Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)

• URL: http://arxiv.org/abs/2104.06349v2
• Date: Mon, 19 Apr 2021 18:29:00 GMT
• Title: Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)
• Authors: Runzhou Tao, Yunong Shi, Jianan Yao, John Hui, Frederic T. Chong, Ronghui Gu
• Abstract summary: We present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the $(hatrho,delta)$-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits.
• Score: 6.349076549152475
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the $(\hat\rho,\delta)$-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state $\hat\rho$ and its distance $\delta$ to the ideal state $\rho$. This predicate $(\hat\rho,\delta)$ can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the $(\hat\rho,\delta)$-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations.

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