Quantum processors can already execute tasks beyond the reach of classical simulation, albeit for artificial problems. At this point, it is essential to design error metrics that test the experimental accuracy of quantum algorithms with potential for a practical quantum advantage. The distinction between coherent errors and incoherent errors is crucial, as they often involve different error suppression tools. The first class encompasses miscalibrations of control signals and crosstalk, while the latter is usually related to stochastic events and unwanted interactions with the environment. We introduce the incoherent infidelity as a measure of incoherent errors and present a scalable method for measuring it. This method is applicable to generic quantum evolutions subjected to time-dependent Markovian noise. Moreover, it provides an error quantifier for the target circuit, rather than an error averaged over many circuits or quantum gates. The estimation of the incoherent infidelity is suitable to assess circuits with sufficiently low error rates, regardless of the circuit size, which is a natural requirement to run useful computations.
Quantum processors can already execute tasks beyond the reach of classical simulation, albeit for artificial problems. At this point, it is essential to design error metrics that test the experimental accuracy of quantum algorithms with potential for a practical quantum advantage. The distinction between coherent errors and incoherent errors is crucial, as they often involve different error suppression tools. The first class encompasses miscalibrations of control signals and crosstalk, while the latter is usually related to stochastic events and unwanted interactions with the environment. We introduce the incoherent infidelity as a measure of incoherent errors and present a scalable method for measuring it. This method is applicable to generic quantum evolutions subjected to time-dependent Markovian noise. Moreover, it provides an error quantifier for the target circuit, rather than an error averaged over many circuits or quantum gates. The estimation of the incoherent infidelity is suitable to assess circuits with sufficiently low error rates, regardless of the circuit size, which is a natural requirement to run useful computations.
Abstract This work introduces a method for quantifying errors in quantum computations using multiple echoes of a target circuit. Our approach addresses a gap in the range of available benchmarking methods: unlike existing approaches that evaluate the average performance of a device, circuit, or gate, our method estimates the error in a target computation using the same initial state and circuit as the computation itself. It therefore captures how noise manifests in the specific computation of interest. We present two variants of the approach. The first estimates incoherent errors through purity loss, while the second estimates the echo infidelity, which captures both incoherent errors and non-invertible coherent errors, such as crosstalk. The purity-loss method applies to low-error circuits, or layers of gates, regardless of system size. The echo-infidelity method applies to circuits of arbitrary size and remains effective even at high error rates. Because our approach does not rely on an explicit noise model, it can complement methods that provide more detailed error information by testing the validity of the sparsity assumptions underlying those models. Finally, we discuss platforms on which our method can be implemented immediately.
This review synthesizes current understanding of decoherence pathways across leading hardware platforms and explains why several experimentally observed noise features—drift, burst events, coherent components, correlated and non-Markovian structure, and leakage—can be disproportionately damaging for QEC. Decoherence remains the dominant impediment to scalable quantum computing because it is not a single error mechanism but a system-level phenomenon arising from materials defects, electromagnetic loss, control electronics, measurement backaction, and the broader environment in which a processor operates. Quantum error correction (QEC) is designed to algorithmically suppress physical noise, yet its practical success depends on how closely real devices satisfy the assumptions under which fault tolerance is proved: approximate locality, weak temporal correlations, sufficiently stochastic error statistics, low leakage, and reliable syndrome extraction. We then evaluate fundamental and engineering challenges that shape the viability of QEC at scale: syndrome measurement fidelity, correlated error suppression, decoding latency and classical co-processing, architectural constraints (connectivity, crosstalk, calibration overhead), and the resource cost of implementing a universal fault-tolerant gate set. Recent demonstrations of below-threshold behaviour and “break-even” regimes show that QEC is transitioning from theory to practice, but also clarify what remains unresolved: maintaining stable noise below fault-tolerance targets over long times, scaling to many logical qubits with low correlated-error rates, and integrating hardware-aware codes and decoders. We conclude with research priorities that treat decoherence and QEC as part of a co-designed stack spanning device physics, control, architecture, and algorithms.
Abstract We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In particular, we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment.
Abstract Fidelity is one of the most valuable and commonly used metrics for assessing the performance of quantum circuits on error-prone quantum processors. Several approaches have been proposed to estimate circuit fidelity without executing it on quantum hardware, but they often face limitations in scalability or accuracy. In this work, we present a comprehensive theoretical framework to predict the fidelity of quantum circuits under depolarizing noise. Building on theoretical results, we propose an efficient fidelity estimation algorithm based on device calibration data. The method is thoroughly validated through simulation and execution on real hardware, demonstrating improved accuracy compared to state-of-the-art alternatives, with enhancements in prediction R 2 ranging from 4.96% to 213.54%. The proposed approach provides a scalable and practical tool for benchmarking quantum hardware, comparing quantum software techniques such as compilation methods, obtaining computation bounds for quantum systems, and guiding hardware design decisions, making it a critical resource for developing and evaluating quantum computing technologies.
Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it is no longer always feasible to use classical simulations to directly check the correctness of quantum computations. Without practical methods for quantifying the accuracy with which a quantum algorithm has been executed, it is difficult to establish trust in the results of a quantum computation. Here we solve this problem, by introducing a simple and efficient technique for measuring the fidelity with which an as-built quantum computer can execute an algorithm. Our technique converts the algorithm's quantum circuits into a set of closely related ``mirror circuits'' whose success rates can be efficiently measured. It enables measuring the fidelity of quantum algorithm executions both in the near-term, with algorithms run on hundreds or thousands of physical qubits, and into the future, with algorithms run on logical qubits protected by quantum error correction.
Evaluating the reliability of noisy quantum circuits is essential for implementing quantum algorithms on noisy quantum devices. While state fidelity is the most faithful indicator of circuit reliability, it is experimentally and computationally prohibitive to obtain. Alternative metrics, although easier to compute, often fail to accurately reflect circuit reliability. We propose a fine-grained, scalable, and interpretable framework for efficient reliability evaluation of noisy quantum circuits. We introduce the Noise Proxy Circuit (NPC), which removes all logical operations while preserving the complete sequence of noise channels, thereby providing an abstraction of cumulative noise effects. Based on the NPC, we define Proxy Fidelity, a reliability metric that quantifies both qubit-level and circuit-level reliability. We further develop an analytical algorithm to estimate Proxy Fidelity under depolarizing, thermal relaxation, and SPAM error channels. The proposed framework achieves fidelity-level reliability estimation while remaining execution-free, scalable, and interpretable. Experimental results on real and simulated IBM quantum devices show that our method accurately estimates circuit fidelity, with an average absolute difference (AAD) ranging from 0.031 to 0.069 across diverse circuits and devices.