PaperlayerView exact revision on arXiv

Source-linked AI summary

Quantum Machine Learning: from physics to software engineering

Alexey Melnikov, Mohammad Kordzanganeh, Alexander Alodjants, Ray-Kuang Lee

arXiv:2301.01851v2quant-phphysics.comp-ph

TL;DR

This review addresses the difficulty of establishing practical quantum advantage amid limits on quantum computers and the complexity of machine-learning models. It surveys quantum and hybrid approaches, including classically trained quantum neural networks and machine learning applied to quantum experiments. It reports that QML has not yet shown a definite practical advantage over classical alternatives, with suggested advantages remaining theoretical.

  • Problem

    The criterion for information-processing speedup remains unknown in many cases, while practical QML has yet to show a definite advantage over classical alternatives.

    Source: §1 · p. 3, §2.5 · p. 13

  • Method

    The review surveys QML approaches, including quantum neural networks with classically updated parameters and machine learning methods for quantum experiments.

    Source: §2.2 · p. 8, §3.1.1 · p. 17, §4 · p. 28

  • Results

    QML has so far provided no definite practical advantage over classical alternatives, and suggested advantages remain purely theoretical.

    Source: §2.5 · p. 13

  • Takeaways & Limitations

    The review identifies hybrid information-processing methods using classical ML algorithms and quantum devices as promising approaches within the NISQ era.

    Source: §4 · p. 28

    QML has so far shown no definite practical advantage over classical alternatives; suggested advantages remain theoretical.

    Source: §2.5 · p. 13

Abstract

from arXiv · show

Quantum machine learning is a rapidly growing field at the intersection of quantum technology and artificial intelligence. This review provides a two-fold overview of several key approaches that can offer advancements in both the development of quantum technologies and the power of artificial intelligence. Among these approaches are quantum-enhanced algorithms, which apply quantum software engineering to classical information processing to improve keystone machine learning solutions. In this context, we explore the capability of hybrid quantum-classical neural networks to improve model generalization and increase accuracy while reducing computational resources. We also illustrate how machine learning can be used both to mitigate the effects of errors on presently available noisy intermediate-scale quantum devices, and to understand quantum advantage via an automatic study of quantum walk processes on graphs. In addition, we review how quantum hardware can be enhanced by applying machine learning to fundamental and applied physics problems as well as quantum tomography and photonics. We aim to demonstrate how concepts in physics can be translated into practical engineering of machine learning solutions using quantum software.

1. Introduction

The introduction frames quantum machine learning as an intersection of quantum technologies, classical information processing, and AI. It reviews two directions: using quantum technologies to enhance machine learning and applying classical ML to quantum-computing challenges.

1. Introduction

  • The review situates QML amid big-data and IoT demands for online recognition, which the introduction links to parallel information processing.It also describes AI and ML as driving progress in distributed intelligent systems.Source: §1 · p. 2
  • Quantum technologies and AI are presented as overlapping disciplines with shared aims in efficient computing, fast and secure communication, and smart IoT.Quantum-inspired methods can apply quantum probability and measurement theory to classical computing.Source: §1 · pp. 2, 4
  • Current quantum computers have few qubits and substantial noise, while the optimality and universality of physical-to-logical qubit mappings remain open questions.The introduction identifies network architecture as a key problem for demonstrating quantum supremacy across physical platforms.Source: §1 · p. 3
  • The introduction presents quantum machine learning as parallel computation at the intersection of quantum computing and network theory, using quantum or classical systems and algorithms.It reviews algorithms proposed to improve computational complexity, accuracy, and efficiency across available hardware.Source: §1 · pp. 3–4
  • Because current NISQ computers are not yet capable of demonstrating quantum supremacy, the review focuses on methods suited to hybrid quantum-classical algorithms.It contrasts this focus with earlier reviews of quantum approaches to machine learning.Source: §1 · pp. 4–5
  • The review covers quantum technologies for enhancing machine learning and classical ML for NISQ-era quantum tasks, including quantum-walk speedup recognition.The first direction includes data encoding and quantum neural networks; the second includes quantum experiments, tomography, and error correction.Source: §1 · p. 5

2. Machine learning enhanced by quantum technologies

This section discusses the impact of quantum technologies on machine learning, with its topic outline shown in Figure 3.

2. Machine learning enhanced by quantum technologies

  • The section surveys how quantum technologies can affect machine learning; Figure 3 outlines the topics discussed.The passage provides no further description of those topics.Source: §2 · p. 5

2.1. Machine learning models

This section introduces three modes of machine learning, discusses the complexity and costs of practical models, and presents quantum-enhanced learning as a possible response.

2.1. Machine learning models

  • Machine learning models use features, labeled outcomes, or action rewards as data, corresponding to unsupervised, supervised, and reinforcement learning.The passage frames ML as a procedural algorithm augmented with external data to model a probability distribution.Source: §2.1 · p. 5

2.1.1. Unsupervised learning

  • Unsupervised learning infers attributes of data points, often to identify clusters; K-means assigns points to a chosen number of clusters whose centers can be trained.The passage gives customer segmentation and criminal-activity detection as application examples.Source: §2.1.1 · p. 6

2.1.2. Supervised learning

  • Supervised learning infers patterns from labeled data and aims to generalize them to unseen points, using regression or categorical-probability models.The passage distinguishes linear interpolation from nonlinear regression where nonlinearity is plausible.Source: §2.1.2 · p. 6

2.1.3. Reinforcement learning

  • Reinforcement learning optimizes an action policy by having an agent explore an environment and update its model variables from action outcomes and rewards.The passage mentions gaming and portfolio management as application areas.Source: §2.1.3 · p. 6

2.1.4. Exponential growth of practical machine learning models

  • Practical ML models can have high complexity, imposing financial and environmental costs and raising scalability concerns as computing power grows more slowly than ML research.The passage reports that some models studied in 2019 could emit more CO2 than an average American car over its lifetime and cost over $3m to train or fine-tune.Source: §2.1.4 · p. 6

2.1.5. Quantum-enhanced machine learning

  • Quantum-enhanced ML aims to use quantum computers for scalable models that exceed expected classical capabilities at a healthier cost.The section also discusses quantum statistical formulations as possible approaches to some behavioral patterns that diverge from classical statistical theory.Source: §2.1.5 · p. 7

2.2. Quantum neural networks

This section reviews QNNs as classically trained parameterized quantum models, with encoding, circuit architecture, optimization, expressivity, and trainability as linked design concerns. It highlights both the expressive potential of repeated encodings and the training constraints imposed by barren plateaus.

2.2. Quantum neural networks

  • QNNs update parameters classically to reduce an objective that includes a parameterized quantum circuit’s expectation value; data encoding and circuit design shape model behavior.Training evaluates the circuit, computes a loss, and adjusts parameters to reduce it.Source: §2.2 · p. 8

2.2.1. Data encoding strategies

  • Three encoding strategies map features to computational bases, qubit-state amplitudes, or a Hamiltonian used for measurement.State embedding is discrete-variable; amplitude and observable embedding are continuous-variable methods in the described taxonomy.Source: §2.2.1 · p. 8

2.2.2. Parametrised architecture

  • Quantum-circuit parameterization can alter outputs, and over-parameterized circuits may contain redundant parameters, so trainability cannot be assumed.The section surveys hardware-efficient, IQP, and tensor-network architectures, including TTN, MPS, and QCNN examples.Source: §2.2.2 · p. 9

2.2.3. Gradient calculation

  • Back-propagation requires quantum state-vector access and is therefore limited to simulators, while parameter-shift gradients run on QPUs but require evaluations scaling linearly with trainable parameters.Finite differences are described as error-prone in the NISQ era; adjoint gradients use a single circuit evaluation but are also simulator-only.Source: §2.2.3 · pp. 9–10

2.2.4. Quantum neural networks as universal Fourier estimators

  • Repeated data encoding adds Fourier bases to a QNN’s functional representation, while whether their coefficients can be independently controlled remains open.The review also notes results characterizing QNNs as universal Fourier estimators.Source: §2.2.4 · p. 10

2.2.5. Barren plateaus and trainability issues

  • Barren plateaus occur when training gradients vanish; deep noisy circuits can also flatten the loss landscape, constraining trainable QNNs toward shallow circuits with fewer qubits.The section reviews remedies and architecture-specific findings, including TTNs and QCNNs reported free of barren plateaus under stated conditions, and other architectures reported to suffer them.Source: §2.2.5 · pp. 10–11

2.3. Quantum learning theory

This section connects supervised QNNs to kernel methods, reviews Bayesian approaches, and surveys measures and bounds for model complexity and generalization. It reports a theoretical generalization-error result scaling as O(T/N).

2.3.1. Supervised QML methods are kernel methods

  • QNNs resemble kernel models by embedding data in a high-dimensional quantum space and measuring similarity through overlaps between encoded states.The review describes a framework for searching for possible quantum advantages and notes that large models can make distances too large for optimization.Source: §2.3.1 · p. 11

2.3.2. Bayesian inference

  • Bayesian QNN research includes exact inference attempts and approximate variational-inference methods using kernel theory or a classical adversary.Quantum circuits can model probability distributions as Born machines or quantum generative models.Source: §2.3.2 · p. 12

2.3.3. Model complexity and generalisation error bounds

  • A reported theoretical result bounds QNN generalization error by O(T/N), where T is the number of parameterized quantum gates and N the dataset sample count.The cited work interprets this result as implying better generalization from fewer data points.Source: §2.3.3 · p. 12

2.4. Hybrid quantum neural networks

The section reviews hybrid networks that combine classical and quantum components, including circuits placed within classical pipelines. Reported studies find better generalization or solution quality in selected settings, with one study observing the generalization difference shrink as sample size grows.

2.4. Hybrid quantum neural networks

  • The example architecture feeds inputs through a classical multilayer perceptron into a quantum-circuit embedding, then routes measurements through a classical output layer for comparison with labels.The caption notes that whether and which circuit measurements are taken depends on the setting.Source: Figure 5 · p. 13
  • On two classical datasets, a four-qubit hybrid network generalized better than its classical-only counterpart, especially with very small training samples; the difference narrowed as sample count grew.The hybrid used a shallow quantum circuit, measured two qubits, and passed their values to a neural network.Source: §2.4 · p. 13
  • A hybrid architecture with a quantum component inserted mid-network achieved slightly better solution quality than the classical comparison in image recognition.The study optimized the quantum circuit’s qubit count and repetition layers and theoretically analyzed the resulting circuit.Source: §2.4 · p. 13

2.5. Applications and realisations

The section surveys classical and quantum-native applications of QML, while noting that definite practical advantage over classical alternatives has not yet been established. Examples span scientific and industrial tasks, variational energy estimation, equation solving, optimization, and language processing.

2.5. Applications and realisations

  • QML has not yet demonstrated definite practical advantage over classical alternatives; suggested advantages remain theoretical.The review notes that QML inherits classical ML problems as well as proposing quantum-native solutions.Source: §2.5 · p. 13

2.5.1. Solving classical problems

  • Classical applications reviewed include science, finance, pharmaceuticals, and automotive work, alongside generative, recurrent, image-recognition, language, reinforcement-learning, and autoencoder approaches.The section says some applications replace previously known classical settings.Source: §2.5.1 · p. 14

2.5.2. Quantum-native problems

  • The variational quantum eigensolver minimizes a parameterized circuit’s Hamiltonian expectation to seek a problem’s ground state and energy; QML approaches also address linear systems and differential equations.The review describes VQE as one of the most promising QML areas.Source: §2.5.2 · p. 14
  • Quantum-native examples include Ising-based QUBO solutions such as max cut and grammar-aware quantum natural language processing, whose potential advantage may lie in Grover-style text-classification speed-up.Max cut seeks a graph-vertex partition with the largest number of crossing edges.Source: §2.5.2 · p. 14, Figure 6 · p. 15

2.6. Open questions

The open questions concern demonstrable quantum advantage, QNN parametrisation, theoretical grounding for hybrid models, and optimisation at very large scales.

2.6.1. Quantum advantage

  • Despite theoretical findings, demonstrable QML success on real-life problems remains limited; Ref. [256] suggests questions about efficient building blocks, learning-theory bridges, and scalable ML software.Other work has identified datasets and mathematical conditions for potential quantum advantage, while attempts have also proposed rules for finding it.Source: §2.6.1 · p. 15

2.6.2. Optimal parametrisation

  • An open question is how to parametrise QNN circuits to avoid barren plateaus, maximize expressivity, and avoid redundancy.High Fourier accessibility is proposed as a possible characteristic, potentially requiring a quantifiable measure.Source: §2.6.2 · p. 15

2.6.3. Theory for hybrid models

  • Theoretical grounding for hybrid models remains limited despite reported success with quantum components at the beginning [41] or middle [44] of architectures.Further information-theoretic investigation could examine whether hybridization introduces an information bottleneck to prevent overfitting or creates high-dimensional models.Source: §2.6.3 · p. 15

2.6.4. An efficient optimisation method

  • Current gradient methods are simulator-only or require linearly many circuit evaluations, limiting their suitability for billion-parameter, million-qubit settings.The section identifies efficient optimization as a long-term need.Source: §2.6.4 · p. 16

3. Quantum technologies enhanced by machine learning

This section surveys how machine learning can support quantum physics and technologies, spanning experiment and protocol design, quantum-walk analysis, quantum-state tomography, photonic structure design, quantum measurements, and automated experiments. It also presents integrated photonics as a platform for these applications and notes that useful applications for non-universal photonic systems remain an open question.

3.1. Machine learning in fundamental and applied quantum physics

  • A learning approach that blends many multilayer perceptrons automatically with generative algorithms may detect and quantify nonlocality and its quantum (or postquantum) nature [278].Source: §3.1 · pp. 16–17

3.1.1. Machine learning in quantum computing

  • Projective-simulation reinforcement learning designs quantum experiments by choosing optical elements and adapting action probabilities, yielding varied entangled states with improved realization efficiency.The agent receives a reward when an optical setup achieves a goal such as creating a desired multiphoton entangled state.Source: §3.1.1 · pp. 17–18

3.1.2. Machine learning in quantum communication

  • Projective-simulation reinforcement learning designed quantum communication protocols for teleportation, entanglement purification, and repeaters, finding better-than-known protocols when optimal conditions lacked assumed symmetries.Hierarchical skill acquisition supports long-distance communication settings involving multiple repeater schemes.Source: §3.1.2 · p. 18

3.2. Machine learning in random walks problems

  • For random graphs (n = 15, 20, 25), CQCNN loss fell below 3×10^-3; classical recall and precision were about 90%, versus 25–35% for quantum-class examples.The network generalized to unseen graphs and classified them without simulating quantum-walk dynamics.Source: Figure 12 · p. 22, §3.2 · p. 22

3.2.1. Quantum walks with decoherence

  • For a six-vertex cycle, CQCNN predicted a quantum-to-classical transport crossover at p ≃ 0.34, suggesting quantum-walk advantage for p < 0.34.The quantum-class vote peaked near p ≃ 0.2, while confidence in the classical class rose with decoherence; the authors relate p to temperature and the crossover to a phase transition.Source: §3.2.1 · p. 23, Figure 13 · p. 23

3.3. Machine learning in quantum tomography

  • A 30-layer CNN reconstructs density matrices from noisy optical homodyne sequences, using shortcuts to address vanishing gradients and average pooling to weight tomography data equally.Training reduced mean squared error to 5 × 10^-6 after 70 epochs; the reconstruction imposes positive semidefiniteness and trace-one normalization.Source: §3.3 · pp. 24–25
  • 0.99 fidelity is maintained at 20 dB anti-squeezing by ML-enhanced QST, which also separates squeezed and noisy components for degradation analysis.Training typically takes less than one hour, and inference averages about 38.1 milliseconds on a standard GPU server. The decomposition identifies contributions from ideal squeezed, squeezed thermal, and thermal states.Source: §3.3 · p. 25
  • A characteristic CNN predicts physical parameters as well as density-matrix reconstruction, while ML-QST can use fewer settings and incomplete measurements.The lightweight supervised model is proposed as an in-line diagnostic tool on edge devices such as FPGAs.Source: §3.3 · pp. 25–26

3.4. Photonic quantum computing

  • Photonic quantum computing offers high integration with mature classical photonics and room-temperature operation, but useful applications for non-universal systems remain an open question.Photonic Boson sampling is described as non-universal and as a possible way to demonstrate quantum advantage.Source: §3.4 · p. 26
  • Machine learning is applied to photonic structure design and light–matter interactions, with quantum optical neural networks and automated experiments among the proposed directions.The passage anticipates integrating thousands of optoelectronic components and combining quantum measurements, metrology, and on-chip or free-space meta-device optimization to automate experiments.Source: §3.4 · p. 27

4. Conclusions

The review frames quantum machine learning as an intersection of AI, quantum information science, and quantum technology, and surveys hybrid approaches to their use. It reports that graph topology affects random-walk speedup even without decoherence, while anticipating quantum computers as components of distributed intelligent systems.

4. Conclusions

  • The review presents quantum machine learning as an intersection of AI, quantum information science, and quantum technology, against limitations of classical hardware..Source: §4 · p. 27
  • The authors anticipate practically significant quantum computers being embedded in distributed intelligent systems.This is presented as an expectation about the near future.Source: §4 · p. 28
  • Even without decoherence, random-walk speedup depends substantially on graph topology, including adjacency-matrix properties.The review's CQCNN learns feature vectors from graph adjacency matrices combined with a decoherence parameter.Source: §4 · p. 28
  • Quantum neural networks use classically updated parameters and can be trained in hybrid quantum-classical variational-circuit algorithms.The described training provides data to the quantum model, calculates a loss, and adapts QNN parameters.Source: §4 · p. 28

Related papers

Loading 2301.01851v2…