Sample Optimal and Memory Efficient Quantum State Tomography

TL;DR

This paper introduces a quantum state tomography algorithm that achieves optimal sample complexity while significantly reducing memory requirements, enabling more practical implementation with streaming data access.

Contribution

It presents a novel memory-efficient quantum state tomography method based on unitary Schur sampling, maintaining sample optimality with streaming sample access.

Findings

Achieves sample-optimal quantum state tomography with reduced memory usage.

Uses unitary Schur sampling for streaming data processing.

Demonstrates practical feasibility of memory-efficient quantum tomography.

Abstract

Quantum state tomography is the fundamental physical task of learning a complete classical description of an unknown state of a quantum system given coherent access to many identical samples of it. The complexity of this task is commonly characterised by its sample-complexity: the minimal number of samples needed to reach a certain target precision of the description. While the sample complexity of quantum state tomography has been well studied, the memory complexity has not been investigated in depth. Indeed, the bottleneck in the implementation of na\"ive sample-optimal quantum state tomography is its massive quantum memory requirements. In this work, we propose and analyse a quantum state tomography algorithm which retains sample-optimality but is also memory-efficient. Our work is built on a form of unitary Schur sampling and only requires streaming access to the samples.