Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates II: Single-Copy Measurements

TL;DR

This paper introduces an efficient algorithm for learning certain quantum states using only single-copy measurements, reducing the need for complex entangled measurements across multiple copies.

Contribution

It presents a novel, efficient learning algorithm for quantum states with few non-Clifford gates that relies solely on single-copy measurements, unlike previous methods.

Findings

Achieves polynomial runtime in key parameters

Uses only single-copy measurements, simplifying experimental requirements

Matches the efficiency of prior entangled-measurement algorithms

Abstract

Recent work has shown that $n$-qubit quantum states output by circuits with at most $t$ single-qubit non-Clifford gates can be learned to trace distance $\epsilon$ using $\mathsf{poly}(n,2^t,1/\epsilon)$ time and samples. All prior algorithms achieving this runtime use entangled measurements across two copies of the input state. In this work, we give a similarly efficient algorithm that learns the same class of states using only single-copy measurements.