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arXiv:2609.01848

Error accumulation in dissipative quantum circuits

Nadir Samos-Sáenz de Buruaga, Rodrigo M. C. Pereira, Karol Życzkowski, Sergey Denisov, Pedro Ribeiro

quant-phSubmitted Sep 1, 2026• Announced Sep 3, 2026• 0 citations
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Abstract

Present-day quantum processors are open systems in which dissipation and decoherence degrade the information carried by a quantum state as it propagates through a circuit. We study this degradation in dissipative random quantum circuits, modeling each two-qubit gate as a diluted unitary that interpolates between the intended unitary operation and a random dissipative quantum channel. Using the fidelity between the ideal and noisy output states as a diagnostic, we show that sufficiently random unitary gates or dissipative Kraus operators lead to a universal decay of the average fidelity. This decay is determined only by the dissipation strength, system size, and circuit depth, while microscopic details of the gates and noise, including the Kraus rank, appear only in subleading corrections to higher moments. We derive a closed-form expression for the average fidelity in terms of three physically meaningful error parameters, dissipation strength, coherent two-qubit gate-error strength, and connectivity-error probability. Finally, we identify the cases when dissipative effects can be reproduced by an unitary-noise model and when dissipation-induced decoherence remains distinguishable from coherent noise at the level of the average fidelity.

Comments
10 pages main text, 12 pages supplemental material and 6 figures

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Present-day quantum processors are open systems in which dissipation and decoherence degrade the information carried by a quantum state as it propagates through a circuit. We study this degradation in dissipative random quantum circuits, modeling each two-qubit gate as a diluted unitary that interpolates between the intended unitary operation and a random dissipative quantum channel. Using the fidelity between the ideal and noisy output states as a diagnostic, we show that sufficiently random unitary gates or dissipative Kraus operators lead to a universal decay of the average fidelity. This decay is determined only by the dissipation strength, system size, and circuit depth, while microscopic details of the gates and noise, including the Kraus rank, appear only in subleading corrections to higher moments. We derive a closed-form expression for the average fidelity in terms of three physically meaningful error parameters, dissipation strength, coherent two-qubit gate-error strength, and connectivity-error probability. Finally, we identify the cases when dissipative effects can be reproduced by an unitary-noise model and when dissipation-induced decoherence remains distinguishable from coherent noise at the level of the average fidelity.
Abstract We study the distribution over measurement outcomes of noisy random quantum circuits in the regime of low fidelity, which corresponds to the setting where the computation experiences at least one gate-level error with probability close to one. We model noise by adding a pair of weak, unital, single-qubit noise channels after each two-qubit gate, and we show that for typical random circuit instances, correlations between the noisy output distribution pnoisyp_{\text {noisy}}pnoisy​ p noisy and the corresponding noiseless output distribution pidealp_{\text {ideal}}pideal​ p ideal shrink exponentially with the expected number of gate-level errors. Specifically, the linear cross-entropy benchmark F that measures this correlation behaves as F=exp(−2sϵ±O(sϵ2))F=\text {exp}(-2s\epsilon \pm O(s\epsilon ^2))F=exp(−2sϵ±O(sϵ2)) F = exp ( - 2 s ϵ ± O ( s ϵ 2 ) ) , where ϵ\epsilon ϵ ϵ is the probability of error per circuit location and s is the number of two-qubit gates. Furthermore, if the noise is incoherent—for example, depolarizing or dephasing noise—the total variation distance between the noisy output distribution pnoisyp_{\text {noisy}}pnoisy​ p noisy and the uniform distribution punifp_{\text {unif}}punif​ p unif decays at precisely the same rate. Consequently, the noisy output distribution can be approximated as pnoisy≈Fpideal+(1−F)punifp_{\text {noisy}}\approx Fp_{\text {ideal}}+ (1-F)p_{\text {unif}}pnoisy​≈Fpideal​+(1−F)punif​ p noisy ≈ F p ideal + ( 1 - F ) p unif . In other words, although at least one local error occurs with probability 1−F1-F1−F 1 - F , the errors are scrambled by the random quantum circuit and can be treated as global white noise, contributing completely uniform output. Importantly, we upper bound the average total variation error in this approximation by O(Fϵs)O(F\epsilon \sqrt{s})O(Fϵs​) O ( F ϵ s ) . Thus, the “white-noise approximation” is meaningful when ϵs≪1\epsilon \sqrt{s} \ll 1ϵs​≪1 ϵ s ≪ 1 , a quadratically weaker condition than the ϵs≪1\epsilon s\ll 1ϵs≪1 ϵ s ≪ 1
Fidelity decay captures the inevitable state degradation in any practical implementation of a quantum process. We devise bounds for the decay of fidelity for a generic evolution given by a random quantum circuit model that encompasses errors arising from the implementation of two-qubit gates and qubit permutations. We show that fidelity decays exponentially with both circuit depth and the number of qubits raised to an architecture-dependent power and we determine the decay rates as a function of the amplitude of the aforementioned errors. Furthermore, we demonstrate the utility of our results in benchmarking quantum processors using the quantum volume figure of merit and provide insights into strategies for improving processor performance. These findings pave the way for understanding how states evolving under generic quantum dynamics degrade due to the accumulation of different kinds of perturbations.
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution pnoisyp_{\text{noisy}}pnoisy​ of a generic noisy circuit instance and the output distribution pidealp_{\text{ideal}}pideal​ of the corresponding noiseless instance shrink exponentially with the expected number of gate-level errors, as F=exp(−2sε±O(sε2))F=\text{exp}(-2sε\pm O(sε^2))F=exp(−2sε±O(sε2)), where εεε is the probability of error per circuit location and sss is the number of two-qubit gates. Furthermore, if the noise is incoherent, the output distribution approaches the uniform distribution punifp_{\text{unif}}punif​ at precisely the same rate and can be approximated as pnoisy≈Fpideal+(1−F)punifp_{\text{noisy}} \approx Fp_{\text{ideal}} + (1-F)p_{\text{unif}}pnoisy​≈Fpideal​+(1−F)punif​, that is, local errors are scrambled by the random quantum circuit and contribute only white noise (uniform output). Importantly, we upper bound the total variation error (averaged over random circuit instance) in this approximation as O(Fεs)O(Fε\sqrt{s})O(Fεs​), so the "white-noise approximation" is meaningful when εs≪1ε\sqrt{s} \ll 1εs​≪1, a quadratically weaker condition than the εs≪1εs\ll 1εs≪1 requirement to maintain high fidelity. The bound applies when the circuit size satisfies s≥Ω(nlog⁡(n))s \geq Ω(n\log(n))s≥Ω(nlog(n)) and the inverse error rate satisfies ε−1≥Ω~(n)ε^{-1} \geq \tildeΩ(n)ε−1≥Ω~(n). The white-noise approximation is useful for salvaging the signal from a noisy quantum computation; it was an underlying assumption in complexity-theoretic arguments that low-fidelity random quantum circuits cannot be efficiently sampled classically. Our method is based on a map from second-moment quantities in random quantum circuits to expectation values of certain stochastic processes for which we compute upper and lower bounds.
Randomized benchmarking (RB) protocols have become an essential tool for providing a meaningful partial characterization of experimental quantum operations. While the RB decay rate is known to enable estimates of the average fidelity of those operations under gate-independent Markovian noise, under gate-dependent noise this rate is more difficult to interpret rigorously. In this paper, we prove that single-qubit RB decay parameter p coincides with the decay parameter of the gate-set circuit fidelity , a novel figure of merit which characterizes the expected average fidelity over arbitrary circuits of operations from the gate-set. We also prove that, in the limit of high-fidelity single-qubit experiments, the possible alarming disconnect between the average gate fidelity and RB experimental results is simply explained by a basis mismatch between the gates and the state-preparation and measurement procedures, that is, to a unitary degree of freedom in labeling the Pauli matrices. Based on numerical evidence and physically motivated arguments, we conjecture that these results also hold for higher dimensions.
We present a (REAS) technique to manage errors in quantum computers. Our method reduces the accumulation of errors in any quantum circuit composed of single- or two-qubit gates expressed as e − i σ θ for Pauli operators σ and θ ∈ [ 0 , π ) , which forms a universal gate set. For coherent errors, which include gate overrotation and crosstalk, we demonstrate a reduction of the error scaling in an L -depth circuit from O ( L ) to O ( L ) . This asymptotic error suppression behavior can be proven in a regime where all gates, including those constituting the error-suppressing protocol itself, are noisy. Going beyond coherent errors, we derive the general form of decoherence noise that can be suppressed by REAS. Lastly, we experimentally demonstrate the effectiveness of our approach regarding realistic errors using 100-qubit circuits with up to 64 two-qubit gate layers on IBM Quantum processors.
Quantum noise is a central challenge in quantum computing across many applications. Extensive work has examined how qubits couple to their environment, leading to decoherence and irreversible relaxation. This work studies a continuous coherent noise model for quantum circuits and compares it with a discrete Pauli model. The focus is on small, coherent gate errors that accumulate across circuit depth. These errors are modeled as random rotations on the Bloch sphere using a von Mises-Fisher distribution. In the small-angle limit, the model reduces to an isotropic Gaussian distribution. We test the model on quantum error-correction circuits based on the [[5,1,3]] and [[7,1,3]] codes. A variant of Grover's search circuit with different qubit counts is also examined. To enable fair comparison, we introduce a model-independent matching scheme. Pauli and continuous noise channels are aligned using the binary entropy at readout. This isolates the effect of noise structure at fixed uncertainty. An approximate analytical method for the propagation of coherent errors is also developed. The method tracks error distributions both on Clifford and non-Clifford circuits without full Monte Carlo sampling. It reduces simulation cost while preserving accuracy for circuit-level error estimates. The approximation is validated against brute-force simulations, identifying its regime of validity with Clifford and non-Clifford circuits under error correction. Our results show that continuous coherent noise and Pauli noise lead to comparable logical-error trends in the stabilizer-code circuits studied here. This behavior is consistent with syndrome extraction projecting a general single-qubit error onto Pauli-error subspaces before recovery. They also show where simplified propagation models work well and where their accuracy is reduced.