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arXiv:2112.00313 · IEEE International Conference on Rebooting Computing (ICRC)

Discriminating Quantum States with Quantum Machine Learning

David Quiroga, Prasanna Date, Raphael C. Pooser

Published Nov 1, 2021• 13 citations
arXivHTMLPDF

Abstract

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 of$\mathcal{O}(NK log(D)I/C)$to apply it to the fundamental problem of discriminating quantum states at readout. Discriminating quantum states allows the identification of quantum states$\vert 0\rangle$and$\vert 1\rangle$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.

DOI
10.1109/icrc53822.2021.00018

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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.
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.
Machine Learning (ML) has changed the way computers work by letting them learn from data and make smart choices. However, traditional ML techniques encounter scalability and efficiency constraints as datasets get larger and computational problems become more complicated[1]. These restrictions could be circumvented by the new paradigms that quantum computing offers by using entanglement and superposition [2], [3]. The combination of the Quantum computing with the Machine Learning is called the Quantum Machine Learning(QML), offers efficiency improvements, new algorithmic opportunities, and speedups in certain linear algebraic operations. So, this review dives deeply into quantum-classical algorithms, with a particular emphasis on the approaches like quantum neural network and quantum support vector machines. We examine computational complexity, architectural design, benchmarking findings, and real-world applications (such as optimization, cryptography, and classification). We also discuss important issues including scalability, data encoding, and noise, and we suggest future paths for error prevention and scalable structures.
The rapid development of machine learning technology leads to make the devices in the industries working autonomously. However, the growth of sensors in the industries leads to produce vast data that is utilized by machine learning algorithms to improve the autonomous devices’ performances. However, classical ML algorithms and hardware systems cannot process large data to meet real-time problems. Hence, the researchers have developed Quantum Computing hardware systems and Quantum Machine learning algorithms to speed up the process. This research work presented the review of quantum computing mechanisms and QML algorithms that are applied to classify the images. This work demonstrated the performance comparison of various QML algorithms. It showed that the images are classified using various QML algorithms faster than classical ML algorithms in terms of time.
Quantum Machine Learning (QML) represents a promising frontier of research where the principles of quantum mechanics are combined with machine learning to offer potentially superior performance over classical counterparts. This review article explores the current advancements in QML, specifically focusing on the performance improvement and comparison between standard classical algorithms and their quantum implementations. We initiate with an overview of fundamental quantum algorithms that have found applicability within machine learning contexts, such as quantum principal component analysis and quantum support vector machines. The review then delves into a critical assessment of these quantum approaches, highlighting case studies where quantum implementations have demonstrated computational speedups or improved accuracy. Furthermore, we investigate the inherent challenges and limitations that currently hinder the widespread adoption of QML technologies, including the issues of decoherence, error rates, and quantum resource requirements. In addition, the review provides insights into the current state of quantum hardware and its scalability for machine learning tasks. Throughout, comparisons are made to outline scenarios in which quantum machine learning presents a genuine advantage over classical techniques, supported by performance metrics and benchmark datasets. The article concludes by discussing future directions in QML research, with an emphasis on algorithmic innovation and hardware improvement, to realize the full potential of quantum-enhanced machine learning.
Due to the superiority and noteworthy progress of Quantum Computing (QC) in a lot of applications such as cryptography, chemistry, Big data, machine learning, optimization, Internet of Things (IoT), Blockchain, communication, and many more. Fully towards to combine classical machine learning (ML) with Quantum Information Processing (QIP) to build a new field in the quantum world is called Quantum Machine Learning (QML) to solve and improve problems that displayed in classical machine learning (e.g. time and energy consumption, kernel estimation). The aim of this paper presents and summarizes a comprehensive survey of the state-of-the-art advances in Quantum Machine Learning (QML). Especially, recent QML classification works. Also, we cover about 30 publications that are published lately in Quantum Machine Learning (QML). we propose a classification scheme in the quantum world and discuss encoding methods for mapping classical data to quantum data. Then, we provide quantum subroutines and some methods of Quantum Computing (QC) in improving performance and speed up of classical Machine Learning (ML). And also some of QML applications in various fields, challenges, and future vision will be presented.
Quantum machine learning (QML) is a promising early use case for quantum computing. There has been progress in the last five years from theoretical studies and numerical simulations to proof of concepts. Use cases demonstrated on contemporary quantum devices include classifying medical images and items from the Iris dataset, classifying and generating handwritten images, toxicity screening, and learning a probability distribution. Potential benefits of QML include faster training and identification of feature maps not found classically. Although, these examples lack the scale for commercial exploitation, and it may be several years before QML algorithms replace the classical solutions, QML is an exciting area. This article is written for those who already have a sound knowledge of quantum computing and now wish to gain a basic overview of the terminology and some applications of classical machine learning ready to study quantum machine learning. The reader will already understand the relevant relevant linear algebra, including Hilbert spaces, a vector space with an inner product.