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Demonstration of measurement-free universal logical quantum computation

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Butt, Friederike, Pogorelov, Ivan, Freund, Robert, Steiner, Alex, Meyer, Marcel, Monz, Thomas, Müller, Markus·2026·Nature Communications
DOI 10.1038/s41467-026-68533-xPMC PMC12848042

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Abstract

The ability to perform quantum error correction (QEC) and robust gate operations on encoded qubits opens the door to demonstrations of quantum algorithms. Contemporary QEC schemes typically require mid-circuit measurements with feed-forward control, which are challenging for qubit control, often slow, and susceptible to relatively high error rates. In this work, we propose and experimentally demonstrate a universal toolbox of fault-tolerant logical operations on error-detecting codes without mid-circuit measurements on a trapped-ion quantum processor. We present modular logical state teleportation between two four-qubit error-detecting codes without measurements during algorithm execution. Moreover, we realize a fault-tolerant universal gate set on an eight-qubit error-detecting code hosting three logical qubits, based on state injection, which can be executed by coherent gate operations only. We apply this toolbox to experimentally realize Grover’s quantum search algorithm fault-tolerantly on three logical qubits encoded in eight physical qubits, with the implementation displaying clear identification of the desired solution states. Our work demonstrates the practical feasibility and provides first steps into the largely unexplored direction of measurement-free quantum computation.

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Crossref · 10.1038/s41467-026-68533-x

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  • The five-qubit code is a perfect code.

    “it is a perfect code, a notion we discuss at the end of this section.”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [59]

    The Results section, “FT toolbox for universal operations on the [[8, 3, 2]]-code” (page unavailable), describes an eight-qubit code, not the five-qubit code. Searches for “five-qubit code perfect code” and “[[5,1,3]]” found no passage in our copy addressing whether the five-qubit code is perfect. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

  • The five-qubit code can correct an arbitrary single-qubit error.

    “the smallest code that can correct an arbitrary single-qubit error.”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [59]

    The Results section on the [[8, 3, 2]] code says that its eight-qubit code can detect any single error, not that a five-qubit code can correct one. Searches for the five-qubit code and arbitrary single-qubit error correction found no passage in our copy addressing that claim or the cited sentence’s ‘smallest code’ qualification. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

  • The five-qubit code is the smallest possible QEC code that can protect a single logical qubit against single-qubit errors.

    “The five-qubit code—the smallest possible QEC code that can protect a single logical qubit against single-qubit errors—was independently proposed by Laflamme, Miquel, Paz, and Zurek [59] and Bennett, DiVincenzo, Smolin, and Wootters [60] in 1996.”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [59]

    The Results section (page unavailable) calls the [[8, 3, 2]] code the smallest instance of a three-dimensional color code and says it detects single errors. Searches for the five-qubit code and single-qubit error correction found no passage in our copy addressing whether the five-qubit code is the smallest code that protects one logical qubit against such errors. (LLM, conf=0.74)

    Experimental — accuracy not yet measured

  • The five-qubit code is denoted as a [[5,1,3]] code.

    “This code, denoted as a J5, 1, 3K code [59]”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [59]

    The Results section, “FT toolbox for universal operations on the [[8, 3, 2]]-code” (page unavailable), identifies the paper’s eight-qubit code as [[8, 3, 2]] but does not address the five-qubit code’s designation. Searches for “[[5, 1, 3]]” and “five-qubit code distance three” found no passage establishing the claimed notation. (LLM, conf=0.73)

    Experimental — accuracy not yet measured

  • The five-qubit code has four independent stabilizer generators g1 = XZZXI, g2 = IXZZX, g3 = XIXZZ, g4 = ZXIXZ.

    “we need 5− 1 = 4 independent stabilizer generators, which can be written as g1 = XZZXI, (4.27) g2 = IXZZX, (4.28) g3 = XIXZZ, (4.29) g4 = ZXIXZ . (4.30)”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [59]

    The Results section on the [[8, 3, 2]]-code describes stabilizers for an eight-qubit code, not the claimed five-qubit code. Searches for the four listed Pauli strings and for five-qubit stabilizer generators found no passage in our copy addressing the claim. The indexed passages provide no page numbers. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

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Cites

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Cited by

Sorted by citations

Authors
Butt, F., Pogorelov, I., Freund, R., Steiner, A., Meyer, M., Monz, T., & Müller, M.
Affiliations
  • Forschungszentrum Jülich (DE)
  • Universität Innsbruck (AT)
Corresponding author
  • Butt, Friederike
  • Müller, Markus
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2026-01-26
Volume
17
Issue
1
Pages
995-995
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-026-68533-x
PMC
PMC12848042
OpenAlex
W7125660688
Cited by
2
References
16
Citations by year
2026: 2
FWCI
6.83
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • PubMed Central (publishedVersion, cc-by)
  • RWTH Publications (RWTH Aachen) (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • JuSER (Forschungszentrum Jülich) (submittedVersion, other-oa)
Funders
ODNI | Intelligence Advanced Research Projects Activity (W911NF-23-2-0216)
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 Mechanics and Applications
Keywords
fault-tolerant quantum computing, logical qubits, error detection codes, trapped-ion quantum computer, Grover's algorithm, universal gate set, quantum error correction

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