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arXiv · 2102.12617

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
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Abstract

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 for the first time 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 $t$-th 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 new 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 the realization of QEC.

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Yoshifumi Nakata, Da Zhao, Takayuki Okuda, Eiichi Bannai, Yasunari Suzuki, Shiro Tamiya, Kentaro Heya, Zhiguang Yan, Kun Zuo, Shuhei Tamate, Yutaka Tabuchi, Yasunobu Nakamura. 2021-02-25. Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking. https://doi.org/10.1103/prxquantum.2.030339

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