Mitigating Errors on Superconducting Quantum Processors Through Fuzzy Clustering
Halima Giovanna Ahmad, Roberto Schiattarella, P. Mastrovito, Angela Chiatto, Anna Levochkina, Martina Esposito, Domenico Montemurro, Giovanni Piero Pepe, Alessandro Bruno, Francesco Tafuri, Autilia Vitiello, Giovanni Acampora, D. Massarotti
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.
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.
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.
Accurate quantum state discrimination is critical for reliable qubit readout in current superconducting quantum processors, as it enables precise measurement outcomes, reduces readout-induced errors, and improves the overall reliability of quantum algorithm execution. Recently, machine learning (ML) techniques have been explored to enhance quantum state discrimination, outperforming traditional methods based on static thresholds. However, these approaches rely on hard-decision schemes that assign binary outcomes without accounting for readout uncertainty, thereby disregarding signal-level variations that can degrade measurement fidelity. This article introduces a measurement-aware classification approach based on Fuzzy C-means (FCM) clustering combined with data filtering, enabling soft-decision readout discrimination through confidence-based shot selection. Experimental validation was conducted on four different real IBM quantum devices, including single- and two-qubit readout scenarios, as well as multi-qubit circuits preparing GHZ and W-state with up to 10 qubits. Results show that the proposed method consistently outperforms state-of-the-art ML-based discriminators in terms of assignment fidelity and state reconstruction accuracy, demonstrating its effectiveness for enhancing readout quality in near-term quantum computing platforms. Quantitatively, the FCM-based discriminator yields 2–3% assignment fidelity improvements in single- and two-qubit readout and statistically significant gains in over 94% of GHZ and 97% of W multi-qubit experiments.
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.
Quantum devices in the noisy intermediate-scale quantum (NISQ) era are highly susceptible to different types of quantum noise, which directly impact the reliability of experimental results. This work provides a characterization of error behavior arising from quantum noises on IBM's superconducting quantum processor, offering practical insights for algorithm design, benchmarking, and error-mitigation strategies on a real superconducting quantum processor in the NISQ era. The study begins with the measurement of the basis state, without applying any gate, to quantify state-preparation and measurement (SPAM) errors. Additionally, the errors are further quantified due to the application of single-qubit Pauli-X, two-qubit CNOT gate and other multi-qubit Controlled-X gates. Each circuit was executed with 1024 shots, and the percentage error between the expected and observed outputs was computed. The results show that the single-qubit Pauli-X gate exhibits relatively low errors in comparison with the two-qubit CNOT gate, whereas other multi-qubit Controlled-X gates lead to significantly higher deviations. This work also analyzes the noise effect of a fourqubit Controlled-X gate being implemented using a three-qubit Controlled-X gate with an extra auxiliary qubit, and the result shows a significant reduction in the error rate.
Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to perform quantum computation in good accuracy with these machines we need to develop alternative approaches for mitigating quantum computational errors. In this work, we propose quantum error mitigation (QEM) scheme for quantum computational errors which occur due to couplings with environments during gate operations, i.e., decoherence. To establish our QEM scheme, first we estimate the quantum noise effects on single-qubit states and represent them as groups of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM scheme is conducted by subtracting expectation values generated by the quantum-noise-effect circuit groups from those obtained by the quantum circuits for the quantum algorithms under consideration. As a result, the quantum noise effects are reduced, and we obtain approximately the ideal expectation values via the quantum-noise-effect circuit groups and the numbers of elementary quantum circuits composing them scale polynomial with respect to the products of the depths of quantum algorithms and the numbers of register bits. To numerically demonstrate the validity of our QEM scheme, we run noisy quantum simulations of qubits under amplitude damping effects for four types of quantum algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience processors and examine its efficacy. Consequently, the validity of our scheme is verified via both the quantum simulations and the quantum computations on the real quantum devices. Our QEM scheme is solely composed of quantum-computational operations (quantum gates and measurements), and thus, it can be conducted by any type of quantum device. In addition, it can be applied to error mitigation for many other types of quantum noise effects as well as noisy quantum computing of long-depth quantum algorithms.
Noisy Intermediate-Scale Quantum (NISQ) computers suffer from gate errors, decoherence, and readout noise that can severely impact even small quantum circuits. In this work, the application of error mitigation techniques was investigated to a simple two-bit quantum comparator circuit executed on real IBM Quantum hardware. The 2-bit comparator is a basic quantum logic circuit that compares two 2-qubit binary numbers and outputs whether the first number is greater than, equal to, or less than the second. This comparator was implemented using Qiskit and studied its performance under realistic noise. This study on error mitigation concentrates on dynamical decoupling (DD), which is a coherent error suppression strategy that cancels coherent errors by inserting echo pulse sequences during idle time periods. The results demonstrate that dynamical decoupling improves accuracy for the comparator circuit - accurate outcomes are closer to the ideal outcome in the absence of noise. These results show that dynamical decoupling yields notable accuracy improvements for the comparator circuit - bringing measured outcomes closer to the ideal noiseless results. A performance analysis (including a bar-chart of accuracy after mitigation vs. before mitigation simulation) is presented to quantify these improvements. Finally, the implications of applying error mitigation in small quantum circuits and its relevance for near-term quantum computing are also discussed, where such techniques can enhance the reliability of quantum computations in the absence of full quantum error correction.