Fault-Tolerant Gates on Hypergraph Product Codes

Quantum computers have the capacity to change the landscape of computing. To make these devices robust to experimental imperfections, we require some form of quantum error correction. Current approaches focus on topological codes, as they appear to be in the realm of experimental capabilities. These...

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Autores principales:	Anirudh Krishna, David Poulin
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/98cb9ab45c97449798039b0b8c8275c3
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id	oai:doaj.org-article:98cb9ab45c97449798039b0b8c8275c3
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spelling	oai:doaj.org-article:98cb9ab45c97449798039b0b8c8275c32021-12-02T13:58:51ZFault-Tolerant Gates on Hypergraph Product Codes10.1103/PhysRevX.11.0110232160-3308https://doaj.org/article/98cb9ab45c97449798039b0b8c8275c32021-02-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.011023http://doi.org/10.1103/PhysRevX.11.011023https://doaj.org/toc/2160-3308Quantum computers have the capacity to change the landscape of computing. To make these devices robust to experimental imperfections, we require some form of quantum error correction. Current approaches focus on topological codes, as they appear to be in the realm of experimental capabilities. These techniques will likely lead to the first proof of principle of fault tolerance in the next 5 yr. In the long run, however, these approaches require a very large number of physical qubits to construct a fault-tolerant quantum circuit that can run interesting algorithms. As an alternative, it is proposed that quantum low-density parity-check (LDPC) codes could serve as an architecture that circumvents this problem. The best candidate class of quantum LDPC codes were discovered by Tillich and Zémor and are called hypergraph product codes. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold. With these features, they asymptotically offer a smaller overhead compared to topological codes. Here, we demonstrate how to perform Clifford gates on this class of codes using code deformation. To this end, we introduce wormhole defects on hypergraph product codes. Together with state injection, we can perform a universal set of gates within a single block of the class of hypergraph product codes.Anirudh KrishnaDavid PoulinAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 1, p 011023 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Anirudh Krishna David Poulin Fault-Tolerant Gates on Hypergraph Product Codes
description	Quantum computers have the capacity to change the landscape of computing. To make these devices robust to experimental imperfections, we require some form of quantum error correction. Current approaches focus on topological codes, as they appear to be in the realm of experimental capabilities. These techniques will likely lead to the first proof of principle of fault tolerance in the next 5 yr. In the long run, however, these approaches require a very large number of physical qubits to construct a fault-tolerant quantum circuit that can run interesting algorithms. As an alternative, it is proposed that quantum low-density parity-check (LDPC) codes could serve as an architecture that circumvents this problem. The best candidate class of quantum LDPC codes were discovered by Tillich and Zémor and are called hypergraph product codes. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold. With these features, they asymptotically offer a smaller overhead compared to topological codes. Here, we demonstrate how to perform Clifford gates on this class of codes using code deformation. To this end, we introduce wormhole defects on hypergraph product codes. Together with state injection, we can perform a universal set of gates within a single block of the class of hypergraph product codes.
format	article
author	Anirudh Krishna David Poulin
author_facet	Anirudh Krishna David Poulin
author_sort	Anirudh Krishna
title	Fault-Tolerant Gates on Hypergraph Product Codes
title_short	Fault-Tolerant Gates on Hypergraph Product Codes
title_full	Fault-Tolerant Gates on Hypergraph Product Codes
title_fullStr	Fault-Tolerant Gates on Hypergraph Product Codes
title_full_unstemmed	Fault-Tolerant Gates on Hypergraph Product Codes
title_sort	fault-tolerant gates on hypergraph product codes
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/98cb9ab45c97449798039b0b8c8275c3
work_keys_str_mv	AT anirudhkrishna faulttolerantgatesonhypergraphproductcodes AT davidpoulin faulttolerantgatesonhypergraphproductcodes
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Fault-Tolerant Gates on Hypergraph Product Codes

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