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.
The standard method for benchmarking quantum error-correction is randomized fault-injection testing. The state-of-the-art tool stim is efficient for error correction implementations with distances of up to 10, but scales poorly to larger distances for low physical error rates. In this paper, we present a scalable approach that combines stratified fault injection with extrapolation. Our insight is that some of the fault space can be sampled efficiently, after which extrapolation is sufficient to complete the testing task. As a result, our tool scales to distance 17 for a physical error rate of 0.0005 with a two-hour time budget on a desktop. For this case, it estimated a logical error rate of
1.51×10−11 with high confidence.
As quantum devices are progressively scaled and refined, quantum codes will become indispensable to guarantee reliable computation in the presence of noise. Due to the difficulties of characterizing physical noise, direct measures of logical performance will be of paramount use to tune quantum codes [18]. Logical Randomized Benchmarking in [5] aimed to characterize the logical operations directly by performing randomized benchmarking using logical operators and following each operation with perfect QEC. However, due to resource limitations, physical implementations such as [14] only measure the syndrome at the end of a computation. \n \nWe develop a generalized framework for procedures that measure the fidelity of logical operations directly, logical fidelity estimation (LFE). We identify several freedoms that arise when attempting to define a fidelity which characterizes quantum error correction, specifically, in how error detection events are processed and in how often error correction is performed. We explore these freedoms by conducting a survey to eliminate inviable procedures guided by the presence of upticks, a standard signature of non-Markovianity [33]. Our survey highlights procedures that are robust to gate-dependent noise and procedures which are implementable in the near-term. We recommend applying post-selection after each gate as a benchmark for quantum codes which is robust to gate-dependent noise. We manage to eliminate some naive near-term protocols, but guaranteeing the robustness when QEC is applied at a at fixed time or when post-selection is applied at the end, are open problems.
Logical error rate is the standard benchmark for quantum error correction (QEC), but it is an aggregate quantity: it says nothing about which circuit components actually drive logical failure. Recent work introduced an error attribution scheme that computes per-component sensitivities
∂PL/∂pi of the logical error rate jointly from the same Monte Carlo samples used to estimate
PL, and showed that halving noise on the 5%–7% most sensitive components reduces logical error rates by roughly 15%–25%, about twice the improvement from randomly chosen components [1],[3]. This paper develops the quantitative structure underlying that result. We formalize the sensitivity map, derive the first-order intervention gain for targeted versus random noise-reduction budgets, and show analytically that the targeted-to-random advantage is
ρ=r/(fr+1−f), where
f is the hotspot fraction and
r the sensitivity contrast; for
f=0.06 and
r=2.136 this ratio is exactly
2, matching the reported factor. We further show that the reported 15%–25% reductions exceed the first-order prediction of about 6% by an amplification factor of approximately
3.15, which we attribute to nonlinear, multiplicative error propagation absent from independent-error models. We derive Monte Carlo sample-complexity requirements for the sensitivity estimator, situate attribution among channel-optimized, reinforcement-learning, and robustness-optimized QEC strategies, and identify failure modes: coherent noise, estimator variance at low
PL, sensitivity redistribution, and non-stationary drift. ## 1. Introduction Quantum error correction protects quantum information by encoding logical qubits redundantly and decoding measured syndromes, and its performance is almost universally reported as a single number: the logical error rate
PL, the probability that a logical operator flips during a memory experiment or computation cycle. This aggregate benchmark is necessary but i Full text and updates: papers.qnfo.org/papers/error-attribution-as-a-resource-allocation-principle-for-quantum-error-correctio/
Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are isolated from the state preparation and measurement errors that plague other methods such as channel tomography and direct fidelity estimation. A decisive factor in the feasibility of randomized benchmarking is the number of sampled sequences required to obtain rigorous confidence intervals. Previous bounds were either prohibitively loose or required the number of sampled sequences to scale exponentially with the number of qubits in order to obtain a fixed confidence interval at a fixed error rate. Here, we show that, with a small adaptation to the randomized benchmarking procedure, the number of sampled sequences required for a fixed confidence interval is dramatically smaller than could previously be justified. In particular, we show that the number of sampled sequences required is essentially independent of the number of qubits and scales favorably with the average error rate of the system under investigation. We also investigate the fitting procedure inherent to randomized benchmarking in light of our results and find that standard methods such as ordinary least squares optimization can give misleading results. We therefore recommend moving to more sophisticated fitting methods such as iteratively reweighted least squares optimization. Our results bring rigorous randomized benchmarking on systems with many qubits into the realm of experimental feasibility.
Randomized benchmarking allows one to efficiently and scalably characterize the average error of a unitary 2-design such as the Clifford group
C on a physical candidate for quantum computation, as long as there are no noncomputational leakage levels in the system. We investigate the effect of leakage errors on randomized benchmarking induced from an additional level per physical qubit and provide a modified protocol that allows us to derive reliable estimates for the error per gate in their presence. We assess the variance of the sequence fidelity corresponding to the number of random sequences needed for valid fidelity estimation. Our protocol allows for gate-dependent error channels without being restricted to perturbations. We show that our protocol is compatible with interleaved randomized benchmarking and expand to benchmarking of arbitrary gates. This setting is relevant for superconducting transmon qubits, among other systems.