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  • Open Access

Universal Quantum Computation via Scalable Measurement-Free Error Correction

Stefano Veroni1, Alexandru Paler1,2, and Giacomo Giudice1,*

  • 1PlanQC GmbH, Münchener Str. 34, 85748 Garching, Germany
  • 2Department of Computer Science, Aalto University, 02150 Espoo, Finland

  • *Contact author: giacomo.giudice@planqc.eu
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PRX Quantum 6, 040337 – Published 14 November, 2025

DOI: https://doi.org/10.1103/lkk1-v6wp

Abstract

We show that universal quantum computation can be concretely made fault-tolerant without mid-circuit measurements. To this end, we introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical CCZ gate. Combined with a fold-transversal logical Hadamard gate, this enables a universal set of fault-tolerant operations using only transversal gates and qubit permutations. For the purpose of benchmarking under circuit-level noise, we develop an efficient method to simulate non-Clifford circuits with a small number of Hadamard gates. Separately, we demonstrate that certain CSS codes can be concatenated without measurements or having to rely on a universal logical gate set. This is made possible by means of a resource-efficient gadget—termed the “disposable Toffoli gadget”—that realizes the error-correcting feedback. Then, under concatenation of the Bacon-Shor code, we observe a fault-tolerance threshold at a circuit-level depolarizing noise rate of approximately 0.12%. Together, the deformation and concatenation protocols outline a blueprint for a fully fault-tolerant architecture without any feed-forward operation, particularly suited to state-of-the-art neutral-atom platforms.

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Physics Subject Headings (PhySH)

Popular Summary

Quantum computers are extremely sensitive to noise. To make them reliable, quantum error correction is used, which spreads information across many qubits so that errors can be detected and fixed. Most current error-correcting schemes rely on frequent measurements during a computation to check for errors. However, those measurements are often slow and disruptive, especially in hardware such as neutral atoms or trapped ions, where reading out a qubit can take much longer than performing a gate.

This work outlines a blueprint for building a universal quantum computer that autonomously corrects its own errors on the fly, pushing us a step closer to practical, large-scale quantum computing. This result is achieved through a new way to perform fault-tolerant quantum computations without requiring mid-circuit measurements or classical decoding. The method builds on the Bacon-Shor error-correcting code and uses “code deformation” tricks to perform all necessary logical operations purely through unitary quantum gates and resets.

We show that their approach can then be scaled up efficiently: errors can be suppressed by layering the code recursively, just like in conventional fault-tolerance. The simulation results suggest that this measurement-free strategy is practically viable and could compete with traditional schemes on platforms where measurement speed is a major limitation.

Article Text

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PRX Quantum 6, 040337– Published 14 November, 2025
  • Received 16 January 2025
  • Revised 23 June 2025
  • Accepted 8 October 2025
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