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arXiv:2404.11663 · Physical Review Research

Optimized measurement-free and fault-tolerant quantum error correction for neutral atoms

Stefano Veroni, Markus Müller, Giacomo Giudice

Published Dec 10, 2024• 19 citations
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Abstract

A major challenge in performing quantum error correction (QEC) is implementing reliable measurements and conditional feed-forward operations. In quantum computing platforms supporting unconditional qubit resets, or a constant supply of fresh qubits, alternative schemes which do not require measurements are possible. In such schemes, the error correction is realized via crafted coherent quantum feedback. We propose implementations of small measurement-free QEC schemes, which are fault tolerant to circuit-level noise. These implementations are guided by several heuristics to achieve fault tolerance: redundant syndrome information is extracted, and additional single-shot flag qubits are used. By carefully designing the circuit, the additional overhead of these measurement-free schemes is moderate compared to their conventional measurement and feed-forward counterparts. We highlight how this alternative approach paves the way towards implementing resource-efficient measurement-free QEC on neutral-atom arrays. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043253

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•Aug 14, 2025•1 citation
A major challenge in performing quantum error correction (QEC) is implementing reliable measurements and conditional feed-forward operations. In quantum computing platforms supporting unconditional qubit resets, or a constant supply of fresh qubits, alternative schemes which do not require measurements are possible. In such schemes, the error correction is realized via crafted coherent quantum feedback. We propose implementations of small measurement-free QEC schemes, which are fault tolerant to circuit-level noise. These implementations are guided by several heuristics to achieve fault tolerance: redundant syndrome information is extracted, and additional single-shot flag qubits are used. By carefully designing the circuit, the additional overhead of these measurement-free schemes is moderate compared to their conventional measurement and feed-forward counterparts. We highlight how this alternative approach paves the way towards implementing resource-efficient measurement-free QEC on neutral-atom arrays. Published by the American Physical Society 2024
Logical qubits can be protected from decoherence by performing quantum error-correction (QEC) cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory that operates for in principle arbitrary long times. All circuit components must be assumed as noisy unless specific assumptions about the form of the noise are made. Modern QEC schemes are challenging to implement experimentally in physical architectures where in-sequence measurements and feed forward of classical information cannot be reliably executed fast enough or even at all. Here we provide a novel scheme to perform QEC cycles without the need of measuring qubits that is fully fault-tolerant with respect to all components used in the circuit. Our scheme can be used for any low-distance CSS code since its only requirement towards the underlying code is a transversal gate. Similarly to Steane-type EC, we coherently copy errors to a logical auxiliary qubit but then apply a coherent feedback operation from the auxiliary system to the logical data qubit. The logical auxiliary qubit is prepared fault tolerantly without measurements, too. We benchmark logical failure rates of the scheme in comparison to a flag-qubit-based EC cycle. We map out a parameter region where our scheme is feasible and estimate physical error rates necessary to achieve the break-even point of beneficial QEC with our scheme. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array. For recently demonstrated capabilities of atom shuttling and native multiatom Rydberg gates, we achieve moderate circuit depths and beneficial performance of our scheme while not breaking fault tolerance. These results thereby enable practical fault-tolerant QEC in hardware architectures that do not support midcircuit measurements. Published by the American Physical Society 2024
In this paper, we derive optimized measurement-free protocols for quantum error correction and the implementation of a universal gate set optimized for an error model that is noise biased. The noise bias is adapted for neutral-atom platforms, where two- and multi-qubit gates are realized with Rydberg interactions and are thus expected to be the dominant source of noise. Careful design of the gates allows us to further reduce the noise model to Pauli- Z errors. In addition, the presented circuits are robust to arbitrary single-qubit gate errors, and we demonstrate that the break-even point can be significantly improved compared to fully fault-tolerant measurement-free schemes. The obtained logical qubits with their suppressed error rates on logical gate operations can then be used as building blocks in a first step of error correction in order to push the effective error rates below the threshold of a fully fault-tolerant and scalable quantum error-correction scheme.
In this paper, we derive optimized measurement-free protocols for quantum error correction and the implementation of a universal gate set optimized for an error model that is noise biased . The noise bias is adapted for neutral atom platforms, where two- and multi-qubit gates are realized with Rydberg interactions and are thus expected to be the dominating source of noise. Careful design of the gates allows to further reduce the noise model to Pauli-Z errors. In addition, the presented circuits are robust to arbitrary single-qubit gate errors, and we demonstrate that the break-even point can be significantly improved compared to fully fault-tolerant measurement-free schemes. The obtained logical qubits with their suppressed error rates on logical gate operations can then be used as building blocks in a first step of error correction in order to push the effective error rates below the threshold of a fully fault-tolerant and scalable quantum error correction scheme.
Measurement-free quantum error correction (MFQEC) offers an alternative to standard measurement-based QEC in platforms with an unconditional qubit reset gate. We revisit the question of fault tolerance (FT) for a measurement-free variant of the Steane code that leverages multiqubit gates and redundant syndrome extraction, finding previously overlooked phase-flip errors that undermine FT. We then construct a revised MFQEC circuit that is resistant to all single-qubit errors, but which nonetheless cannot tolerate certain correlated errors. In order to investigate FT systematically, we introduce an efficient method to classically simulate MFQEC circuits with (i) Clifford gates for syndrome extraction, (ii) syndrome-controlled Pauli operations for decoding, and (iii) a Pauli noise model. We thereby find a pseudothreshold of $\ensuremath{\sim}0.7%$ for our revised MFQEC Steane code under a restricted noise model previously considered in the literature. We then relax noise model assumptions to identify general requirements for FT with multiqubit gates, finding that existing multiqubit neutral atom gates are incompatible with fault-tolerant syndrome extraction in a straightforward implementation of both measurement-based and measurement-free variants of the Steane code. Decomposing multiqubit gates into two-qubit gates similarly spoils FT. Finally, we discuss the theoretical ingredients that are necessary to recover FT for MFQEC codes, including single-shot FT and a recent proposal by Heu\ss{}en et al. [arXiv:2307.13296] to achieve FT by ``copying'' errors onto an ancilla register. By combining multiqubit gates, redundant syndrome extraction, and copy-assisted FT, we construct a measurement-free and fault-tolerant variant of the Steane code with a pseudothreshold of $\ensuremath{\sim}0.1%$.
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 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.
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 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.