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Systematic Literature Review: Quantum Machine Learning and its applications

David Peral García, Juan Cruz-Benito, Francisco José García-Peñalvo

arXiv:2201.04093v2quant-phcs.LG

TL;DR

Quantum machine learning is being studied because current quantum devices are not yet sufficiently capable for their intended computational advantages, while potentially useful applications remain available. This paper systematically reviews literature from 2017 to 2023 to identify, classify, and analyze QML algorithms and applications. The review finds prominent neural-network and classical-machine-learning implementations, but concludes that hardware limitations still constrain the field’s potential.

  • Problem

    Current quantum devices lack enough qubits and fault tolerance to achieve their intended computational advantages, motivating study of applications usable with present hardware.

  • Method

    The paper conducts a systematic literature review of quantum machine-learning algorithms, applications, and implementation settings in literature published from 2017 to 2023.

  • Results

    The review identifies neural-network designs, classical-machine-learning implementations, image-classification applications, and quantum-circuit or ansatz improvements among the main reported patterns.

  • Takeaways & Limitations

    Quantum machine learning shows promising results on problems also addressed by classical machine learning, including applications using current quantum devices.

  • Takeaways & Limitations

    The review is constrained by quantum hardware limitations, including insufficient quality, speed, scale, and qubit counts that restrict possible output labels.

Abstract

from arXiv · show

Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale information processing. These capabilities can give quantum computers an advantage in terms of computational time and cost over classical computers. Nowadays, there are scientific challenges that are impossible to perform by classical computation due to computational complexity or the time the calculation would take, and quantum computation is one of the possible answers. However, current quantum devices have not yet the necessary qubits and are not fault-tolerant enough to achieve these goals. Nonetheless, there are other fields like machine learning or chemistry where quantum computation could be useful with current quantum devices. This manuscript aims to present a Systematic Literature Review of the papers published between 2017 and 2023 to identify, analyze and classify the different algorithms used in quantum machine learning and their applications. Consequently, this study identified 94 articles that used quantum machine learning techniques and algorithms. The main types of found algorithms are quantum implementations of classical machine learning algorithms, such as support vector machines or the k-nearest neighbor model, and classical deep learning algorithms, like quantum neural networks. Many articles try to solve problems currently answered by classical machine learning but using quantum devices and algorithms. Even though results are promising, quantum machine learning is far from achieving its full potential. An improvement in the quantum hardware is required since the existing quantum computers lack enough quality, speed, and scale to allow quantum computing to achieve its full potential.

1. Introduction

Quantum machine learning is presented as a response to the challenge of obtaining useful computational advantages from currently limited quantum hardware. The review connects quantum machine-learning algorithms with their application domains and examines recent related developments.

  • Current quantum computers do not yet provide substantial advantages for many scientifically difficult problems.
  • Quantum algorithm research has expanded into chemistry, communications, linear systems, physics simulations, and cybersecurity.
  • Machine-learning techniques have been applied to quantum problems, including entanglement detection, quantum-system noise reduction, and molecular analysis.
  • Hybrid deep-learning approaches such as quantum graphical convolutional networks are among the proposed links between machine learning and quantum applications.
  • The review asks which quantum machine-learning algorithms are used and where they are implemented, using a systematic literature review.

2. Materials and methods

The study uses a structured systematic-review protocol to identify and evaluate quantum machine-learning literature from selected databases and sources. Its search, screening, quality assessment, and research questions define a reproducible scope for analyzing algorithms, applications, metrics, and execution settings.

  • Review planning: The review follows Kitchenham et al.’s methodology through planning, conducting, and reporting stages.
  • Review planning: The study uses Parsifal for traceability, Mendeley for bibliography management, and a public repository to support reproducibility.
  • Research questions: The review questions address algorithm types, hybrid versus pure quantum methods, application domains, success metrics, and simulator versus real-device experiments.
  • Review planning: The PICOC framework defines the review scope around quantum machine learning, QML-supporting interventions, improvements and implementations, and QML-related environments.
  • Selection criteria: Studies were included when they offered practical solutions applicable in software, simulators, or quantum devices and met publication and language criteria.
  • Query string: The search targeted literature from 2017 to 2023, a period associated with the growth of quantum devices and NISQ systems.
  • Review process: The search produced 5497 articles, which were progressively screened through deduplication, title and abstract review, full review, and quality assessment.
  • Quality assessment: Each paper needed at least 3.0 of 4.0 quality-assessment points, yielding 70 articles after selection.

3.1. Algorithm types

The review organizes quantum machine learning algorithms around data encoding, quantum-circuit construction, and qubit measurement. It covers quantum adaptations of classical models, hybrid neural architectures, reservoir computing, and variational circuits.

  • Quantum machine learning workflows first encode classical bits into qubits, construct a quantum circuit or ansatz, and then read and measure qubits.
  • Quantum Boltzmann machines (QBM): Quantum Boltzmann machines use Hamiltonian models with visible and hidden qubits to represent measured configurations through a quantum Gibbs state.
  • Variable depth quantum circuits (vVQC): Variable-depth variational circuits adapt their structure during training, with circuit depth treated as a tunable parameter.
  • Hybrid quantum autoencoders (HQA): Hybrid quantum autoencoders combine classical neural networks with parameterized quantum neural networks in encoder–decoder designs.The encoder maps quantum states from Hilbert space to a lower-dimensional real vector space, while the decoder performs the inverse operation.
  • Quantum reservoir computing (QRC): Quantum reservoir computing uses an input-dependent dynamical quantum system to transform time series into target outputs for forecasting and pattern classification.The system state is represented by a density operator evolved through a completely positive, trace-preserving map.
  • Quantum multiclass classifier (QMCC): Variational circuit models prepare qubit states, apply layered adjustable rotations, and measure auxiliary qubits to obtain class labels.The described architecture uses four qubits and an implementation consisting of seven layers.

3.1.6. Support vector machines with a quantum kernel estimator (QSVM-Kernel)

QSVM-Kernel maps classical inputs into quantum feature spaces and evaluates kernel inputs on quantum computers, while classical optimization determines the separating hyperplane. Related quantum-kernel work reports lower prediction error than tested classical models, and quantum neural and nearest-neighbor methods extend the same feature-space strategy.

  • QSVM-Kernel: QSVM-Kernel nonlinearly maps classical data into an N-qubit quantum state, producing a 2^N-dimensional feature space that is hard to estimate classically.
  • QSVM-Kernel: Quantum circuits encode classical inputs through unitary operators, and repeated circuit layers are used to construct the quantum feature representation.
  • QSVM-Kernel: Quantum computers evaluate kernel inputs, whereas classical computers optimize the separation hyperplane and classify new data as in a classical SVM.
  • Quantum kernels: Projected quantum kernels outperformed all tested classical models in prediction error.The approach first applies principal component analysis and then uses separable rotation, IQP, or Hamiltonian-evolution circuits for embedding.
  • Quantum neural networks: Quantum neural networks encode classical input and weight vectors of size m in quantum hardware using N = log2m qubits.Training can use global variational optimization or separately trained layers of decreasing complexity and size.
  • Quantum KNN: A swap-test circuit measures state overlap as a similarity measure, enabling distances between classical vectors in quantum KNN algorithms.

3.1.9. Orthogonal neural networks

Orthogonal quantum neural-network approaches address the difficulty of maintaining orthogonal weights during training. The reviewed designs use quantum circuits and gates to implement orthogonal layers or simplify neural-network computation.

  • Orthogonal neural networks constrain layer weight matrices, but classical gradient-descent updates can be slow and only approximately orthogonal.
  • Pyramidal Circuit layers implement orthogonal matrix multiplication with perfect orthogonality and standard-layer execution time.
  • The proposed quantum fully connected layer uses parameterized Reconfigurable Beam Splitter gates to construct an orthogonal weight matrix.
  • QFS-Net uses qutrit neurons, transformation gates, Hadamard-mapped interconnection weights, and sigmoid-guided self- and counter-propagation.
  • The CNOT measured network uses only CNOT gates and measurement, accommodates AND and OR operators, and maintains an optimized learning rate with a constant number of auxiliary qubits.

3.1.12. Quantum convolutional deep convolutional neural networks (QDCNN)

Quantum convolutional and feedforward architectures adapt classical image and neural-network processing to quantum circuits. The reviewed designs encode inputs quantum mechanically, apply parameterized operations, and combine quantum and classical components where needed.

  • QDCNN is a quantum adaptation of convolutional networks, consisting of successive quantum convolutional layers followed by a quantum classifier layer.
  • A 2^n × 2^n grayscale image is represented by pixel values c_x,y ∈ [0, 255] before quantum-state preparation.
  • QDCNN initializes registers, prepares images and kernels with Hadamard gates and QRAM, then applies quantum multiplication and auxiliary bifurcation and rotation qubits.
  • The QDCNN G oracle applies quantum phase estimation to estimate a quantum amplitude before adding a register and nonlinear modulus for compatibility with DCNN processing.
  • Quantum feedforward networks encode inputs and weights through unitary transformations, use parallel registers and measurements, and may repeatedly upload data with classically optimized rotations.

3.1.15. Long short-term memory neural networks LSTM-QNN

LSTM-QNN research combines recurrent sequence modeling with quantum circuits and hybrid classical layers. The reviewed approaches also include quantum optimization and quantum generative adversarial architectures.

  • LSTM-QNN foundations: Classical LSTM cells process short- and long-term sequence dependencies through input, hidden, and cell-state inputs with input, forget, and output gates.
  • Hybrid LSTM-QNN: A hybrid LSTM-QNN architecture uses two 32-cell layers, fully connected layers, IQP and StronglyEntanglingLayers ansätze, and a final classical output layer.
  • Hybrid LSTM-QNN: A 10-qubit layer with 32 cells requires an intervening classical dense layer before connection to a 10-qubit QNN.
  • Quantum optimization: MetaQAOA combines a parameterized QNN with a classical LSTM optimizer to find approximate optimal QAOA parameters for MaxCut.
  • Quantum GANs: Quantum GANs alternate generator and discriminator optimization, repeating circuit execution until the generator reconstructs the training-set state distribution.

3.1.17. Recurrent quantum neural networks (RQNN)

Recurrent quantum neural networks transmit information across measurement rounds and use quantum transformations to model recurrent processing. Related architectures extend this approach with attention, attractor-based recurrent units, transformers, and quantum Monte Carlo applications.

  • RQNN: RQNN architectures pass gate parameters and measurement results from one measurement round to the next.
  • RQNN: RQNN work reports that linear circuit transformations can produce nonlinear behavior when state amplitudes depend nonlinearly on rotation angles.
  • Quantum recurrent encoder-decoder: QREDNN uses attention to suppress redundant information, while QGRU represents activation values and weights with quantum rotation matrices.
  • Quantum Vision Transformers: Quantum Vision Transformers decompose images into patches, apply transformer feature extraction and attention, then use normalization and an MLP.
  • Quantum Monte Carlo: Quantum Monte Carlo applications use unitary operators to model classical functions and have been applied to Gaussian sampling, bank stress testing, and DSGE models with deep learning.

3.2. Application Domains and Metrics

The review covers classical- and quantum-purpose applications of quantum machine learning, with classification prominent among classical applications and quantum-circuit development prominent among quantum applications. Accuracy is the most commonly used metric, enabling comparisons with classical algorithms across shared datasets.

  • Classical-purpose applications: Classical-purpose applications include classification, image classification, natural language processing, and improvements to machine-learning processes.
  • Classical-purpose applications: Classification models address tasks including temporal information processing, object recognition from sensor data, entanglement-based problems, and image pattern recognition.
  • Classical-purpose applications: Image-classification studies use datasets including MNIST, IRIS, TCIA, GTSRB, BNA, WIL, Plane Point, Cats vs. Dogs, and CIFAR-10.Other studies use small 2x2- and 4x4-pixel image problems with few categories.
  • Metrics: Accuracy is used in most papers because shared open-access datasets permit comparison with classical algorithms.The review presents dataset-level accuracy results in its metrics tables.
  • Quantum-purpose applications: Quantum-purpose applications include data encoding, compilers, entanglement detection, faulty-gate identification, feature reduction, and quantum natural language processing.
  • Quantum-purpose applications: Quantum machine-learning studies address noisy gradient calculation, parameter reduction in quantum neural networks and generative adversarial networks, and quantum error mitigation.

3.3. Devices

The reviewed studies use diverse quantum hardware platforms, simulators, and software ecosystems. Implementations differ in physical characteristics and execution behavior, while cloud access provides limited availability rather than routine everyday access.

  • Hardware characteristics: Hardware implementations differ in relaxation time, decoherence time, state preparation, gate efficiency, and readout results.The same circuit can therefore produce different results on different implementations.
  • Platforms and software: IBM Quantum provides simulated and real experiments through visual circuit tools, OpenQASM, and Qiskit, with transpilation into device-supported physical gates.IBM devices use superconducting qubits with decoherence times of approximately 100 us.
  • Platforms and software: Rigetti uses superconducting-qubit processors and provides PyQuil for programming and compilation.Its stated advantages include fast gate and program-execution times for NISQ-era applications.
  • Platforms and software: TensorFlow Quantum supports prototyping classical-quantum hybrid models through Cirq, TensorFlow APIs, and quantum-circuit simulators.Amazon Braket provides access to QPUs from multiple vendors and a local simulator.
  • Platforms and software: The literature uses multiple IBM devices, Rigetti devices, Google TensorFlow Quantum Simulator, and Amazon Braket Local Simulator.

4. Discussion

The review finds that quantum machine-learning research is dominated by qubit-based neural-network variants and classification-oriented classical applications, while quantum applications focus on improving circuits and noisy hardware. Simulators broaden experimentation, but device access and methodological validity remain bounded.

  • Algorithms: Most reviewed algorithms use qubits, while quantum neural networks commonly employ rotational gates and auxiliary qubits.The review also identifies convolutional, orthogonal, feedback, deep, and autoencoder-derived neural-network techniques.
  • Algorithms: Quantum support vector machines can create a 2^N-dimensional feature space, whose potential is expected after the NISQ era.
  • Classical applications: Classification is a leading classical application, with image-classification studies using reduced-category problems because current devices have few available qubits.These studies report accuracy comparable to classical machine-learning results, and one hybrid approach trains in less CPU time than other classical approaches.
  • Quantum applications: Quantum applications largely seek to improve quantum-circuit creation and neural-network construction for current noisy quantum computers.Examples include reducing quantum resources on NISQ devices and developing platforms implementing quantum linear regression and quantum neural networks.
  • Devices and access: Quantum simulators can emulate quantum devices and their noise, supporting algorithm and software development despite limited hardware capacity.The literature reports no consensus on a predominant physical technology among superconducting, trapped-ion, photonic, and other platforms.
  • Devices and access: Everyday access to quantum devices remains unavailable because of their size, implementation complexity, and continual improvement.
  • Validity: The review mitigates validity threats with a quality-assurance checklist, multi-author validation, a public repository, broad databases, and explicit search and selection criteria.

5. Conclusions

The review identified and analyzed 94 relevant quantum machine learning papers, finding diverse algorithmic designs and applications but limited evidence of advantage over classical models. It concludes that improved quantum hardware is needed because current techniques are constrained by device qubit counts.

  • 94 papers were selected after reviewing publications from 2017–2022, following duplicate removal, quality assessment, and other eligibility criteria.The initial search retrieved 5497 papers from five databases.
  • Quantum machine learning research prominently uses varied neural-network designs alongside linear regression, QAE, vVQC, and QBM methods.Reported neural-network variants include orthogonal, convolutional, feed-forward, and self-supervised architectures.
  • Classical applications commonly target image classification, whereas quantum applications often focus on creating, simulating, and executing ansatzes.MNIST is among the well-known datasets used for image classification.
  • Data encoding and state initialization show standardization, but oracle and quantum-circuit implementations remain diverse.
  • Classical applications generally emulate problems already solved by classical machine learning and, at best, match existing classical models.
  • Quantum hardware improvements are needed because some techniques, including image classification, are limited by output-label counts proportional to available qubits.
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