2018/03/30 by Atsushi Shimbo, Shimbo, Atsushi, Akihito Soeda +3
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1803.11414
17 pages with 9 pages of supplemental material
arxiv created 2018/03/30 · openalex publication_date 2018/03/30 · arxiv updated 2018/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study equivalence determination of unitary operations, a task analogous to quantum state discrimination. The candidate states are replaced by unitary operations given as a quantum sample, i.e., a black-box device implementing a candidate unitary operation, and the discrimination target becomes another black-box. The task is an instance of higher-order quantum computation with the black-boxes as input. The optimal error probability is calculated by semidefinite programs. Arbitrary quantum operations applied between the black-boxes in a general protocol provide advantages over protocols restricted to parallelized use of the black-boxes. We provide a numerical proof of such an advantage. In contrast, a parallelized scheme is analytically shown to exhibit the optimal performance of general schemes for a particular number of quantum samples of the candidates. We find examples of finite-sample equivalence determination that achieve the same performance as when a classical description of the candidates are provided, although an exact classical description cannot be obtained from finite quantum samples.