Quantum Circuits for Exact Unitary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>t</mml:mi></mml:math> -Designs and Applications to Higher-Order Randomized Benchmarking

A unitary t-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general t. In this paper, we provide circuits that generate exact t-designs any t on an arbitrary number of qubits. Our construction inductive practical use small systems. We then introduce tth-order generalization randomized benchmarking (t-RB) as application 2t-designs. particularly study the 2-RB detail show it reveals self-adjointness noise, metric related to feasibility error correction (QEC). numerically demonstrate one- two-qubit systems feasible, experimentally characterize background noise superconducting qubit by 2-RB. It shown from experiment interactions with adjacent qubits induce may result obstacle toward realization QEC.3 MoreReceived 25 March 2021Accepted 13 August 2021DOI:https://doi.org/10.1103/PRXQuantum.2.030339Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum benchmarkingQuantum gatesQuantum protocolsQuantum Information