Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking

• URL: http://arxiv.org/abs/2011.00007v2
• Date: Mon, 1 Feb 2021 19:56:46 GMT
• Title: Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking
• Authors: Jahan Claes, Eleanor Rieffel, Zhihui Wang
• Abstract summary: We extend the original character RB derivation to explicitly treat non-multiplicity-free groups. We develop a new leakage RB protocol that applies to more general groups of gates. This example provides one of the few examples of a scalable non-Clifford RB protocol.
• Score: 14.315027895958304
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Randomized benchmarking (RB) is a powerful method for determining the error rate of experimental quantum gates. Traditional RB, however, is restricted to gatesets, such as the Clifford group, that form a unitary 2-design. The recently introduced character RB can benchmark more general gates using techniques from representation theory; up to now, however, this method has only been applied to "multiplicity-free" groups, a mathematical restriction on these groups. In this paper, we extend the original character RB derivation to explicitly treat non-multiplicity-free groups, and derive several applications. First, we derive a rigorous version of the recently introduced subspace RB, which seeks to characterize a set of one- and two-qubit gates that are symmetric under SWAP. Second, we develop a new leakage RB protocol that applies to more general groups of gates. Finally, we derive a scalable RB protocol for the matchgate group, a group that like the Clifford group is non-universal but becomes universal with the addition of one additional gate. This example provides one of the few examples of a scalable non-Clifford RB protocol. In all three cases, compared to existing theories, our method requires similar resources, but either provides a more accurate estimate of gate fidelity, or applies to a more general group of gates. In conclusion, we discuss the potential, and challenges, of using non-multiplicity-free character RB to develop new classes of scalable RB protocols and methods of characterizing specific gates.

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