Scalable Quantum Tomography with Fidelity Estimation

TL;DR

This paper introduces a scalable quantum tomography method for pure qudit systems that uses random measurements and generative learning, with fidelity estimation to ensure reliability, showing efficiency and robustness in simulations.

Contribution

It presents a novel, scalable quantum tomography scheme combining random measurements, generative learning, and fidelity estimation, validated through theoretical proof and numerical experiments.

Findings

Number of replicas grows polynomially with system size

Scheme demonstrates high efficiency and robustness in simulations

Achieves high scalability for practical quantum state tomography

Abstract

We propose a quantum tomography scheme for pure qudit systems which adopts random base measurements and generative learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic states. We prove the validity of the scheme theoretically, and we perform numerically simulated experiments on several target states including three typical quantum information states and randomly initiated states, demonstrating its efficiency and robustness. The number of replicas required by a certain convergence criterion grows in the manner of low-degree polynomial when the system scales, thus the scheme achieves high scalability that is crucial for practical quantum state tomography.