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arXiv:2610.41528

FaultScope: A software package for fast error attribution in quantum error correction

Yuguo Shao, Zhenyu Chen, Ningfeng Wang, Song Cheng, Zhaohui Wei, Zi-Wen Liu, Zhengwei Liu

quant-phSubmitted Oct 30, 2026• Announced Nov 2, 2026
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Abstract

We introduce FaultScope, a classical simulator for quantum error correction circuits, implemented in Rust with a Python interface. FaultScope estimates logical error rates and their derivatives with respect to component error rates from the same sampled and decoded shots, without modifying or differentiating through the decoder. These derivatives enable error attribution to individual noisy components, helping identify noise hotspots for targeted noise reduction. FaultScope supports forward simulation of error propagation through circuits and direct sampling of detector and logical observable outcomes from detector error models. In our noiseless and noisy benchmarks, FaultScope has the lowest runtime among the tested simulators at every size. Computing all derivatives adds only 0.33--0.97\% to the runtime of logical error rate estimation across five repetition code sizes with 7--2047 error locations. FaultScope can be used to benchmark large-scale quantum error correction schemes and guide targeted noise reduction efficiently, thereby facilitating the design and optimization of fault-tolerant quantum computing architectures.

AI Summary

FaultScope addresses how to identify which noisy components most affect logical failure rates while performing routine QEC simulation. The Rust package, with a Python interface, implements an existing attribution approach: estimate derivatives $S_j=\partial P_{\mathrm L}/\partial p_j$ from the same sampled error events and decoded outcomes used to estimate the logical error rate, without modifying or differentiating through the decoder. The package supports forward Clifford simulation and detector-error-model sampling under independent Bernoulli error events. Packed shot masks enable bit-parallel propagation and sensitivity estimation using population counts. After compilation, attribution adds $O(M\lceil N/64\rceil)$ work and event-record storage for $M$ events and $N$ shots. Sensitivities can be grouped by physical component, gate, or round. CPU benchmarks compare six simulators using one million shots per circuit, including preparation, compilation, sampling, and output processing. FaultScope reports the lowest median runtime at every size with completed comparisons: a median $1.70\times$ speedup over Stim for 1024-qubit, depth-64 noiseless random Clifford circuits, and $1.93$–$3.31\times$ speedups for noisy surface-code memories. It alone completes distance 100 within the specified resource limits, taking 2043 seconds. Attribution overhead is 0.33–0.97% in repetition-code tests with 7–2047 error locations and 100,000 shots, using error probability $p=0.5$. The stated statistical limitation is that scarce logical failures can prevent reliable sensitivity comparisons at fixed shot count; rare-event extensions remain future work. DEM sampling requires independent-event representations, with restricted support for general Pauli mixtures.

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We introduce FaultScope, a classical simulator for quantum error correction circuits, implemented in Rust with a Python interface. FaultScope estimates logical error rates and their derivatives with respect to component error rates from the same sampled and decoded shots, without modifying or differentiating through the decoder. These derivatives enable error attribution to individual noisy components, helping identify noise hotspots for targeted noise reduction. FaultScope supports forward simulation of error propagation through circuits and direct sampling of detector and logical observable outcomes from detector error models. In our noiseless and noisy benchmarks, FaultScope has the lowest runtime among the tested simulators at every size. Computing all derivatives adds only 0.33--0.97% to the runtime of logical error rate estimation across five repetition code sizes with 7--2047 error locations. FaultScope can be used to benchmark large-scale quantum error correction schemes and guide targeted noise reduction efficiently, thereby facilitating the design and optimization of fault-tolerant quantum computing architectures.
FaultScope addresses how to identify which noisy components most affect logical failure rates while performing routine QEC simulation. The Rust package, with a Python interface, implements an existing attribution approach: estimate derivatives Sj=∂PL/∂pjS_j=\partial P_{\mathrm L}/\partial p_jSj​=∂PL​/∂pj​ from the same sampled error events and decoded outcomes used to estimate the logical error rate, without modifying or differentiating through the decoder.
The package supports forward Clifford simulation and detector-error-model sampling under independent Bernoulli error events. Packed shot masks enable bit-parallel propagation and sensitivity estimation using population counts. After compilation, attribution adds O(M⌈N/64⌉)O(M\lceil N/64\rceil)O(M⌈N/64⌉) work and event-record storage for MMM events and NNN shots. Sensitivities can be grouped by physical component, gate, or round.
CPU benchmarks compare six simulators using one million shots per circuit, including preparation, compilation, sampling, and output processing. FaultScope reports the lowest median runtime at every size with completed comparisons: a median 1.70×1.70\times1.70× speedup over Stim for 1024-qubit, depth-64 noiseless random Clifford circuits, and 1.931.931.93–3.31×3.31\times3.31× speedups for noisy surface-code memories. It alone completes distance 100 within the specified resource limits, taking 2043 seconds. Attribution overhead is 0.33–0.97% in repetition-code tests with 7–2047 error locations and 100,000 shots, using error probability p=0.5p=0.5p=0.5.
The stated statistical limitation is that scarce logical failures can prevent reliable sensitivity comparisons at fixed shot count; rare-event extensions remain future work. DEM sampling requires independent-event representations, with restricted support for general Pauli mixtures.
Logical error rate is a standard benchmark for quantum error correction, providing an aggregate measure of the overall effect of physical noise. In actual QEC architectures, errors at different circuit locations can have markedly different effects on logical failure even when their probabilities are equal. Here we introduce an error attribution scheme to quantitatively characterize the influence of individual circuit components on the logical error rate and use this refined information to guide targeted intervention and design for improved QEC performance. Our attribution estimator computes all component sensitivities jointly from the same Monte Carlo samples used to estimate the logical error rate. The resulting sensitivity maps identify hotspots where targeted noise reduction can most effectively improve logical performance. We test the scheme in circuit simulations of rotated surface code memories and high-rate lifted product codes: halving the noise strength on about 5\%-7\% of physical components selected by sensitivity reduces logical error rates by approximately 15\%-25\%, roughly twice the mean reduction from the same intervention on an equal number of randomly selected components. By connecting performance benchmarking to targeted optimization, our scheme provides a practical strategy for improving quantum error correction with limited resources.
Quantum error correction (QEC), the lynchpin of fault-tolerant quantum computing (FTQC), is designed and validated against well-behaved Pauli stochastic error models. But in real-world deployment, QEC protocols encounter a vast array of other errors -- coherent and non-Pauli errors -- whose impacts on quantum circuits are vastly different than those of stochastic Pauli errors. The impacts of these errors on QEC and FTQC protocols have been largely unpredictable to date due to exponential classical simulation cost. Here, we show how to accurately and efficiently model the effects of coherent and non-Pauli errors on FTQC, and we study the effects of such errors on syndrome extraction for surface and bivariate bicycle codes, and on magic state cultivation. Our analysis suggests that coherent error can shift fault-tolerance thresholds, increase the space-time cost of magic state cultivation, and can increase logical error rates by an order of magnitude compared to equivalent stochastic errors. These analyses are enabled by a new technique for mapping any Markovian circuit-level error model with sufficiently small error rates onto a detector error model (DEM) for an FTQC circuit. The resulting DEM enables Monte Carlo estimation of logical error rates and noise-adapted decoding, and its parameters can be analytically related to the underlying physical noise parameters to enable approximate strong simulation.
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses these measurements to infer which error most likely occurred, so that the system can correct it. The decoder's accuracy-how rarely it makes the wrong guess-directly determines the scale of quantum computation that can be reliably executed. With a wealth of competing decoding algorithms, a QEC system designer needs reliable methods to evaluate them. Today, the dominant approach is to evaluate decoders using Monte Carlo simulation. However, simulation has several drawbacks such as requiring many samples to produce low variance estimates. In this work, we develop a new systematic analysis for evaluating decoders. We introduce a novel formal semantics of a core language for QEC programs that captures the de facto standard Stim circuit format, providing a principled theoretical foundation for the emerging space of fault-tolerant quantum systems design. Given a QEC program and a decoder, our verifier can quantify both the decoder accuracy and the decoder robustness to drift in physical error rate. Our approach has two key components: (i) a structured search over the space of possible errors; and (ii) a constrained polynomial optimization kernel. A thorough empirical evaluation of our approach suggests that it can outperform simulation, especially in low error rate regimes, and that it can be deployed to quantify decoder robustness over an interval of physical error rates.
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
While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of p=10−3p=10^{-3}p=10−3, fault-tolerant simulation requires approximately 2 hours and 3.7×1053.7 \times 10^53.7×105 physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of p=10−4p=10^{-4}p=10−4 leads to at least an order of magnitude reduction in qubit count (3.1×1043.1 \times 10^43.1×104 physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.
The classical simulation of universal quantum circuits is crucial both fundamentally and practically for quantum computation. We propose SyQMA, a simulator with several convenient features, particularly suited for quantum error correction (QEC). SyQMA simulates universal quantum circuits with incoherent Pauli noise and computes exact expectation values and measurement probabilities as symbolic functions of circuit parameters: rotation angles, measurement outcomes, and noise rates. This simulator can sample measurement outcomes, enabling the simulation of dynamic quantum programs where circuit composition depends on prior measurement outputs. For QEC, it performs circuit-level maximum-likelihood decoding, provides exact symbolic expressions for logical error rates, and verifies the fault distance of fault-tolerant (FT) stabiliser and magic state preparation protocols. These features are enabled by an intuitive extension of stabiliser simulators, where each non-Clifford Pauli rotation and incoherent Pauli channel is compactly represented via auxiliary qubits and a modified trace. Representing the state requires only polynomial memory and time, while computing expectation values and measurement probabilities takes exponential time in the number of non-Clifford rotations and deterministic measurements, but only polynomial memory. The FT preparation of stabiliser and magic states, including the first stage of magic state cultivation, is analysed without approximations. We also exactly convert the disjoint error probabilities of a general multi-qubit Pauli channel to independent ones, a key step for creating and sampling from detector error models. The code is publicly available and open-source.