Extracting error thresholds through the framework of approximate quantum error correction condition

The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability and the decoder-dependent error threshold which assesses if the logical error rate diminishes with system size. Here we un...

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Main Authors: Yuanchen Zhao, Dong E. Liu
Format: Article
Language:English
Published: American Physical Society 2024-12-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.6.043258
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author Yuanchen Zhao
Dong E. Liu
author_facet Yuanchen Zhao
Dong E. Liu
author_sort Yuanchen Zhao
collection DOAJ
description The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability and the decoder-dependent error threshold which assesses if the logical error rate diminishes with system size. Here we unravel their relations and propose a unified framework to extract an intrinsic error threshold from the approximate QEC condition, which could upper bound other decoder-dependent error thresholds. Our proof establishes that relative entropy, effectively measuring deviations from exact QEC conditions, serves as the order parameter delineating the transition from asymptotic recoverability to unrecoverability. Consequently, we establish a unified framework for determining the error threshold across both exact and approximate QEC codes, addressing errors originating from noise channels as well as those from code space imperfections. This result sharpens our comprehension of error thresholds across diverse QEC codes and error models.
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series Physical Review Research
spelling doaj-art-867a85f56a034d71b32b9693b21c69642024-12-11T16:24:25ZengAmerican Physical SocietyPhysical Review Research2643-15642024-12-016404325810.1103/PhysRevResearch.6.043258Extracting error thresholds through the framework of approximate quantum error correction conditionYuanchen ZhaoDong E. LiuThe robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability and the decoder-dependent error threshold which assesses if the logical error rate diminishes with system size. Here we unravel their relations and propose a unified framework to extract an intrinsic error threshold from the approximate QEC condition, which could upper bound other decoder-dependent error thresholds. Our proof establishes that relative entropy, effectively measuring deviations from exact QEC conditions, serves as the order parameter delineating the transition from asymptotic recoverability to unrecoverability. Consequently, we establish a unified framework for determining the error threshold across both exact and approximate QEC codes, addressing errors originating from noise channels as well as those from code space imperfections. This result sharpens our comprehension of error thresholds across diverse QEC codes and error models.http://doi.org/10.1103/PhysRevResearch.6.043258
spellingShingle Yuanchen Zhao
Dong E. Liu
Extracting error thresholds through the framework of approximate quantum error correction condition
Physical Review Research
title Extracting error thresholds through the framework of approximate quantum error correction condition
title_full Extracting error thresholds through the framework of approximate quantum error correction condition
title_fullStr Extracting error thresholds through the framework of approximate quantum error correction condition
title_full_unstemmed Extracting error thresholds through the framework of approximate quantum error correction condition
title_short Extracting error thresholds through the framework of approximate quantum error correction condition
title_sort extracting error thresholds through the framework of approximate quantum error correction condition
url http://doi.org/10.1103/PhysRevResearch.6.043258
work_keys_str_mv AT yuanchenzhao extractingerrorthresholdsthroughtheframeworkofapproximatequantumerrorcorrectioncondition
AT dongeliu extractingerrorthresholdsthroughtheframeworkofapproximatequantumerrorcorrectioncondition