Efficient learning of $t$-doped stabilizer states with single-copy measurements

TL;DR

This paper presents a quantum algorithm that efficiently learns $t$-doped stabilizer states generated by Clifford circuits with up to $O( ext{log} n)$ non-Clifford gates using only single-copy measurements, bridging a gap in quantum state learning methods.

Contribution

The work introduces the first efficient algorithm for learning certain quantum states with only single-copy measurements, expanding practical quantum state learning capabilities.

Findings

Efficient learning of $t$-doped stabilizer states with single-copy measurements.

Algorithm works for states with up to $O( ext{log} n)$ non-Clifford gates.

Fills a gap between previous positive and negative results in quantum state learning.

Abstract

One of the primary objectives in the field of quantum state learning is to develop algorithms that are time-efficient for learning states generated from quantum circuits. Earlier investigations have demonstrated time-efficient algorithms for states generated from Clifford circuits with at most $\log(n)$ non-Clifford gates. However, these algorithms necessitate multi-copy measurements, posing implementation challenges in the near term due to the requisite quantum memory. On the contrary, using solely single-qubit measurements in the computational basis is insufficient in learning even the output distribution of a Clifford circuit with one additional $T$ gate under reasonable post-quantum cryptographic assumptions. In this work, we introduce an efficient quantum algorithm that employs only nonadaptive single-copy measurement to learn states produced by Clifford circuits with a maximum of $O(\log n)$ non-Clifford gates, filling a gap between the previous positive and negative results.