Movassagh, R. and Ouyang, Y. orcid.org/0000-0003-1115-0074 (2024) Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians. Quantum, 8. p. 1541. ISSN 2521-327X
Abstract
Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes any classical code and explicitly constructs the corresponding QEC code. Our framework can be seen to generalize the CSS codes, and goes beyond the stabilizer formalism (Fig. 1). A concrete advantage is that the desirable properties of a classical code are automatically incorporated in the design of the resulting quantum code. We reify the theory by various illustrations some of which outperform the best previous constructions. We then introduce a local quantum spin-chain Hamiltonian whose ground space we analytically completely characterize. We utilize our framework to demonstrate that the ground space contains explicit quantum codes with linear distance. This side-steps the Bravyi-Terhal no-go theorem.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 Quantum. Published under CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/). |
Keywords: | Quantum Physics; Mathematical Sciences; Physical Sciences |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/M024261/1 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/R043825/1 Engineering and Physical Sciences Research Council EP/W028115/1 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/W028115/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 09 Jan 2025 10:49 |
Last Modified: | 09 Jan 2025 10:49 |
Status: | Published |
Publisher: | Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften |
Refereed: | Yes |
Identification Number: | 10.22331/q-2024-11-27-1541 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221562 |