Sample-optimal and memory-efficient quantum state tomography
Phys. Rev. A 113, 052446 – Published 21 May, 2026
DOI: https://doi.org/10.1103/z93d-tw3m
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 characterized 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 naïve sample-optimal quantum state tomography is its massive quantum memory requirements. In this work, we propose and analyze 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.
