Recently, Quantum Computing is entered in the so-called Noisy Intermediate-Scale Quantum (NISQ) era, where devices characterized by a few number of qubits are potentially able to overcome classical computers in performing specific tasks. However, noise in quantum operators still limits the size of quantum circuits that can be run in a reliable way. Consequently, there is a strong need for error mitigation approaches aimed at increasing reliability in quantum computation and making this paradigm really useful and productive in real world applications. In this paper, a fuzzy method, such as Fuzzy C-Means (FCM) clustering, has been used, for the very first time, to support the identification of matrices for error mitigation in quantum measurement. As shown in experiments, mitigation matrices identified with the support of FCM are able to strongly reduce error in computation when compared to mitigation matrices conventionally identified, like those used by IBM in its quantum library named Qiskit.
Recently, Quantum Computing is entered in the so-called Noisy Intermediate-Scale Quantum (NISQ) era, where devices characterized by a few number of qubits are potentially able to overcome classical computers in performing specific tasks. However, noise in quantum operators still limits the size of quantum circuits that can be run in a reliable way. Consequently, there is a strong need for error mitigation approaches aimed at increasing reliability in quantum computation and making this paradigm really useful and productive in real world applications. In this paper, a fuzzy method, such as Fuzzy C-Means (FCM) clustering, has been used, for the very first time, to support the identification of matrices for error mitigation in quantum measurement. As shown in experiments, mitigation matrices identified with the support of FCM are able to strongly reduce error in computation when compared to mitigation matrices conventionally identified, like those used by IBM in its quantum library named Qiskit.
Abstract Quantum utility is severely limited in superconducting quantum hardware until now by the modest number of qubits and the relatively high level of control and readout errors, due to the intentional coupling with the external environment required for manipulation and readout of the qubit states. Practical applications in the Noisy Intermediate Scale Quantum (NISQ) era rely on Quantum Error Mitigation (QEM) techniques, which are able to improve the accuracy of the expectation values of quantum observables by implementing classical post‐processing analysis from an ensemble of repeated noisy quantum circuit runs. In this work, a recent QEM technique that uses Fuzzy C‐Means (FCM) clustering to specifically identify measurement error patterns is focused. For the first time, a proof‐of‐principle validation of the technique on a two‐qubit register, obtained as a subset of a real NISQ five‐qubit superconducting quantum processor based on transmon qubits is reported. It is demonstrated that the FCM‐based QEM technique allows for reasonable improvement of the expectation values of single‐ and two‐qubit gates‐based quantum circuits, without necessarily invoking state‐of‐the‐art coherence, gate, and readout fidelities.
Noisy Intermediate Scale Quantum (NISQ) devices are expected to demonstrate the real potential of quantum computing in solving hard problems. However, quantum noise that characterizes this kind of devices still remains an obstacle for their practical exploitation in real world scenarios. As a consequence, there is a strong emergence for error correction techniques aimed at making NISQ devices stable and fully operative. Unfortunately, current approaches for quantum error correction are prohibitive for NISQ devices because of the enormous multiplicative cost in resources that they require. For this reason, so-called quantum error mitigation methods are emerging as alternative approaches able to attenuate the quantum error as much as possible, without requiring a strong additional computational effort. Among the most error-prone operations, there is surely the quantum measurement. Conventionally, mitigation methods for quantum measurement error compute a so-called mitigation matrix capable of correcting results outputted by a quantum processor. In this paper, a new measurement error mitigation approach based on genetic algorithms is proposed to learn an appropriate mitigation matrix. As shown in the experimental session, the proposed measurement error mitigation method is comparable with or better than a conventional algebraic approach in terms of the Hellinger fidelity.
Quantum computing is entering a transitional regime between noisy intermediate-scale quantum (NISQ) processing and early fault-tolerant quantum computation (FTQC), in which increasingly capable hardware is beginning to support repeated syndrome measurements, partial error correction, and logical-qubit operations, while residual physical and logical errors remain non-negligible. In this regime, error suppression, error mitigation, and quantum error correction are increasingly better viewed as complementary layers of a unified error-reduction strategy rather than as separate approaches, with each acting at a different stage of the quantum computation to improve simulation reliability. Thus, in this review, we provide a practical and forward-looking overview of the principal hardware error sources and the corresponding error suppression and mitigation methods for reducing their impact across the current NISQ-FTQC transition. We discuss hardware-aware circuit design, coherent-error suppression, readout mitigation, noise extrapolation, classical inference, and software-supported workflows, with particular emphasis on their implementation on actual quantum processors. We further examine how error mitigation techniques can be adapted to encoded and logical-qubit settings so that they can operate alongside quantum error correction to suppress residual logical errors and improve the accuracy of computation in the early fault-tolerant regime.
In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation will be a necessary tool to extract useful performance out of quantum devices. However, there is a big gap between the noise models often assumed by error mitigation techniques and the actual noise on quantum devices. As a consequence, there arises a gap between the theoretical expectations of the techniques and their everyday performance. Cloud users of quantum devices in particular, who often take the devices as they are, feel this gap the most. How should they parametrize their uncertainty in the usefulness of these techniques and be able to make judgement calls between resources required to implement error mitigation and the accuracy required at the algorithmic level? To answer the first question, we introduce hypothesis testing within the framework of quantum error mitigation and for the second question, we propose an inclusive figure of merit that accounts for both resource requirement and mitigation efficiency of an error mitigation implementation. The figure of merit is useful to weigh the trade-offs between the scalability and accuracy of various error mitigation methods. Finally, using the hypothesis testing and the figure of merit, we experimentally evaluate 16 error mitigation pipelines composed of singular methods such as zero noise extrapolation, randomized compilation, measurement error mitigation, dynamical decoupling, and mitigation with estimation circuits. In total our data involved running 275,640 circuits on two IBM quantum computers.
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.
In the past few years, the first commercially available quantum computers have emerged, in an early stage of development, the so-called Noisy Intermediate-Scale Quantum (NISQ) era. Although these devices are still very prone to errors of different natures, they also have shown to deal successfully with small computational problems. Nowadays, one of the challenges in quantum computation is exactly to be able to show that quantum computers are useful, whereby mitigating the effects of the faulty hardware is pivotal. Recently, a wide range of quantum error mitigation techniques have been proposed and successfully implemented, alternative to quantum error correction codes. Herein, we discuss several types of noise in a quantum computer and techniques available to mitigate them, as well as their limitations and conditions of applicability. We also suggest an hierarchy for them, towards the conception of a layered software framework of error mitigation techniques, and implement some of them in a quantum simulation of the Heisenberg model on an IBM quantum computer, improving the fidelity of the simulation by 2.8x.