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

• URL: http://arxiv.org/abs/2308.07014v3
• Date: Tue, 6 Feb 2024 04:54:52 GMT
• Title: Efficient learning of $t$-doped stabilizer states with single-copy measurements
• Authors: Nai-Hui Chia, Ching-Yi Lai, Han-Hsuan Lin
• Abstract summary: 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.
• Score: 7.5275459858139175
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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