-modal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity orders of magnitude faster, and from less data, than a standard maximum-likelihood method. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pre-trained on similar quantum states.
N = 32
The QST-CGAN reaches high-fidelity reconstructions with substantially fewer measurement points and can also reconstruct noisy experimental states from limited data.
- N = 32: QST-CGAN performance is evaluated using reconstruction fidelity for a cat state from 1024 displacements on a 32 × 32 grid.The comparison uses 100 runs with randomly initialized QST-CGAN weights and iMLE starting density matrices.
- N = 32: The QST-CGAN starts outperforming iMLE around N = 32 data points and reaches near-unity fidelity with fewer than 100 points.For the same task, iMLE requires approximately 1000 data points to attain good fidelity.
- N = 32: The QST-CGAN reconstructs a Wigner-negative state from noisy experimental data despite substantial state-preparation-and-measurement noise.The reconstruction remains effective using only approximately 15% of the measurement data.
QST-CGAN
The QST-CGAN reconstructs quantum states from noisy measurement data and supports rapid single-shot inference after pre-training. The paper also identifies extensions to broader neural-network architectures and adaptive tomography.
- QST-CGAN: A QST-CGAN reconstructs a Wigner-negative state from 4281 experimental Wigner-function data points measured inside a reliable region.Approximately 600 points suffice to achieve fidelity approximately 0.9 relative to the full reconstruction.
- QST-CGAN: Pre-trained QST-CGANs reconstruct 200 cat states in a single shot, with further iterations improving the fidelity.The states have |α| ∈[1, 3] and up to six coherent states in superposition.
- QST-CGAN: The pre-trained network achieves a high average fidelity of approximately 0.98 for different cat states.Further improvement is difficult with only a few iterations but becomes clear after tens of iterations.
- QST-CGAN: Pre-training yields a reconstruction approximately four orders of magnitude faster than the iterative reconstruction benchmark.The comparison is made with the reconstruction procedure shown in Fig. 3(a).
- QST-CGAN: The custom layers could be incorporated into other neural networks, including Transformers, for QST and other quantum-information applications.The authors also propose potential uses for denoising and adaptive tomography.