Universal noise-precision relations in variational hybrid quantum-classical algorithms

• Item type: SIG Technical Reports(1)
• 公開日: 2021-06-24
• タイトル: Universal noise-precision relations in variational hybrid quantum-classical algorithms
• タイトル / 言語: en
• タイトル: Universal noise-precision relations in variational hybrid quantum-classical algorithms
• 言語: eng
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: Center for Quantum Information and Quantum Biology, International Advanced Research Institute, Osaka University
• 著者所属: Center for Quantum Information and Quantum Biology, International Advanced Research Institute, Osaka University／Graduate School of Engineering Science, Osaka University／JST, PRESTO
• 著者所属: Center for Quantum Information and Quantum Biology, International Advanced Research Institute, Osaka University／Graduate School of Engineering Science, Osaka University／RIKEN Center for Quantum Computing (RQC)
• 著者所属(英): en
• 著者所属(英): Center for Quantum Information and Quantum Biology, International Advanced Research Institute, Osaka University
• 著者所属(英): en
• 著者所属(英): Center for Quantum Information and Quantum Biology, International Advanced Research Institute, Osaka University / Graduate School of Engineering Science, Osaka University / JST, PRESTO
• 著者所属(英): en
• 著者所属(英): Center for Quantum Information and Quantum Biology, International Advanced Research Institute, Osaka University / Graduate School of Engineering Science, Osaka University / RIKEN Center for Quantum Computing (RQC)
• 著者名: Kosuke, Ito; Wataru, Mizukami; Keisuke, Fujii
• 著者名(英): Kosuke, Ito; Wataru, Mizukami; Keisuke, Fujii
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Variational quantum algorithms (VQAs) are expected to become a practical application of near-term noisy quantum computers. Although the effect of the noise crucially determines whether a VQA works or not, the heuristic nature of VQAs makes it difficult to establish analytic theories. Analytic estimations of the impact of the noise are urgent for searching for quantum advantages, as numerical simulations of noisy quantum computers on classical computers are heavy and quite limited to small scale problems. In this work, we establish an analytic estimation of the error in the cost function of VQAs due to the noise. The estimation is applicable to any typical VQAs under the Gaussian noise, which is equivalent to a class of stochastic noise models. Notably, the depolarizing noise is included in this model. As a result, we obtain an estimation of the noise level to guarantee a required precision. Our formulae show how the Hessian of the cost function affects the sensitivity to the noise. This insight implies a trade-off relation between the trainability and the noise resilience of the cost function. As a highlight of the applications of the formula, we propose a quantum error mitigation method which is different from the extrapolation and the probabilistic error cancellation.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Variational quantum algorithms (VQAs) are expected to become a practical application of near-term noisy quantum computers. Although the effect of the noise crucially determines whether a VQA works or not, the heuristic nature of VQAs makes it difficult to establish analytic theories. Analytic estimations of the impact of the noise are urgent for searching for quantum advantages, as numerical simulations of noisy quantum computers on classical computers are heavy and quite limited to small scale problems. In this work, we establish an analytic estimation of the error in the cost function of VQAs due to the noise. The estimation is applicable to any typical VQAs under the Gaussian noise, which is equivalent to a class of stochastic noise models. Notably, the depolarizing noise is included in this model. As a result, we obtain an estimation of the noise level to guarantee a required precision. Our formulae show how the Hessian of the cost function affects the sensitivity to the noise. This insight implies a trade-off relation between the trainability and the noise resilience of the cost function. As a highlight of the applications of the formula, we propose a quantum error mitigation method which is different from the extrapolation and the probabilistic error cancellation.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA12894105
• 書誌情報: 量子ソフトウェア（QS）; 巻 2021-QS-3, 号 16, p. 1-8, 発行日 2021-06-24
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2435-6492
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会