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ACM Transactions on Quantum Computing

Quantum Measurement Classification Using Statistical Learning

Zachery Utt, Daniel Volya, Prabhat Mishra

Published Feb 9, 2024• 7 citations
Publisher

Abstract

Interpreting the results of a quantum computer can pose a significant challenge due to inherent noise in these mesoscopic quantum systems. Quantum measurement, a critical component of quantum computing, involves determining the probabilities linked with quantum states post-multiple circuit computations based on quantum readout values provided by hardware. While there are promising classification-based solutions, they can either misclassify or necessitate excessive measurements, thereby proving to be costly. This article puts forth an efficient method to discern the quantum state by analyzing the probability distributions of data post-measurement. Specifically, we employ cumulative distribution functions to juxtapose the measured distribution of a sample against the distributions of basis states. The efficacy of our approach is demonstrated through experimental results on a superconducting transmon qubit architecture, which shows a substantial decrease (88%) in single qubit readout error compared to state-of-the-art measurement techniques. Moreover, we report additional error reduction (12%) compared to state-of-the-art measurement techniques when our technique is applied to enhance existing multi-qubit classification techniques. We also demonstrate the applicability of our proposed method for higher dimensional quantum systems, including classification of single qutrits as well as multiple qutrits.

DOI
10.1145/3644823

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Interpreting the results of a quantum computer can pose a significant challenge due to inherent noise in these mesoscopic quantum systems. Quantum measurement, a critical component of quantum computing, involves determining the probabilities linked with quantum states post-multiple circuit computations based on quantum readout values provided by hardware. While there are promising classification-based solutions, they can either misclassify or necessitate excessive measurements, thereby proving to be costly. This article puts forth an efficient method to discern the quantum state by analyzing the probability distributions of data post-measurement. Specifically, we employ cumulative distribution functions to juxtapose the measured distribution of a sample against the distributions of basis states. The efficacy of our approach is demonstrated through experimental results on a superconducting transmon qubit architecture, which shows a substantial decrease (88%) in single qubit readout error compared to state-of-the-art measurement techniques. Moreover, we report additional error reduction (12%) compared to state-of-the-art measurement techniques when our technique is applied to enhance existing multi-qubit classification techniques. We also demonstrate the applicability of our proposed method for higher dimensional quantum systems, including classification of single qutrits as well as multiple qutrits.
Quantum measurement is one of the critical steps in quantum computing that determines the probabilities associated with qubit states after conducting several circuit ex-ecutions and measurements. As a mesoscopic quantum system, real quantum computers are prone to noise. Therefore, a major challenge in quantum measurement is how to correctly inter-pret the noisy results of a quantum computer. While there are promising classification based solutions, they either produce incorrect results (misclassify) or require many measurements (expensive). In this paper, we present an efficient technique to estimate a qubit's state through analysis of probability distributions of post-measurement data. Specifically, we estimate the state of a qubit using cumulative distribution functions to compare the measured distribution of a sample with the distributions of basis states∣0⟩\vert 0\rangle∣0⟩and∣1⟩\vert 1\rangle∣1⟩. Our experimental results demonstrate a drastic reduction (78%) in single qubit readout error. It also provides significant reduction (12%) when used to boost existing multi-qubit discriminator models.
Quantum computers promise a potentially disruptive approach to improving computation in fields such as physics, chemistry, cryptography, optimisation, and machine learning. However, testing quantum computations for faults is currently impractical because of the existence of noise and errors associated with the output. Executing in a quantum system a circuit with only a few valid output states can generate a significant number of implausible states that have zero probability in an ideal computation. Among other sources of noise, readout errors come from the difficulty of discriminating a measurement between 0 and 1 for the different qubits. These issues are affected by readout drift, requiring regular recalibration of the process. In this paper, we provide a novel technique for post-computation analysis of the output probability distributions that permits better discrimination of kerneled data, delaying the need for recalibration. We achieve this by altering the linear discrimination of the final output states by way of a dynamic state selection process that combines Gaussian mixture models with a probability threshold. As an initial assessment of the technique we examine its effect on three to five qubits GHZ states. Our results on almost every one of nine IBM quantum computers show that the number of implausible states is reduced significantly and that the resulting probability distribution is closer to the expected one.
Quantum computing has shown considerable promise for compute-intensive tasks in recent years. For instance, classification tasks based on quantum neural networks (QNN) have garnered significant interest from researchers and have been evaluated in various scenarios. However, the majority of quantum classifiers are currently limited to binary classification tasks due to either constrained quantum computing resources or the need for intensive classical post-processing. In this paper, we propose an efficient quantum multi-classifier called MORE, which stands for measurement and correlation based variational quantum multi-classifier. MORE adopts the same variational ansatz as binary classifiers while performing multi-classification by fully utilizing the quantum information of a single readout qubit. To extract the complete information from the readout qubit, we select three observables that form the basis of a two-dimensional Hilbert space. We then use the quantum state tomography technique to reconstruct the readout state from the measurement results. Afterward, we explore the correlation between classes to determine the quantum labels for classes using the variational quantum clustering approach. Next, quantum label-based supervised learning is performed to identify the mapping between the input data and their corresponding quantum labels. Finally, the predicted label is determined by its closest quantum label when using the classifier. We implement this approach using the Qiskit Python library and evaluate it through extensive experiments on both noise-free and noisy quantum systems. Our evaluation results demonstrate that MORE, despite using a simple ansatz and limited quantum resources, achieves advanced performance.
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 We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.
Abstract A qutrit represents a three-level quantum system, so that one qutrit can encode more information than a qubit, which corresponds to a two-level quantum system. This work investigates the potential of qutrit circuits in machine learning classification applications. We propose and evaluate different data-encoding schemes for qutrits, and find that the classification accuracy varies significantly depending on the used encoding. We therefore propose a training method for encoding optimization that allows to consistently achieve high classification accuracy, and show that it can also improve the performance within a data re-uploading approach. Our theoretical analysis and numerical simulations indicate that the qutrit classifier can achieve high classification accuracy using fewer components than a comparable qubit system. We showcase the qutrit classification using the encoding optimization method on a superconducting transmon qutrit, demonstrating the practicality of the proposed method on noisy hardware. Our work demonstrates high-precision ternary classification using fewer circuit elements, establishing qutrit quantum circuits as a viable and efficient tool for quantum machine learning applications.