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IEEE International Conference on Quantum Computing and Engineering (QCE)

Discriminating Quantum States with Quantum Machine Learning

David Quiroga, Prasanna Date, Raphael C. Pooser

Published Oct 1, 2021• 8 citations
Publisher

Abstract

An important use-case for machine learning (ML) is that of determining readout results in quantum computers. In quantum computing (QC), classical ML models are currently being used to discriminate in-phase and quadrature (IQ) signal data to discriminate between quantum states, which is a fundamental QC operation. In our research we propose a Quantum K-Means (QK-Means) clustering technique to discriminate quantum states on the IBM Bogota quantum device, and compare its performance to the K-Means technique (its classical counterpart). We used both algorithms to perform a correlation analysis and probe cross-talk between couples of qubits on the device. We observed that QK-Means obtained test and training scores at par with the classical K-Means, and testing scores that were marginally lower than K-Means when the clusters weren’t visually separable. The training times for QK-Means were observed to be at par with an implementation of the K-Means that was not optimized. In this case, we concluded a weak correlation with a Pearson correlation coefficient of 0.2 on the (1, 2) and (2, 3) qubit couples. After analyzing the training scores, we also conclude that the 1 qubit has the worst performance at readout evidenced by the signal data not being visually separable and the low scores obtained on both clustering algorithms compared to the other qubits. Its poor performance is further verified by the calibration data showing a high readout error of 8,4%. This technique can be used to find correlations present in readout of quantum circuits and to determine cross-talk.

DOI
10.1109/qce52317.2021.00088

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An important use-case for machine learning (ML) is that of determining readout results in quantum computers. In quantum computing (QC), classical ML models are currently being used to discriminate in-phase and quadrature (IQ) signal data to discriminate between quantum states, which is a fundamental QC operation. In our research we propose a Quantum K-Means (QK-Means) clustering technique to discriminate quantum states on the IBM Bogota quantum device, and compare its performance to the K-Means technique (its classical counterpart). We used both algorithms to perform a correlation analysis and probe cross-talk between couples of qubits on the device. We observed that QK-Means obtained test and training scores at par with the classical K-Means, and testing scores that were marginally lower than K-Means when the clusters weren’t visually separable. The training times for QK-Means were observed to be at par with an implementation of the K-Means that was not optimized. In this case, we concluded a weak correlation with a Pearson correlation coefficient of 0.2 on the (1, 2) and (2, 3) qubit couples. After analyzing the training scores, we also conclude that the 1 qubit has the worst performance at readout evidenced by the signal data not being visually separable and the low scores obtained on both clustering algorithms compared to the other qubits. Its poor performance is further verified by the calibration data showing a high readout error of 8,4%. This technique can be used to find correlations present in readout of quantum circuits and to determine cross-talk.
Quantum machine learning (QML) algorithms have obtained great relevance in the machine learning (ML) field due to the promise of quantum speedups when performing basic linear algebra subroutines (BLAS), a fundamental element in most ML algorithms. By making use of BLAS operations, we propose, implement and analyze a quantum k-means (qk-means) algorithm with a low time complexity ofO(NKlog(D)I/C)\mathcal{O}(NK log(D)I/C)O(NKlog(D)I/C)to apply it to the fundamental problem of discriminating quantum states at readout. Discriminating quantum states allows the identification of quantum states∣0⟩\vert 0\rangle∣0⟩and∣1⟩\vert 1\rangle∣1⟩from low-level in-phase and quadrature signal (IQ) data, and can be done using custom ML models. In order to reduce dependency on a classical computer, we use the qk-means to perform state discrimination on the IBMQ Bogota device and managed to find assignment fidelities of up to 98.7% that were only marginally lower than that of the k-means algorithm. We also performed a cross-talk benchmark on the quantum device by applying both algorithms to perform state discrimination on a combination of quantum states and using Pearson Correlation coefficients and assignment fidelities of discrimination results to conclude on the presence of cross-talk on qubits. Evidence shows cross-talk in the (1, 2) and (2, 3) neighboring qubit couples for the analyzed device.
Quantum computing is one of the most promising solutions for solving optimization problems in the healthcare world. Quantum computing development aims to light up the execution of a vast and complex set of algorithmic instructions. For its implementation, the machine learning models are continuously evolving. Hence, the new challenge is to improve the existing complex and critical machine learning training models. Therefore, the healthcare sector is shifting from a classical to a quantum domain to sustain patient-oriented attention to healthcare patrons. This paper presents a hybrid classical-quantum approach for training the unsupervised data models. In order to achieve good performance and optimization of the machine learning algorithms, a quantum k-means (QK-means) clustering problem was deployed on the IBM quantum simulators, i.e.,the IBM QASM simulator. In the first place, the approach was theoretically studied and then implemented to analyze the experimental results. The approach was further tested using small synthetics and cardiovascular datasets on a qsam simulator to obtain the clustering solution. The future direction connecting the dots is the incremental k-means algorithm with the quantum platform, which would open hitherto unimaginable technological doors.
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.
Recently, the volume of the generated data has increased significantly, leading to the need for computational techniques capable of handling such data efficiently. As a result, many quantum algorithms have been developed, and the domain of quantum machine learning (QML) has become more extensive. Traditional k-means algorithms for quantum computers usually make use of deep or shallow quantum circuits, resulting in sub-optimal clustering results. In our work, we introduce two types of quantum-inspired k-means algorithm: (1) the quantum subtraction operation and (2) the rotational-difference dissimilarity measure. Our second framework measures the dissimilarity using a quantum rotation-based dissimilarity circuit, which encodes the relative difference of the states. We employ a Hadamard-test-based circuit design, as well as an alternative technique that is not used in other quantum dissimilarities like the swap test. The introduced algorithms are evaluated on six different datasets—Iris, Wine, Breast Cancer Wisconsin, Blobs, Moons, and the noisier Iris dataset. Evaluation involves clustering validity metrics, as well as the classic classification performance metrics. The findings show that the rotational-based dissimilarity metric allows us to obtain clustering results comparable with the results obtained by the classical counterpart, thus showing the feasibility of the introduced distance calculation technique.
This research focuses on the implementation of quantum machine learning with the classical models such as Gradient Boosting and K-means clustering for efficient classification and clustering of most complex datasets in advanced systems. Taking advantage of the large datasets that are handled by the qc, this work examines Quantum Support Vector Machines (QSVM), Quantum Boosting, and Quantum K-means. To compare the efficiency of these hybrid models three datasets - the healthcare, the financial, and the cyber-security datasets - are used. Our findings indicate that quantum optimization algorithms achieve better accuracy in clustering in comparison to the classical counterparts and are computationally faster. This work shows how quantum machine learning can lead to the enhancement of difficult data processing tasks, a major issue in the quantum computing domain, with specific reference to resources and high-dimensional data. The opportunity to integrate quantum and classical models successfully is the best basis for further developments in machine learning.
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.