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ACM Transactions on Quantum Computing

Qubit Readout Discrimination through Fuzzy Clustering

Giovanni Acampora, Roberto Schiattarella, Autilia Vitiello

Published Oct 3, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1145/3847660

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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.
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.
Accurate quantum state readout is crucial for error correction and algorithms, but measurement errors are detrimental. Readout fidelity is typically limited by a poor signal-to-noise ratio (SNR) and energy relaxation (T1T_1T1​ decay), a significant problem for superconducting qubits. While most approaches classify results using clustering algorithms on integrated readout signals, these methods cannot distinguish a qubit that was initially in the ground state from one that decayed to it during measurement. We instead propose using machine learning (ML) on the raw, non-integrated analog signal. We apply time-series classification models, such as a long short-term memory (LSTM) network, to the full data trajectory. We find that our LSTM model, combined with filtering and feature engineering, consistently outperforms clustering. The largest improvements come from reclassifying points in the boundary regions between clusters. These points correspond to atypical measurement records, likely due to transient or noisy features lost during data integration. By retaining temporal information, sequence-aware models like LSTMs can better discriminate these trajectories, whereas clustering methods based on integrated values are more prone to misclassification.
Abstract Measurement errors in quantum computers are very detrimental to quantum computations. The ability to efficiently and accurately readout quantum states is crucial for quantum error correction schemes and quantum algorithms. Readout fidelity is typically limited by a poor signal-to-noise (SNR) ratio between the quantum states we intend to classify, as well as energy relaxation (e.g., T1T_1T1​ decay) from an excited state to a lower state during readout. Superconducting quantum bits (qubit), one of the leading candidates for scalable quantum computing hardware, are particularly limited by energy relaxation due to their relatively short coherence times. While most approaches for classifying the results of readout on superconducting qubits typically utilize clustering algorithms (e.g., a Gaussian mixture model) on integrated readout signals, these cannot distinguish between a quantum bit that was in the ground state prior to measurement from a qubit that decays to the ground state during measurement. For this reason, we instead propose using machine learning (ML) on the raw (non-integrated) analog signal and classification models on the full time series data (i.e., the \emph{trajectory}). We observe that time series classification methods, such as our chosen long short-term memory (LSTM) model, in combination with filtering and feature engineering techniques, consistently outperform clustering models. In particular, we find that the largest improvements come from reclassifying points in the boundary regions between neighboring clusters. These boundary points correspond to measurement records that deviate from the typical cluster, likely due to transient or noisy features in the signal that are not captured when the data is integrated. By retaining temporal information, sequence-aware models such as LSTMs can better discriminate these trajectories, whereas clustering methods based on integrated values are more prone to misclassifications.
Reliable qubit readout is a critical bottleneck toward fault-tolerant quantum computing (FTQC). In superconducting quantum processors, readout operations are both error-prone and high-latency. These challenges become more severe in frequency-multiplexed architectures, where signal crosstalk among neighboring qubits significantly degrades readout fidelity. Existing machine learning (ML)-based approaches rely on feed-forward neural networks (FNNs) that suffer from large parameter sizes and lack an end-to-end network that jointly addresses relaxation errors and discriminates qubit states. In this work, we present a multi-stage qubit state discriminator based on the Mamba model, which enables efficient sequence modeling with linear complexity. The first stage performs initial state discrimination, followed by a refinement stage that identifies and mitigates relaxation-induced errors. Our lightweight model achieves a geometric mean readout fidelity of 0.906, outperforming the best-reported state-of-the-art method while reducing parameter size by 49.6%; our optimal model further reaches 0.911. Both models remain robust across varying input trace lengths, maintaining a high fidelity of 0.893 at readout durations as short as 500 nsnsns, achieving up to a 26% reduction in logical error rate over prior work in quantum error correction (QEC).
Current methods for classifying measurement trajectories in superconducting qubit systems produce fidelities systematically lower than those predicted by experimental parameters. Here, we place current classification methods within the framework of machine learning (ML) algorithms and improve on them by investigating more sophisticated ML approaches. We find that nonlinear algorithms and clustering methods produce significantly higher assignment fidelities that help close the gap to the fidelity possible under ideal noise conditions. Clustering methods group trajectories into natural subsets within the data, which allows for the diagnosis of systematic errors. We find large clusters in the data associated with T1 processes and show these are the main source of discrepancy between our experimental and ideal fidelities. These error diagnosis techniques help provide a path forward to improve qubit measurements.
A limiting factor for readout fidelity for superconducting qubits is the relaxation of the qubit to the ground state before the time needed for the resonator to reach its final target state. A technique known as excited state promoted (ESP) readout was proposed to reduce this effect and further improve the readout contrast on superconducting hardware. In this work, we use readout data from five-qubit IBMQ devices to measure the effectiveness of using deep neural networks, like feedforward neural networks, and various classification algorithms, like k-nearest neighbors, decision trees, and Gaussian naive Bayes, for single-qubit and multi-qubit discrimination. These methods were compared to standardly used linear and quadratic discriminant analysis algorithms based on their qubit-state-assignment fidelity performance, robustness to readout crosstalk, and training time.