Quantum Low-Density Parity-Check Codes
Open accessAbstract
Quantum error correction is an indispensable ingredient for scalable quantum computing.In this Perspective we discuss a particular class of quantum codes called "quantum low-density parity-check (LDPC) codes."The codes we discuss are alternatives to the surface code, which is currently the leading candidate to implement quantum fault tolerance.We introduce the zoo of quantum LDPC codes and discuss their potential for making quantum computers robust with regard to noise.In particular, we explain recent advances in the theory of quantum LDPC codes related to certain product constructions and discuss open problems in the field.
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Junction-based architectures open the design space for fault tolerance to high-efficiency encodings, transversal logic, low-overhead magic state factories and single-shot error correction.
“Junction-based architectures should allow QCCD machines to maintain all-to-all connectivity for large numbers of qubits, opening the design space for fault tolerance to high-efficiency encodings58, transversal logic59,60, low-overhead magic state factories61 and single-shot error correction62–76.”
From A 98-qubit trapped-ion quantum computer with all-to-all connectivity (2026) · cites this paper as [58]
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- Authors
- Breuckmann, N. P., & Eberhardt, J. N.
- Affiliations
- University College London (GB)
- University of Bonn (DE)
- Venue
- PRX Quantum
- Publisher
- American Physical Society (APS)
- Published
- 2021-10-11
- Volume
- 2
- Issue
- 4
- ISSN
- 2691-3399 (ISSN-L)
- OpenAlex
- W3207755657
- Cited by
- 328
- References
- 10
- Citations by year
- 2026: 67 · 2025: 124 · 2024: 74 · 2023: 34 · 2022: 26 · 2021: 3
- FWCI
- 12.10
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- PRX Quantum (publishedVersion, cc-by)
- Explore Bristol Research (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- UCL Discovery (University College London) (submittedVersion)
- arXiv (Cornell University)
- Funders
- EPSRC (EP/S005021/1)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum low-density parity-check codes, quantum error correction, surface code, quantum fault tolerance, product construction, noise robustness, quantum error-correcting codes
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