Abstract
A unitary -design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general . In this paper, we provide quantum circuits that generate exact unitary -designs for any on an arbitrary number of qubits. Our construction is inductive and is of practical use in small systems. We then introduce a -order generalization of randomized benchmarking (-RB) as an application of exact -designs. We particularly study the -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 -RB in one- and two-qubit systems is feasible, and experimentally characterize background noise of a superconducting qubit by the -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.
- Received 25 March 2021
- Accepted 13 August 2021
DOI:https://doi.org/10.1103/PRXQuantum.2.030339
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum pseudorandomness plays a key role in the recent progress of quantum technologies, ranging from proving quantum computational advantage to a practical use of benchmarking noisy quantum devices. In this work, we show how to generate exact quantum pseudorandomness by quantum circuits, solving a long-open problem. We also provide its practical application to an indispensable task in quantum engineering, that is, to experimentally characterizing quantum noise. We experimentally implement the protocol in a superconducting quantum device and demonstrate that the protocol is useful for improving quantum devices.
Quantum pseudorandomness has a strength parameter of randomness: the larger the parameter is, the more random it is. Despite an intensive investigation for a long time, how to generate exact quantum pseudorandomness with an arbitrary strength remained open. We solve the problem from a multidisciplinary approach and provide quantum circuits that generate exact quantum pseudorandomness with any strength. We also show that the construction can be used to experimentally characterize high-order properties of quantum noises. In particular, the noise property that is closely related to quantum error correction, one of the goals of near-future quantum devices, can be experimentally estimated in a concise manner.
Our multidisciplinary approach to quantum pseudorandomness will accelerate the theory of randomness in a quantum regime, and the proposed protocol will substantially contribute to further advances in quantum information technology.
