Quantum Circuits for Exact Unitary t -Designs and Applications to Higher-Order Randomized Benchmarking
Yoshifumi Nakata, Da Zhao, Takayuki Okuda, Eiichi Bannai, Yasunari Suzuki, Shiro Tamiya, Kentaro Heya, Zhiguang Yan, Kun Zuo, Shuhei Tamate, Yutaka Tabuchi, Yasunobu Nakamura · PRX Quantum · 2021
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 quantum circuits that generate exact unitary t-designs for any t on an arbitrary number of qubits.Our construction is inductive and is of practical use in small systems.We then introduce a tth-order generalization of randomized benchmarking (t-RB) as an application of exact 2t-designs.We particularly study the 2-RB in detail and show that it reveals self-adjointness of quantum noise, a metric related to the feasibility of quantum error correction (QEC).We numerically demonstrate that the 2-RB in one-and two-qubit systems is feasible, and experimentally characterize background noise of a superconducting qubit by the 2-RB.It is shown from the experiment that interactions with adjacent qubits induce the noise that may result in an obstacle toward a realization of QEC.