We present a modular error mitigation protocol for running $\mathsf{BQP}$ computations on a quantum computer with time-dependent noise. Utilising existing tools from quantum verification and measurement-based quantum computation, our protocol interleaves standard computation rounds alongside test rounds for noise sampling and inherits an exponential bound (in the number of circuit runs) on the probability that a returned classical output is correct. We introduce a post-selection technique called \textit{basketing} to address time-dependent noise and reduce overhead. The result is an error mitigation protocol which requires minimal noise assumptions, making it straightforwardly implementable on existing, NISQ devices. We perform a demonstration of the protocol using classical noisy simulation, presenting a universal measurement pattern which directly maps to (and can be tiled on) the heavy-hex layout of current IBM hardware.
We present a modular error mitigation protocol for running BQP computations on a quantum computer with time-dependent noise. Utilising existing tools from quantum verification and measurement-based quantum computation, our protocol interleaves standard computation rounds alongside test rounds for noise sampling and inherits an exponential bound (in the number of circuit runs) on the probability that a returned classical output is correct. We introduce a post-selection technique called \textit{basketing} to address time-dependent noise and reduce overhead. The result is an error mitigation protocol which requires minimal noise assumptions, making it straightforwardly implementable on existing, NISQ devices. We perform a demonstration of the protocol using classical noisy simulation, presenting a universal measurement pattern which directly maps to (and can be tiled on) the heavy-hex layout of current IBM hardware.
We present a modular error mitigation protocol for running bounded-error quantum polynomial time (BQP) computations on a quantum computer with time-dependent noise. Utilizing existing tools from quantum verification and measurement-based quantum computation, our protocol interleaves standard computation rounds alongside test rounds for noise sampling and inherits an exponential bound (in the number of circuit runs) on the probability that a returned classical output is correct. We introduce a postselection technique called to address time-dependent noise and reduce overhead. The result is an error mitigation protocol which requires minimal noise assumptions, making it straightforwardly implementable on existing, noisy intermediate-scale quantum devices. We perform a demonstration of the protocol using classical noisy simulation, presenting a universal measurement pattern which directly maps to (and can be tiled on) the heavy-hex layout of current IBM hardware.
Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits efficiently classically simulable, thereby destroying any quantum advantage potentially offered by an ideal (noiseless) implementation of these circuits. Although the technique of quantum error correction (QEC) allows correcting these errors very accurately, QEC usually requires a large overhead of physical qubits which is not reachable with currently available quantum hardware. This has been the motivation behind the field of quantum error mitigation, which aims at developing techniques to correct an important part of the errors in quantum circuits, while also being compatible with current and near-term quantum hardware. In this work, we present a technique for quantum error mitigation which is based on a technique from quantum verification, the so-called accreditation protocol, together with postselection. Our technique allows for correcting the expectation value of an observable O, which is the output of multiple runs of noisy quantum circuits, where the noise in these circuits is at the level of preparations, gates, and measurements. We discuss the sample complexity of our procedure and provide rigorous guarantees of errors being mitigated under some realistic assumptions on the noise. Our technique is tailored to time-dependent behaviors, as we allow for the output states to be different between different runs of the accreditation protocol. We validate our findings by running our technique on currently available quantum hardware.
Abstract Quantum computing has recently emerged as a novel paradigm for solving problems otherwise intractable on classical computers, yet the practical progress of quantum computers is severely impacted by noise, decoherence, and imperfect gate operations in Noisy Intermediate-Scale Quantum (NISQ) devices. Specific to IBM Quantum hardware, imperfections due to readout error, gate errors, and device drift, which depends on time, resolves limits for the accuracy of outputs from our algorithms. The mitigation strategies currently used, for example, Measurement Error Mitigation (MEM), Zero Noise Extrapolation (ZNE), and Clifford Data Regression (CDR), offer improvement over raw, unmitigated outputs, but they are static and not dynamic; the reduction of noise in within an NISQ device is temporal and can vary in patterns that are non-zero. In addition to this, using the conventional methods provides inconsistent and suboptimal results.This study will provide enhanced reliability with respect to performing quantum computation on IBM Quantum hardware with a unique mitigation framework that is adaptive and computationally efficient for a high-fidelity output. The problem taken on here is the failure of existing error mitigation strategies to provide adaptive noise compensation, as they assume a statically-distributed error, despite the performance-related characteristics already being documented in regards to calibration drift and variation over time.To achieve this, we propose a Hybrid Adaptive Error Mitigation (HAEM) approach that includes baseline measurement error mitigation and an additional correction layer that utilizes realtime calibration information, along with lightweight machine learning models. The approach can be broken down into three steps: (i) perform standard measurement error mitigation to reduce classical readout noise, (ii) execute compact calibration circuits, such as Bell states, GHZ states and Clifford benchmarks to capture then current error profile of the device, and (iii) use a lightweight machine learning model (having been trained on historical and newest calibration data) to dynamically change the mitigation weights applied for the target quantum algorithm. All implementation is done using Qiskit Runtime to ensure low-latency execution, and we completed experiments on both Qiskit Aer noisy simulators and IBM Quantum devices.Initial results suggest HAEM improved the outputs of quantum algorithms' fidelity compared to the unmitigated runs and the baseline measurement error mitigation (MEM) runs. On the noisy simulators, HAEM increased fidelity from a raw performance of 0.65 to 0.87, nearly a 34% improvement. In fairer hardware-like scenarios, fidelity-on-average was persistently 12% better than MEM, with nearly equal time duration for the additional adaptive measurements. The adaptive aspect of HAEM consistently supported subsequent calibration cycles of the device and was effective to continue providing fidelity improvements despite the static mitigation performance degrading.To sum up, the proposed HAEM framework is a modern and viable alternative for error mitigation which brings together the benefits of baseline approaches with corrections that are driven by fixed-function error-corrective, adaptive learning. As both learning-based and standard baseline approaches can only achieve fixed levels of performance, HAEM, through its use of noise mitigation both at execution time and through correlating it with standard data, provides a route towards reliable quantum computations on current IBM hardware. HAEM also presents a contribution to the NISQ error-resilient landscape, and however it is intended that it will continue to improve future applications of hybrid workflows of quantum and classical computation where error mitigation and resilience is important.
Quantum error mitigation (QEM) is critical for extracting reliable computations from noisy quantum processors, proving itself essential not only in the near term but also as a valuable supplement to fully fault-tolerant systems in the future. Despite the necessity, practical QEM deployment still confronts challenges, including the excessive cost of sampling quantum circuits and reliance on unrealistic assumptions such as gate-independent noise. In this paper, we propose Classical Noise Inversion (CNI), which shifts the QEM from sampling diverse quantum circuits to repeated single-circuit measurement, a drastic cost reduction given that the former incurs far heavier time overhead than the latter on realistic quantum hardware. We target general noise models and establish critical conditions for their classical tractability, under which CNI remains effective. For noise models that violate the condition, we propose partial CNI, which mitigates the classically tractable factor of noise via CNI and mitigates the other part via probabilistic error cancellation tailored to gate-dependent noise. To minimize the sampling overhead, we introduce noise compression, which groups noise components with equivalent effects on measurement outcomes, thereby attaining theoretically optimal error-mitigation overhead. The proposed protocols are particularly efficient for error-propagatable circuits, including adaptive universal quantum computing represented by Clifford+T fault-tolerant circuits, and generalized measurement represented by classical shadows. To demonstrate the practical merits of CNI, we integrate it with thrifty classical shadow, and use analysis and numerical simulations to show its advantages in both efficiency and accuracy over existing approaches.
Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named ``Noiseless Output Extrapolation" and ``Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.
Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\ensuremath{\epsilon}n$, where $\ensuremath{\epsilon}$ is the maximum error rate and n is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\ensuremath{\le}12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.