Abstract Measurement errors limit the fidelity of sampling-based quantum tasks, yet extending error mitigation to sampling remains challenging. Here, we introduce a simple and scalable repetition-based scheme that mitigates measurement errors directly at the sampling level. By encoding each data qubit into multiple physical qubits prior to readout and applying majority-vote decoding, physical errors are converted into a higher-order process, enabling exponential suppression that persists despite realistic gate imperfections during encoding. Using experimental noise profiles from leading superconducting platforms, we demonstrate that a modest linear qubit overhead suppresses measurement errors by several orders of magnitude, significantly boosting fidelities for typical sampling tasks, such as measurement-based quantum computation and random circuit sampling. These results establish a practical, hardware-compatible, and scalable approach for improving the reliability of near-term quantum sampling experiments.
Abstract Measurement errors limit the fidelity of sampling-based quantum tasks, yet extending error mitigation to sampling remains challenging. Here, we introduce a simple and scalable repetition-based scheme that mitigates measurement errors directly at the sampling level. By encoding each data qubit into multiple physical qubits prior to readout and applying majority-vote decoding, physical errors are converted into a higher-order process, enabling exponential suppression that persists despite realistic gate imperfections during encoding. Using experimental noise profiles from leading superconducting platforms, we demonstrate that a modest linear qubit overhead suppresses measurement errors by several orders of magnitude, significantly boosting fidelities for typical sampling tasks, such as measurement-based quantum computation and random circuit sampling. These results establish a practical, hardware-compatible, and scalable approach for improving the reliability of near-term quantum sampling experiments.
Quantum error mitigation (QEM) infers noiseless expectation values from noisy variants of a target quantum circuit. Unlike quantum error correction, QEM requires no additional hardware resources and is therefore routinely employed in experiments on contemporary quantum processors. QEM strategies based on agnostic noise amplification (ANA) are intrinsically resilient to temporal noise drift during the execution of the experiment, but their sampling cost (runtime overhead) remains a major practical bottleneck. In this work, we introduce the virtual noise scaling framework and combine it with layered mitigation to further enhance performance. While virtual noise scaling consistently reduces sampling overhead, we identify a specific noise threshold for the layered mitigation approach. When the noise level is above this threshold, layered mitigation decreases the sampling overhead; conversely, when below it, the overhead increases. Notably, this threshold is circuit-independent and depends solely on the number of layers. For strong noise, the combination of virtual noise scaling and layered mitigation yields several orders of magnitude reduction in sampling overhead compared with conventional zero-noise extrapolation post-processing. As a result, mitigation tasks that once seemed unrealistic are now challenging but achievable. The proposed approach is compatible with dynamic circuits and can be seamlessly integrated with error detection and quantum error correction schemes. In addition, it is also applicable to ANA-based mitigation of mid-circuit measurements and preparation errors. Our findings extend to any constant-step amplification factors and therefore also apply to probabilistic error amplification (PEA) QEM. We validate our post-processing approach by applying it to previously reported experimental data, where we observe a substantial improvement in mitigation efficiency and accuracy.
Abstract Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which requires large qubit overhead, we turn to quantum error mitigation, in which we make use of extra measurements. Error extrapolation is an error mitigation technique that has been successfully implemented experimentally. Numerical simulation and heuristic arguments have indicated that exponential curves are effective for extrapolation in the large circuit limit with an expected circuit error count around unity. In this Article, we extend this to multi-exponential error extrapolation and provide more rigorous proof for its effectiveness under Pauli noise. This is further validated via our numerical simulations, showing orders of magnitude improvements in the estimation accuracy over single-exponential extrapolation. Moreover, we develop methods to combine error extrapolation with two other error mitigation techniques: quasi-probability and symmetry verification, through exploiting features of these individual techniques. As shown in our simulation, our combined method can achieve low estimation bias with a sampling cost multiple times smaller than quasi-probability while without needing to be able to adjust the hardware error rate as required in canonical error extrapolation.
Readout errors are one of the dominant sources of noise in current quantum processors, limiting both expectation-value estimation and sampling-based applications. Since they affect only the classical measurement outcomes, they can be addressed using classical coding techniques: immediately before measurement, each data qubit is redundantly encoded with ancilla qubits, and the resulting bit string is decoded either by post-selection or by majority voting. Unlike conventional readout error mitigation, which corrects only aggregate quantities such as expectation values, this approach operates on individual measurement shots and can therefore produce approximately corrected samples. We present a systematic cross-platform and cross-generation experimental evaluation of repetition-code readout error detection and correction. We benchmark the same protocol on IBM Heron r1-r3 superconducting processors and Quantinuum H1 and H2 trapped-ion processors while independently varying the code distance, hardware generation, and encoding layout. We find that both error detection and correction improve readout fidelity on every device and generation tested, even as the unencoded baseline improves substantially across successive hardware releases. At the same time, the value of additional redundancy depends strongly on the underlying hardware. On superconducting processors, the extra gate errors introduced by the encoding rapidly offset its benefits, whereas on trapped-ion processors the much lower gate error rates allow larger code distances to remain advantageous.
The pursuit of practical quantum utility on near-term quantum processors is critically challenged by their inherent noise. Quantum error mitigation (QEM) techniques are leading solutions to improve computation fidelity with relatively low qubit-overhead, while full-scale quantum error correction remains a distant goal. However, QEM techniques incur substantial measurement overheads, especially when applied to families of quantum circuits parameterized by classical inputs. Focusing on zero-noise extrapolation (ZNE), a widely adopted QEM technique, here we devise the surrogate-enabled ZNE (S-ZNE), which leverages classical learning surrogates to perform ZNE entirely on the classical side. Unlike conventional ZNE, whose measurement cost scales linearly with the number of circuits, S-ZNE requires only constant measurement overhead for an entire family of quantum circuits, offering superior scalability. Theoretical analysis indicates that S-ZNE achieves accuracy comparable to conventional ZNE in many practical scenarios, and numerical experiments on up to 100-qubit ground-state energy and quantum metrology tasks confirm its effectiveness. Our approach provides a template that can be effectively extended to other quantum error mitigation protocols, opening a promising path toward scalable error mitigation.
Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on quantum hardware because of its two main drawbacks: (i) the number of samples increases exponentially in the circuit depth/noise level, and (ii) the classical processing generally grows exponentially in the code distance, though exceptions exist. Additionally, the constant (but often large) overhead of embedding the code and logical operations on hardware can make accuracy worse instead of better. In this work, we seek to provide a clear picture of these opportunities and challenges for scaling quantum error detection on hardware. We do so by performing a detailed benchmarking study on real and simulated noisy quantum computers, using the repetition code and triangular color code for memory experiments and logical computations with up to 74 physical qubits. In addition to these benchmarks, we estimate the pseudothreshold of codes to map the frontier of error detection on current and future quantum computers. Despite the challenges, our results show strong promise for scaling quantum error detection on hardware.
Abstract The pursuit of practical quantum utility on near-term quantum processors is critically challenged by their inherent noise. Quantum error mitigation (QEM) techniques are leading solutions to improve computation fidelity with relatively low qubit-overhead, while full-scale quantum error correction remains a distant goal. However, QEM techniques incur substantial measurement overheads, especially when applied to families of quantum circuits parameterized by classical inputs. Focusing on zero-noise extrapolation (ZNE), a widely adopted QEM technique, here we devise the surrogate-enabled ZNE (S-ZNE), which leverages classical learning surrogates to perform ZNE entirely on the classical side. Unlike conventional ZNE, whose measurement cost scales linearly with the number of circuits, S-ZNE requires only constant measurement overhead for an entire family of quantum circuits, offering superior scalability. Theoretical analysis indicates that S-ZNE achieves accuracy comparable to conventional ZNE in many practical scenarios, and numerical experiments on up to 100-qubit ground-state energy and quantum metrology tasks confirm its effectiveness. Our approach provides a template that can be effectively extended to other quantum error mitigation protocols, opening a promising path toward scalable error mitigation.