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  • Open Access

In Situ Benchmarking of Fault-Tolerant Quantum Circuits: Clifford Circuits

Xiao Xiao1,*, Dominik Hangleiter2,3, Dolev Bluvstein4, Mikhail D. Lukin4, and Michael J. Gullans1,5,†

  • *Contact author: xiaoxiao@umd.edu
  • †Contact author: mgullans@umd.edu
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PRX Quantum 7, 033055 – Published 14 September, 2026

DOI: https://doi.org/10.1103/ghn4-8y96

Abstract

Benchmarking physical devices and verifying logical algorithms are important tasks for scalable fault-tolerant quantum computing. Numerous protocols exist for benchmarking devices before running actual algorithms. In this work, we show that both physical and logical errors of fault-tolerant circuits can even be characterized in situ using syndrome data. To achieve this, we map general fault-tolerant Clifford circuits to subsystem codes using the spacetime code formalism and develop a scheme for estimating Pauli noise in Clifford circuits using syndrome data. We give necessary and sufficient conditions for the learnability of physical and logical noise from given syndrome data, and show that we can accurately predict logical fidelities from the same data. Importantly, our approach requires only a polynomial sample size, even when the logical error rate is exponentially suppressed by the code distance, and thus gives an exponential advantage against methods that use only logical data such as direct fidelity estimation. We demonstrate the practical applicability of our methods in various scenarios using synthetic data as well as the experimental data from a recent demonstration of fault-tolerant circuits by Bluvstein et al. [Nature 626, 7997 (2024)]. Our methods provide an efficient, in situ way of characterizing a fault-tolerant quantum computer to help gate calibration, improve decoding accuracy, and verify logical circuits.

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Popular Summary

Fault-tolerant quantum computers are designed to run long algorithms, but doing so in practice requires reliable ways to benchmark the hardware and verify that the encoded computation is working as intended. We show that this can be done in situ using the syndrome data that fault-tolerant circuits already generate, rather than relying only on separate calibration experiments. Our method learns the device’s Pauli-type error rates directly from the observed syndrome patterns. We also prove necessary and sufficient conditions for when the physical error rates and the resulting encoded error rates are learnable from a given set of syndrome measurements. Crucially, our approach needs only a practical amount of data even when encoded errors are exponentially rare, yielding an exponential sample-size advantage over methods that estimate performance from encoded outcomes alone. This enables practical characterization of fault-tolerant processors to guide calibration, improve decoding, and verify encoded circuits.

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PRX Quantum 7, 033055– Published 14 September, 2026
  • Received 5 February 2026
  • Revised 10 June 2026
  • Accepted 3 August 2026
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