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Main Authors:	Tanggara, Andrew, Gu, Mile, Bharti, Kishor
Format:	Preprint
Published:	2024
Subjects:	Quantum Physics
Online Access:	https://arxiv.org/abs/2405.17567
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author	Tanggara, Andrew Gu, Mile Bharti, Kishor
author_facet	Tanggara, Andrew Gu, Mile Bharti, Kishor
contents	Quantum error-correcting code (QECC) is the central ingredient in fault-tolerant quantum information processing. An emerging paradigm of dynamical QECC shows that one can robustly encode logical quantum information both temporally and spatially in a more resource-efficient manner than traditional QECCs. Nevertheless, an overarching theory of how dynamical QECCs achieve fault-tolerance is lacking. In this work, we bridge this gap by proposing a unified spatio-temporal QECC framework called the ``strategic code'' built around an ``interrogator'' device which sequentially measures and evolves the spatial QECC in an adaptive manner based on the ``quantum combs'' formalism, a generalization of the channel-state duality. The strategic code covers all existing dynamical and static QECC, as well as all physically plausible QECCs to be discovered in the future, including those that involve adaptivity in its operational dynamics. Within this framework, we show an algebraic and an information-theoretic necessary and sufficient error-correction conditions for a strategic code, which consider spatially and temporally correlated errors. These conditions include the analogous known static QECC conditions as a special case. Lastly, we also propose an optimization-theoretic approach to obtain an approximate strategic code adapting to a correlated error.
format	Preprint
id	arxiv_https___arxiv_org_abs_2405_17567
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Strategic Code: A Unified Spatio-Temporal Framework for Quantum Error-Correction Tanggara, Andrew Gu, Mile Bharti, Kishor Quantum Physics Quantum error-correcting code (QECC) is the central ingredient in fault-tolerant quantum information processing. An emerging paradigm of dynamical QECC shows that one can robustly encode logical quantum information both temporally and spatially in a more resource-efficient manner than traditional QECCs. Nevertheless, an overarching theory of how dynamical QECCs achieve fault-tolerance is lacking. In this work, we bridge this gap by proposing a unified spatio-temporal QECC framework called the ``strategic code'' built around an ``interrogator'' device which sequentially measures and evolves the spatial QECC in an adaptive manner based on the ``quantum combs'' formalism, a generalization of the channel-state duality. The strategic code covers all existing dynamical and static QECC, as well as all physically plausible QECCs to be discovered in the future, including those that involve adaptivity in its operational dynamics. Within this framework, we show an algebraic and an information-theoretic necessary and sufficient error-correction conditions for a strategic code, which consider spatially and temporally correlated errors. These conditions include the analogous known static QECC conditions as a special case. Lastly, we also propose an optimization-theoretic approach to obtain an approximate strategic code adapting to a correlated error.
title	Strategic Code: A Unified Spatio-Temporal Framework for Quantum Error-Correction
topic	Quantum Physics
url	https://arxiv.org/abs/2405.17567

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