Fast and robust quantum state tomography from few basis measurements

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.

Corrected typos and added numerical examples

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Cited by in corpus (6)

• Projected Least-Squares Quantum Process Tomography
• Learning quantum many-body systems from a few copies
• Quantum State Tomography for Matrix Product Density Operators
• Efficient learning of $t$-doped stabilizer states with single-copy measurements
• Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates
• Comparison of confidence regions for quantum state tomography