Title
Markov Chains and Hitting Times for Error Accumulation in Quantum Circuits
Author
Ma, L. (TU Delft Network Architectures and Services)
Sanders, Jaron (Eindhoven University of Technology)
Contributor
Zhao, Qianchuan (editor)
Xia, Li (editor)
Date
2021
Abstract
We study a classical model for the accumulation of errors in multi-qubit quantum computations. By modeling the error process in a quantum computation using two coupled Markov chains, we are able to capture a weak form of time-dependency between errors in the past and future. By subsequently using techniques from the field of discrete probability theory, we calculate the probability that error quantities such as the fidelity and trace distance exceed a threshold analytically. The formulae cover fairly generic error distributions, cover multi-qubit scenarios, and are applicable to the randomized benchmarking protocol. To combat the numerical challenge that may occur when evaluating our expressions, we additionally provide an analytical bound on the error probabilities that is of lower numerical complexity. Besides this, we study a model describing continuous errors accumulating in a single qubit. Finally, taking inspiration from the field of operations research, we illustrate how our expressions can be used to decide how many gates one can apply before too many errors accumulate with high probability, and how one can lower the rate of error accumulation in existing circuits through simulated annealing.
Subject
Error accumulation
Markov chains
Quantum circuits
To reference this document use:
http://resolver.tudelft.nl/uuid:fc0c17be-7409-402e-9070-d4a19f1cb69c
DOI
https://doi.org/10.1007/978-3-030-92511-6_3
Publisher
Springer
Embargo date
2022-01-05
ISBN
9783030925109
Source
Performance Evaluation Methodologies and Tools - 14th EAI International Conference, VALUETOOLS 2021, Proceedings
Event
14th International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2021, 2021-10-30 → 2021-10-31, Virtual, Online
Series
Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST, 1867-8211, 404 LNICST
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Part of collection
Institutional Repository
Document type
conference paper
Rights
© 2021 L. Ma, Jaron Sanders