Low-overhead quantum computing with the color code
Open accessPublished version of a preprint
Abstract
Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an approach based on the color code can lead to considerable reductions in the resource overheads compared with conventional methods, while remaining compatible with a two-dimensional layout. We propose a lattice surgery scheme that exploits the rich structure of the color-code phase to perform arbitrary pairs of commuting logical Pauli measurements in parallel while keeping the space cost low. Compared to lattice surgery schemes based on the surface code with the same code distance, and assuming the same amount of time is needed to complete a round of syndrome measurements, our approach yields about a 3 × improvement in the space-time overhead, obtained from a combination of a 1.5 × improvement in spatial overhead together with a 2 × speedup due to the parallelization of commuting logical measurements. Even when taking into account the color code's lower error threshold using current decoders, the overhead is reduced by 10% at a physical error rate of 10 − 3 and by 50% at 10 − 4 . Published by the American Physical Society 2024
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Lattice surgery enables the efficient realization of multi-qubit fault-tolerant operations, such as the CNOT gate, with only nearest-neighbour interactions.
“Lattice surgery22,39,43,56 enables the efficient realization of multi-qubit fault-tolerant operations, such as the CNOT gate, with only nearest-neighbour interactions.”
From Scaling and logic in the colour code on a superconducting quantum processor (2025) · cites this paper as [43]
The Overview (p. 2) describes fault-tolerant logical operations performed through lattice surgery, and the Introduction (p. 1) describes a resource-efficient, two-dimensional architecture with nearest-neighbour readout. Our copy does not specifically show a CNOT gate implemented by lattice surgery using only nearest-neighbour interactions, so that example is not established by the cited paper. (LLM, conf=0.82)
Experimental — accuracy not yet measuredColour codes enable multi-qubit entangling operations with less space-time overhead because of their ability for simultaneous fault-tolerant multi-qubit Pauli measurements.
“Colour codes also enable multi-qubit entangling operations with less space-time overhead because of their ability for simultaneous fault-tolerant multi-qubit Pauli measurements43.”
From Scaling and logic in the colour code on a superconducting quantum processor (2025) · cites this paper as [43]
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- Authors
- Thomsen, F., Kesselring, M. S., Bartlett, S. D., & Brown, B. J.
- Affiliations
- The University of Sydney (AU)
- Freie Universität Berlin (DE)
- Venue
- Physical Review Research
- Publisher
- American Physical Society (APS)
- Published
- 2024-11-12
- Volume
- 6
- Issue
- 4
- ISSN
- 2643-1564 (ISSN-L)
- OpenAlex
- W4404257466
- Cited by
- 15
- References
- 69
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 2 · 2023: 2 · 2022: 2
- FWCI
- 1.62
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review Research (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver
- Funders
- Australian Research Council
- Army Research Office (W911NF-21-1-0007)
- Deutsche Forschungsgemeinschaft
- 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
- color codes, fault-tolerant quantum computing, resource overhead, lattice surgery, error threshold, syndrome measurement
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