Identification of a reversible quantum gate: assessing the resources

TL;DR

This paper investigates the resources and strategies required to identify reversible quantum gates, establishing bounds on query complexity and introducing generalized t-designs to unify various discrimination approaches.

Contribution

It introduces generalized t-designs for quantum gate discrimination and proves parallel strategies suffice for unambiguous identification with minimal queries.

Findings

Parallel strategies are sufficient for unambiguous gate identification.

Explicit expression for maximum correct identification probability for generalized t-designs.

No performance gap between deterministic and probabilistic strategies for gates in t-designs.

Abstract

We assess the resources needed to identify a reversible quantum gate among a finite set of alternatives, including in our analysis both deterministic and probabilistic strategies. Among the probabilistic strategies we consider unambiguous gate discrimination, where errors are not tolerated but inconclusive outcomes are allowed, and we prove that parallel strategies are sufficient to unambiguously identify the unknown gate with minimum number of queries. This result is used to provide upper and lower bounds on the query complexity and on the minimum ancilla dimension. In addition, we introduce the notion of generalized t-designs, which includes unitary t-designs and group representations as special cases. For gates forming a generalized t-design we give an explicit expression for the maximum probability of correct gate identification and we prove that there is no gap between the performances of deterministic strategies an those of probabilistic strategies. Hence, evaluating of the query complexity of perfect deterministic discrimination is reduced to the easier problem of evaluating the query complexity of unambiguous discrimination. Finally, we consider discrimination strategies where the use of ancillas is forbidden, providing upper bounds on the number of additional queries needed to make up for the lack of entanglement with the ancillas.