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 (ρ,δ)-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state ρ and its distance δ to the ideal state ρ. This predicate (ρ,δ) 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 (ρ,δ)-diamond norm metric. Furthermore, 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.
Tao, Runzhou, et al. "Gleipnir: toward practical error analysis for Quantum programs." Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Jun. 2021. https://doi.org/10.1145/3453483.3454029
Tao, Runzhou, Shi, Yunong, Yao, Jianan, et al., "Gleipnir: toward practical error analysis for Quantum programs," Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation (2021), https://doi.org/10.1145/3453483.3454029
@conference{osti_1865582,
author = {Tao, Runzhou and Shi, Yunong and Yao, Jianan and Hui, John and Chong, Frederic T. and Gu, Ronghui},
title = {Gleipnir: toward practical error analysis for Quantum programs},
annote = {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 (ρ,δ)-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state ρ and its distance δ to the ideal state ρ. This predicate (ρ,δ) 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 (ρ,δ)-diamond norm metric. Furthermore, 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.},
doi = {10.1145/3453483.3454029},
url = {https://www.osti.gov/biblio/1865582},
journal = {Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation},
place = {United States},
organization = {Univ. of Chicago, IL (United States)},
year = {2021},
month = {06}}
USDOE Office of Science (SC), Engineering & Technology
DOE Contract Number:
SC0020289
OSTI ID:
1865582
Journal Information:
Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Journal Name: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation
Murali, Prakash; Baker, Jonathan M.; Javadi-Abhari, Ali
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