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27 pages, 2016 KiB

Open AccessArticle

by Andreas Wichert

Entropy 2023, 25(6), 871; https://doi.org/10.3390/e25060871 - 29 May 2023

Viewed by 777

We introduce a quantum Lernmatrix based on the Monte Carlo Lernmatrix in which n units are stored in the quantum superposition of

\log_{2} (n)

units representing

O (\frac{n^{2}}{\log {(n)}^{2}})

binary sparse coded patterns. During the [...] Read more.

We introduce a quantum Lernmatrix based on the Monte Carlo Lernmatrix in which n units are stored in the quantum superposition of

\log_{2} (n)

units representing

O (\frac{n^{2}}{\log {(n)}^{2}})

binary sparse coded patterns. During the retrieval phase, quantum counting of ones based on Euler’s formula is used for the pattern recovery as proposed by Trugenberger. We demonstrate the quantum Lernmatrix by experiments using qiskit. We indicate why the assumption proposed by Trugenberger, the lower the parameter temperature t; the better the identification of the correct answers; is not correct. Instead, we introduce a tree-like structure that increases the measured value of correct answers. We show that the cost of loading L sparse patterns into quantum states of a quantum Lernmatrix are much lower than storing individually the patterns in superposition. During the active phase, the quantum Lernmatrices are queried and the results are estimated efficiently. The required time is much lower compared with the conventional approach or the of Grover’s algorithm. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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19 pages, 3239 KiB

Open AccessArticle

Boosted Binary Quantum Classifier via Graphical Kernel

by Yuan Li and Duan Huang

Entropy 2023, 25(6), 870; https://doi.org/10.3390/e25060870 - 29 May 2023

Viewed by 901

Abstract

In terms of the logical structure of data in machine learning (ML), we apply a novel graphical encoding method in quantum computing to build the mapping between feature space of sample data and two-level nested graph state that presents a kind of multi-partite [...] Read more.

In terms of the logical structure of data in machine learning (ML), we apply a novel graphical encoding method in quantum computing to build the mapping between feature space of sample data and two-level nested graph state that presents a kind of multi-partite entanglement state. By implementing swap-test circuit on the graphical training states, a binary quantum classifier to large-scale test states is effectively realized in this paper. In addition, for the error classification caused by noise, we further explored the subsequent processing scheme by adjusting the weights so that a strong classifier is formed and its accuracy is greatly boosted. In this paper, the proposed boosting algorithm demonstrates superiority in certain aspects as demonstrated via experimental investigation. This work further enriches the theoretical foundation of quantum graph theory and quantum machine learning, which may be exploited to assist the classification of massive-data networks by entangling subgraphs. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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18 pages, 5463 KiB

Open AccessArticle

Suppression of Crosstalk in Quantum Circuit Based on Instruction Exchange Rules and Duration

by Zhijin Guan, Renjie Liu, Xueyun Cheng, Shiguang Feng and Pengcheng Zhu

Entropy 2023, 25(6), 855; https://doi.org/10.3390/e25060855 - 26 May 2023

Cited by 1 | Viewed by 1287

Abstract

Crosstalk is the primary source of noise in quantum computing equipment. The parallel execution of multiple instructions in quantum computation causes crosstalk, which causes coupling between signal lines and mutual inductance and capacitance between signal lines, destroying the quantum state and causing the [...] Read more.

Crosstalk is the primary source of noise in quantum computing equipment. The parallel execution of multiple instructions in quantum computation causes crosstalk, which causes coupling between signal lines and mutual inductance and capacitance between signal lines, destroying the quantum state and causing the program to fail to execute correctly. Overcoming crosstalk is a critical prerequisite for quantum error correction and large-scale fault-tolerant quantum computing. This paper provides an approach for suppressing crosstalk in quantum computers based on multiple instruction exchange rules and duration. Firstly, for the majority of the quantum gates that can be executed on quantum computing devices, a multiple instruction exchange rule is proposed. The multiple instruction exchange rule reorders quantum gates in quantum circuits and separates double quantum gates with high crosstalk on quantum circuits. Then, time stakes are inserted based on the duration of different quantum gates, and quantum gates with high crosstalk are carefully separated in the process of quantum circuit execution by quantum computing equipment to reduce the influence of crosstalk on circuit fidelity. Several benchmark experiments verify the proposed method’s effectiveness. In comparison to previous techniques, the proposed method improves fidelity by 15.97% on average. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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19 pages, 584 KiB

Open AccessArticle

Programming Quantum Neural Networks on NISQ Systems: An Overview of Technologies and Methodologies

by Stefano Markidis

Entropy 2023, 25(4), 694; https://doi.org/10.3390/e25040694 - 20 Apr 2023

Cited by 2 | Viewed by 3093

Abstract

Noisy Intermediate-Scale Quantum (NISQ) systems and associated programming interfaces make it possible to explore and investigate the design and development of quantum computing techniques for Machine Learning (ML) applications. Among the most recent quantum ML approaches, Quantum Neural Networks (QNN) emerged as an [...] Read more.

Noisy Intermediate-Scale Quantum (NISQ) systems and associated programming interfaces make it possible to explore and investigate the design and development of quantum computing techniques for Machine Learning (ML) applications. Among the most recent quantum ML approaches, Quantum Neural Networks (QNN) emerged as an important tool for data analysis. With the QNN advent, higher-level programming interfaces for QNN have been developed. In this paper, we survey the current state-of-the-art high-level programming approaches for QNN development. We discuss target architectures, critical QNN algorithmic components, such as the hybrid workflow of Quantum Annealers and Parametrized Quantum Circuits, QNN architectures, optimizers, gradient calculations, and applications. Finally, we overview the existing programming QNN frameworks, their software architecture, and associated quantum simulators. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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22 pages, 488 KiB

Open AccessArticle

Quantum Computing Approaches for Vector Quantization—Current Perspectives and Developments

by Alexander Engelsberger and Thomas Villmann

Entropy 2023, 25(3), 540; https://doi.org/10.3390/e25030540 - 21 Mar 2023

Cited by 1 | Viewed by 1629

Abstract

In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a [...] Read more.

In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a small set of prototypes, and hence, it belongs to interpretable models in machine learning. Further, the low complexity of vector quantizers makes them interesting for the application of quantum concepts for their implementation. This is especially true for current and upcoming generations of quantum devices, which only allow the execution of simple and restricted algorithms. Motivated by different adaptation and optimization paradigms for vector quantizers, we provide an overview of respective existing quantum algorithms and routines to realize vector quantization concepts, maybe only partially, on quantum devices. Thus, the reader can infer the current state-of-the-art when considering quantum computing approaches for vector quantization. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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11 pages, 273 KiB

Open AccessArticle

A Method Based on Timing Weight Priority and Distance Optimization for Quantum Circuit Transformation

by Yang Qian, Zhijin Guan, Shenggen Zheng and Shiguang Feng

Entropy 2023, 25(3), 465; https://doi.org/10.3390/e25030465 - 07 Mar 2023

Viewed by 1198

Abstract

In order to implement a quantum circuit on an NISQ device, it must be transformed into a functionally equivalent circuit that satisfies the device’s connectivity constraints. However, NISQ devices are inherently noisy, and minimizing the number of SWAP gates added to the circuit [...] Read more.

In order to implement a quantum circuit on an NISQ device, it must be transformed into a functionally equivalent circuit that satisfies the device’s connectivity constraints. However, NISQ devices are inherently noisy, and minimizing the number of SWAP gates added to the circuit is crucial for reducing computation errors. To achieve this, we propose a subgraph isomorphism algorithm based on the timing weight priority of quantum gates, which provides a better initial mapping for a specific two-dimensional quantum architecture. Additionally, we introduce a heuristic swap sequence selection optimization algorithm that uses a distance optimization measurement function to select the ideal sequence and reduce the number of SWAP gates, thereby optimizing the circuit transformation. Our experiments demonstrate that our proposed algorithm is effective for most benchmark quantum circuits, with a maximum optimization rate of up to 43.51% and an average optimization rate of 13.51%, outperforming existing related methods. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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10 pages, 295 KiB

Open AccessArticle

Quantum-Inspired Applications for Classification Problems

by Cesarino Bertini and Roberto Leporini

Entropy 2023, 25(3), 404; https://doi.org/10.3390/e25030404 - 23 Feb 2023

Cited by 1 | Viewed by 1041

Abstract

In the context of quantum-inspired machine learning, quantum state discrimination is a useful tool for classification problems. We implement a local approach combining the k-nearest neighbors algorithm with some quantum-inspired classifiers. We compare the performance with respect to well-known classifiers applied to benchmark [...] Read more.

In the context of quantum-inspired machine learning, quantum state discrimination is a useful tool for classification problems. We implement a local approach combining the k-nearest neighbors algorithm with some quantum-inspired classifiers. We compare the performance with respect to well-known classifiers applied to benchmark datasets. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

21 pages, 344 KiB

Open AccessArticle

An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization

by Zeguan Wu, Mohammadhossein Mohammadisiahroudi, Brandon Augustino, Xiu Yang and Tamás Terlaky

Entropy 2023, 25(2), 330; https://doi.org/10.3390/e25020330 - 10 Feb 2023

Cited by 1 | Viewed by 1146

Abstract

Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior point methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization problems. IPMs solve a Newton linear system at each iteration to [...] Read more.

Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior point methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization problems. IPMs solve a Newton linear system at each iteration to compute the search direction; thus, QLSAs can potentially speed up IPMs. Due to the noise in contemporary quantum computers, quantum-assisted IPMs (QIPMs) only admit an inexact solution to the Newton linear system. Typically, an inexact search direction leads to an infeasible solution, so, to overcome this, we propose an inexact-feasible QIPM (IF-QIPM) for solving linearly constrained quadratic optimization problems. We also apply the algorithm to

ℓ_{1}

-norm soft margin support vector machine (SVM) problems, and demonstrate that our algorithm enjoys a speedup in the dimension over existing approaches. This complexity bound is better than any existing classical or quantum algorithm that produces a classical solution. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

13 pages, 969 KiB

Open AccessArticle

Multi-Objective Evolutionary Architecture Search for Parameterized Quantum Circuits

by Li Ding and Lee Spector

Entropy 2023, 25(1), 93; https://doi.org/10.3390/e25010093 - 03 Jan 2023

Cited by 3 | Viewed by 2069

Abstract

Recent work on hybrid quantum-classical machine learning systems has demonstrated success in utilizing parameterized quantum circuits (PQCs) to solve the challenging reinforcement learning (RL) tasks, with provable learning advantages over classical systems, e.g., deep neural networks. While existing work demonstrates and exploits the [...] Read more.

Recent work on hybrid quantum-classical machine learning systems has demonstrated success in utilizing parameterized quantum circuits (PQCs) to solve the challenging reinforcement learning (RL) tasks, with provable learning advantages over classical systems, e.g., deep neural networks. While existing work demonstrates and exploits the strength of PQC-based models, the design choices of PQC architectures and the interactions between different quantum circuits on learning tasks are generally underexplored. In this work, we introduce a Multi-objective Evolutionary Architecture Search framework for parameterized quantum circuits (MEAS-PQC), which uses a multi-objective genetic algorithm with quantum-specific configurations to perform efficient searching of optimal PQC architectures. Experimental results show that our method can find architectures that have superior learning performance on three benchmark RL tasks, and are also optimized for additional objectives including reductions in quantum noise and model size. Further analysis of patterns and probability distributions of quantum operations helps identify performance-critical design choices of hybrid quantum-classical learning systems. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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16 pages, 565 KiB

Open AccessArticle

A Preprocessing Perspective for Quantum Machine Learning Classification Advantage in Finance Using NISQ Algorithms

by Javier Mancilla and Christophe Pere

Entropy 2022, 24(11), 1656; https://doi.org/10.3390/e24111656 - 15 Nov 2022

Cited by 5 | Viewed by 3192

Abstract

Quantum Machine Learning (QML) has not yet demonstrated extensively and clearly its advantages compared to the classical machine learning approach. So far, there are only specific cases where some quantum-inspired techniques have achieved small incremental advantages, and a few experimental cases in hybrid [...] Read more.

Quantum Machine Learning (QML) has not yet demonstrated extensively and clearly its advantages compared to the classical machine learning approach. So far, there are only specific cases where some quantum-inspired techniques have achieved small incremental advantages, and a few experimental cases in hybrid quantum computing are promising, considering a mid-term future (not taking into account the achievements purely associated with optimization using quantum-classical algorithms). The current quantum computers are noisy and have few qubits to test, making it difficult to demonstrate the current and potential quantum advantage of QML methods. This study shows that we can achieve better classical encoding and performance of quantum classifiers by using Linear Discriminant Analysis (LDA) during the data preprocessing step. As a result, the Variational Quantum Algorithm (VQA) shows a gain of performance in balanced accuracy with the LDA technique and outperforms baseline classical classifiers. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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Review

Jump to: Research

41 pages, 1277 KiB

Open AccessReview

Quantum Machine Learning: A Review and Case Studies

by Amine Zeguendry, Zahi Jarir and Mohamed Quafafou

Entropy 2023, 25(2), 287; https://doi.org/10.3390/e25020287 - 03 Feb 2023

Cited by 27 | Viewed by 11980

Abstract

Despite its undeniable success, classical machine learning remains a resource-intensive process. Practical computational efforts for training state-of-the-art models can now only be handled by high speed computer hardware. As this trend is expected to continue, it should come as no surprise that an [...] Read more.

Despite its undeniable success, classical machine learning remains a resource-intensive process. Practical computational efforts for training state-of-the-art models can now only be handled by high speed computer hardware. As this trend is expected to continue, it should come as no surprise that an increasing number of machine learning researchers are investigating the possible advantages of quantum computing. The scientific literature on Quantum Machine Learning is now enormous, and a review of its current state that can be comprehended without a physics background is necessary. The objective of this study is to present a review of Quantum Machine Learning from the perspective of conventional techniques. Departing from giving a research path from fundamental quantum theory through Quantum Machine Learning algorithms from a computer scientist’s perspective, we discuss a set of basic algorithms for Quantum Machine Learning, which are the fundamental components for Quantum Machine Learning algorithms. We implement the Quanvolutional Neural Networks (QNNs) on a quantum computer to recognize handwritten digits, and compare its performance to that of its classical counterpart, the Convolutional Neural Networks (CNNs). Additionally, we implement the QSVM on the breast cancer dataset and compare it to the classical SVM. Finally, we implement the Variational Quantum Classifier (VQC) and many classical classifiers on the Iris dataset to compare their accuracies. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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