Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
| Autor: | Nakata, Yoshifumi, Zhao, Da, Okuda, Takayuki, Bannai, Eiichi, Suzuki, Yasunari, Tamiya, Shiro, Heya, Kentaro, Yan, Zhiguang, Zuo, Kun, Tamate, Shuhei, Tabuchi, Yutaka, Nakamura, Yasunobu |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | PRX Quantum 2, 030339 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PRXQuantum.2.030339 |
| Popis: | 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. Comment: 26 pages + 4 pages of appendices, and 10 figures. v2: minor update. v3: published version |
| Databáze: | arXiv |
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