Fast and robust quantum state tomography from few basis measurements

TL;DR

This paper introduces an online quantum state tomography algorithm that optimizes resource use, including state copies, measurement settings, and classical processing, achieving provably optimal performance and potential quantum speedup.

Contribution

The work presents the first provably optimal online tomography protocol in terms of rank, dimension, and resource efficiency, with significant reductions in classical runtime.

Findings

Achieves optimal resource performance in quantum state tomography.

Reduces classical runtime significantly compared to existing methods.

Potential for quantum speedup when executed on a quantum computer.

Abstract

Quantum state tomography is a powerful, but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially and numerical experiments demonstrate a favorable comparison with other state-of-the-art techniques. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.