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arXiv:2603.12054

Noise Correlations as a Resource in Pauli-Twirled Circuits

Antoine Brillant, Rohan N Rajmohan, Peter Groszkowski, Alireza Seif, Jens Koch, Aashish Clerk

quant-phSubmitted Mar 12, 2026• Announced Mar 13, 2026• 0 citations• Revised Apr 27, 2026 (v2)
v1 · Mar 12, 2026v2 · Apr 27, 2026
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Abstract

Randomized compiling (RC) is an established tool to tailor arbitrary quantum noise channels into Pauli errors. The effect of both spatial and temporal noise correlations in randomly compiled circuits, however, is not fully understood. Here, we show that for a broad class of correlated Gaussian noise, RC reduces both the strength and temporal range of correlations. For Clifford circuits, we derive a simple analytical expression for the circuit fidelity of randomly compiled circuits. Surprisingly, we show that this fidelity is always increased by the presence of correlations, suggesting that correlations are a resource in randomly compiled circuits. To leading order in system-bath coupling, we also show that RC suppresses the quantum component of bath correlations, implying that one can safely treat weak noise as being classical. Finally, through extensive numerical simulations, we show that our results remain valid for many relevant non-Clifford circuits. These results clarify how RC mitigates memory effects and enhances circuit robustness.

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Randomized compiling (RC) is an established tool to tailor arbitrary quantum noise channels into Pauli errors. The effect of both spatial and temporal noise correlations in randomly compiled circuits, however, is not fully understood. Here, we show that for a broad class of correlated Gaussian noise, RC reduces both the strength and temporal range of correlations. For Clifford circuits, we derive a simple analytical expression for the circuit fidelity of randomly compiled circuits. Surprisingly, we show that this fidelity is always increased by the presence of correlations, suggesting that correlations are a resource in randomly compiled circuits. To leading order in system-bath coupling, we also show that RC suppresses the quantum component of bath correlations, implying that one can safely treat weak noise as being classical. Finally, through extensive numerical simulations, we show that our results remain valid for many relevant non-Clifford circuits. These results clarify how RC mitigates memory effects and enhances circuit robustness.
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore the role and effectiveness of using noise tailoring techniques to improve the performance of error correcting codes. Noise tailoring methods such as randomized compiling (RC) convert complex coherent noise processes to effective stochastic noise. While it is known that this can be leveraged to design efficient diagnostic tools, we explore its impact on the performance of error correcting codes. Of particular interest is the important class of coherent errors, arising from control errors, where RC has the maximum effect---converting these into purely stochastic errors. For these errors, we show here that RC delivers an improvement in performance of the concatenated Steane code by several orders of magnitude. We also show that below a threshold rotation angle, the gains in logical fidelity can be arbitrarily magnified by increasing the size of the codes. These results suggest that using randomized compiling can lead to a significant reduction in the resource overhead required to achieve fault tolerance.
Randomized compiling reduces the effects of errors on quantum computers by tailoring arbitrary Markovian errors into stochastic Pauli noise. Here we prove that randomized compiling also tailors non-Markovian errors into local stochastic Pauli noise and investigate the technique's limitations. We show through analysis and numerical results that randomized compiling alters errors in three distinct helpful ways. First, it prevents the coherent accumulation of errors (including hard to remove crosstalk effects) across gate cycles by destroying intercycle coherent correlations. Second, it converts individual gate cycle errors into Pauli noise. Finally, randomized compiling reduces the variability inherent to noisy devices. We confirm these theoretical predictions with the IBM Quantum Experience platform and describe experimental data that illustrates a drastic performance improvement across public devices. These results cement the importance of randomized compiling in near- and long-term quantum information processing.
Traditional discrete randomized compiling (RC) tailors errors with random control frames at logical-gate boundaries, but fails to capture intra-instrument control evolution or persistent system-environment coupling. In memory-bearing environments, errors correlate across times, not just single gates. We build continuous-process randomized compilation (CPRC) in the continuous process tensor (cPT) framework, unifying random unitary control trajectories, pointwise-covariant finite-duration instruments, and environmental dynamics on one time axis. We study four protocols: fixed Pauli refresh, bounded Cayley paths, unitary Brownian motion, Ornstein-Uhlenbeck driving. We obtain three key results: (1) Pointwise covariance ensures each trajectory exactly reproduces the target logic without system-environment coupling; a closed-frame counterexample proves endpoint-only compensation causes first-order instrument errors. (2) Independent Pauli conjugations over full intervals diagonalize error histories at boundaries, but classical labels retain environment-induced correlations, confirmed by an exact static-bath solution. (3) We derive a total-variation error bound for full adaptive output records under bounded centered coupling and mixing conditions. We prove the Fock norm convergence of the entire trajectory-averaged cPT for finite non-Gaussian environments and Gaussian baths with time-integrable covariance, including the uncut Drude spectrum. We numerically validate the theory in a qubit model via output probabilities, operator conditional mutual information, and all two-particle coefficients for both qubit and thermal Drude baths. This work extends RC from discrete circuits to continuous-time memory-bearing quantum processes, offering a unified framework, quantitative tools, implementable schemes, and benchmarks for non-Markovian error tailoring.
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors are even partially coherent, they present a major obstacle to performing robust computations. Here, we propose a method for introducing independent random single-qubit gates into the logical circuit in such a way that the effective logical circuit remains unchanged. We prove that this randomization tailors the noise into stochastic Pauli errors, which can dramatically reduce error rates while introducing little or no experimental overhead. Moreover, we prove that our technique is robust to the inevitable variation in errors over the randomizing gates and numerically illustrate the dramatic reductions in worst-case error that are achievable. Given such tailored noise, gates with significantly lower fidelity---comparable to fidelities realized in current experiments---are sufficient to achieve fault-tolerant quantum computation. Furthermore, the worst-case error rate of the tailored noise can be directly and efficiently measured through randomized benchmarking protocols, enabling a rigorous certification of the performance of a quantum computer.
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.
Randomized compiling (RC) is an efficient method for tailoring arbitrary Markovian errors into stochastic Pauli channels. However, the standard procedure for implementing the protocol in software comes with a large experimental overhead -- namely, it scales linearly in the number of desired randomizations, each of which must be generated and measured independently. In this work, we introduce a hardware-efficient algorithm for performing RC on a cycle-by-cycle basis on the lowest level of our FPGA-based control hardware during the execution of a circuit. Importantly, this algorithm performs a different randomization per shot with zero runtime overhead beyond measuring a circuit without RC. We implement our algorithm using the QubiC control hardware, where we demonstrate significant reduction in the overall runtime of circuits implemented with RC, as well as a significantly lower variance in measured observables.