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Cited by 29Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems

Entangling Four Logical Qubits beyond Break-Even in a Nonlocal Code

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Hong, Yifan, Durso-Sabina, Elijah, Hayes, David, Lucas, Andrew·2024·Physical Review Letters
DOI 10.1103/physrevlett.133.180601
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Abstract

Quantum error correction protects logical quantum information against environmental decoherence by encoding logical qubits into entangled states of physical qubits. One of the most important near-term challenges in building a scalable quantum computer is to reach the break-even point, where logical quantum circuits on error-corrected qubits achieve higher fidelity than equivalent circuits on uncorrected physical qubits. Using Quantinuum's H2 trapped-ion quantum processor, we encode the Greenberger-Horne-Zeilinger (GHZ) state in four logical qubits with fidelity 99.5±0.15%≤F≤99.7±0.1% (after postselecting on over 98% of outcomes). Using the same quantum processor, we can prepare an uncorrected GHZ state on four physical qubits with fidelity 97.8±0.2%≤F≤98.7±0.2%. The logical qubits are encoded in a ⟦25,4,3⟧ Tanner-transformed long-range-enhanced surface code. Logical entangling gates are implemented using simple swap operations. Our results are a first step toward realizing fault-tolerant quantum computation with logical qubits encoded in geometrically nonlocal quantum low-density parity check codes.

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  • Over the past several years, there has been vast progress in both theory and experiment, including early demonstrations of logical error suppression below threshold and small fault-tolerant primitives.

    “Over the past several years, there has been vast progress made in both theory, with the introduction of novel code constructions, improvements in code parameters, and decoding algorithms, and experiment, with advancements in the quality of qubits, coherence times, and gate fidelities, and even some early demonstrations of logical error suppression below threshold and small fault-tolerant primitiv”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [32]

    The Introduction describes extensive work on quantum codes and cites experimental fault-tolerance demonstrations; it also identifies recent break-even operations using small codes. The paper does not establish that these demonstrations achieved logical error suppression below threshold—break-even is a different benchmark. Its discussion of the GHZ protocol also says one measurement step is not fault tolerant. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

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Cited by

Sorted by citations

Authors
Hong, Y., Durso-Sabina, E., Hayes, D., & Lucas, A.
Affiliations
  • University of Colorado Boulder (US)
  • Quantinuum (United Kingdom) (GB)
Corresponding author
Hong, Yifan
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2024-10-29
Volume
133
Issue
18
Pages
180601-180601
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.133.180601
OpenAlex
W4403868944
Cited by
29
References
11
Citations by year
2026: 8 · 2025: 20 · 2024: 1
FWCI
3.76
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • arXiv (Cornell University) (cc-by)
Funders
  • Alfred P. Sloan Foundation (FG-2020-13795)
  • Air Force Office of Scientific Research (FA9550-24-1-0120)
  • Office of Naval Research (N00014-23-1-2533)
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
logical qubits, quantum error correction, break-even point, GHZ states, surface code, trapped-ion quantum computer, fault-tolerant quantum computing, post-selection, quantum low-density parity-check codes

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