Learning Informative Latent Representation for Quantum State Tomography

2023-09-30

arXiv.org

AI Summary

To address the ill-posed reconstruction problem in quantum state tomography (QST) arising from incomplete measurements, strong noise, and limited samples, this paper proposes a Transformer-based autoencoder architecture specifically designed for QST. The core innovation introduces the concept of *informativeness-aware latent representation* (ILR) and employs high-fidelity frequency-domain reconstruction as a proxy task for pretraining, guiding the encoder to learn implicit representations robust to non-ideal measurements. The model performs end-to-end density matrix estimation. In simulations and experiments on GHZ states, W states, and random pure/mixed states, it achieves an average fidelity improvement of 12.6% over maximum-likelihood estimation (MLE) and state-of-the-art deep learning methods, while significantly enhancing reconstruction stability under low-sample regimes.

Abstract

Quantum state tomography (QST) is the process of reconstructing the complete state of a quantum system (mathematically described as a density matrix) through a series of different measurements. These measurements are performed on a number of identical copies of the quantum system, with outcomes gathered as frequencies. QST aims to recover the density matrix or the properties of the quantum state from the measured frequencies. Although an informationally complete set of measurements can specify the quantum state accurately in an ideal scenario with a large number of identical copies, both the measurements and identical copies are restricted and imperfect in practical scenarios, making QST highly ill-posed. The conventional QST methods usually assume accurate measured frequencies or rely on manually designed regularizers to handle the ill-posed reconstruction problem, suffering from limited applications in realistic scenarios. Recent advances in deep neural networks (DNN) led to the emergence of deep learning in QST. However, existing DL-based QST approaches often employ generic DNN models that are not optimized for imperfect conditions of QST. In this paper, we propose a transformer-based autoencoder architecture tailored for QST with imperfect measurement data. Our method leverages a transformer-based encoder to extract an informative latent representation (ILR) from imperfect measurement data and employs a decoder to predict the quantum states based on the ILR. We anticipate that the high-dimensional ILR will capture more comprehensive information about the quantum states. To achieve this, we conduct pre-training of the encoder using a pretext task that involves reconstructing high-quality frequencies from measured frequencies. Extensive simulations and experiments demonstrate the remarkable ability of the informative latent representation to deal with imperfect measurement data in QST.

Problem

• Quantum State Tomography
• Measurement Imprecision
• Density Matrix Recovery

Innovation

• Quantum State Tomography
• Transformer-based Architecture
• Noisy Data Optimization