Fault-tolerant measurement-free quantum error correction with multi-qubit gates

Abstract

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 multi-qubit 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 $\sim 0.7\%$ 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 multi-qubit gates, finding that existing multi-qubit 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 multi-qubit 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 Heußen \textit{et al.}~[arXiv:2307.13296] to achieve FT by ``copying'' errors onto an ancilla register. By combining multi-qubit 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 $\sim 0.1\%$.

added analysis of related work, and an explicit FT circuit

References in corpus (5)

• Stim: a fast stabilizer circuit simulator
• Multiqubit Spectroscopy of Gaussian Quantum Noise
• On fault-tolerance with noisy and slow measurements
• Measurement-free implementations of small-scale surface codes for quantum dot qubits
• Parallel implementation of CNOT${}^N$ and C${}_2$NOT${}^2$ gates via homonuclear and heteronuclear Förster interactions of Rydberg atoms

Cited by in corpus (16)

• A universal neutral-atom quantum computer with individual optical addressing and non-destructive readout
• Measurement-free fault-tolerant quantum error correction in near-term devices
• Computational Capabilities and Compiler Development for Neutral Atom Quantum Processors: Connecting Tool Developers and Hardware Experts
• Fault-tolerant quantum computation using large spin cat-codes
• Optimized measurement-free and fault-tolerant quantum error correction for neutral atoms
• Quantum computer error structure probed by quantum error correction syndrome measurements
• Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms
• Parametrized multiqubit gate design for neutral-atom based quantum platforms
• Readout Error Mitigation for Mid-Circuit Measurements and Feedforward
• Enhancing Quantum Memory Lifetime with Measurement-Free Local Error Correction and Reinforcement Learning
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
• Measurement-free quantum error correction optimized for biased noise
• Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing
• Multiqubit Rydberg Gates for Quantum Error Correction
• Impure codes exceeding the pure bounds for quantum local recovery
• Universal quantum computation via scalable measurement-free error correction