Quantum Machine Learning in Multi-Qubit Phase-Space Part I: Foundations

• URL: http://arxiv.org/abs/2507.12117v2
• Date: Wed, 08 Oct 2025 10:26:16 GMT
• Title: Quantum Machine Learning in Multi-Qubit Phase-Space Part I: Foundations
• Authors: Timothy Heightman, Edward Jiang, Ruth Mora-Soto, Maciej Lewenstein, Marcin Płodzień,
• Abstract summary: We construct a closed, composable dynamical formalism for one- and many-qubit systems in phase-space.<n>It recasts the curse of dimensionality in terms of harmonic support on a domain that scales linearly with the number of qubits.
• Score: 0.3425341633647625
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of the Hilbert space, QML faces practical limits in classical simulations with the state-vector representation of quantum system. On the other hand, phase-space methods offer an alternative by encoding quantum states as quasi-probability functions. Building on prior work in qubit phase-space and the Stratonovich-Weyl (SW) correspondence, we construct a closed, composable dynamical formalism for one- and many-qubit systems in phase-space. This formalism replaces the operator algebra of the Pauli group with function dynamics on symplectic manifolds, and recasts the curse of dimensionality in terms of harmonic support on a domain that scales linearly with the number of qubits. It opens a new route for QML based on variational modelling over phase-space.

Related papers

• Digital Quantum Simulation of the Holstein-Primakoff Transformation on Noisy Qubits [40.8066152850216]
  We study the digital quantum simulation of bosonic modes on a cloud-based superconducting quantum processor.<n>We examine the interplay between algorithmic and hardware-induced errors to identify optimal simulation parameters.
  arXiv  Detail & Related papers  (2026-02-19T20:14:04Z)
• Implementing the Koopman-von Neumann approach on continuous-variable photonic quantum computers [0.0]
  Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators.<n>Mapped to quantum computing, KvN offers a promising route to simulate classical dynamical systems.<n>We specifically explore the implementation of the KvN approach on continuous-variable photonic quantum computing architectures.
  arXiv  Detail & Related papers  (2025-12-15T20:45:33Z)
• Classically Prepared, Quantumly Evolved: Hybrid Algorithm for Molecular Spectra [41.99844472131922]
  We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems.<n>The method combines classical preparation of a perturbed ground state with short-time quantum evolution of product states sampled from it.
  arXiv  Detail & Related papers  (2025-10-28T19:27:12Z)
• Qumode-Based Variational Quantum Eigensolver for Molecular Excited States [43.148034499498586]
  We introduce the Qumode Subspace Variational Quantum Eigensolver (QSS-VQE), a hybrid quantum-classical algorithm for computing molecular excited states.<n>We demonstrate the performance of QSS-VQE through simulations of molecular excited states, including dihydrogen and a conical intersection in cytosine.
  arXiv  Detail & Related papers  (2025-09-05T00:53:51Z)
• Quantum Visual Fields with Neural Amplitude Encoding [70.86293548779774]
  We introduce a new type of Quantum Implicit Neural Representation (QINR) for 2D image and 3D geometric field learning.<n>QVF encodes classical data into quantum statevectors using neural amplitude encoding grounded in a learnable energy manifold.<n>Our ansatz follows a fully entangled design of learnable parametrised quantum circuits, with quantum (unitary) operations performed in the real Hilbert space.
  arXiv  Detail & Related papers  (2025-08-14T17:59:52Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [60.996803677584424]
  Variational Quantum Circuits (VQCs) offer a novel pathway for quantum machine learning.<n>Their practical application is hindered by inherent limitations such as constrained linear expressivity, optimization challenges, and acute sensitivity to quantum hardware noise.<n>This work introduces VQC-MLPNet, a scalable and robust hybrid quantum-classical architecture designed to overcome these obstacles.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Variational Quantum Simulation of the Interacting Schwinger Model on a Trapped-Ion Quantum Processor [26.47874938214435]
  In this work, we explore the multi-flavor lattice Schwinger model - a toy model inspired by quantum chromodynamics.<n>We employ a parametric quantum circuit executed on our quantum processor to identify ground states in different parameter regimes of the model.<n>The resulting states are analyzed via quantum state tomography, to reveal how characteristic properties such as correlations in the output state change.
  arXiv  Detail & Related papers  (2025-04-29T14:43:57Z)
• Robust Simulations of Many-Body Symmetry-Protected Topological Phase Transitions on a Quantum Processor [7.515748475237134]
  Topology and symmetry play critical roles in characterizing quantum phases of matter.<n>Recent advancements have unveiled symmetry-protected topological (SPT) phases in many-body systems.<n>We demonstrate the robust simulation of many-body ground states of an Ising-cluster model on a quantum computer.
  arXiv  Detail & Related papers  (2025-03-11T18:00:02Z)
• Real-Time Scattering Processes with Continuous-Variable Quantum Computers [0.0]
  We propose a framework for simulating the real-time dynamics of quantum field theories.<n>We implement non-Gaussian operations for continuous-variable quantum computing platforms.
  arXiv  Detail & Related papers  (2025-02-03T19:11:38Z)
• Simulating continuous-space systems with quantum-classical wave functions [0.0]
  Non-relativistic interacting quantum many-body systems are naturally described in terms of continuous-space Hamiltonians. Current algorithms require discretization, which usually amounts to choosing a finite basis set, inevitably introducing errors. We propose an alternative, discretization-free approach that combines classical and quantum resources in a global variational ansatz.
  arXiv  Detail & Related papers  (2024-09-10T10:54:59Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Exploring quantum localization with machine learning [39.58317527488534]
  We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the pattern recognition capabilities of a modified convolutional model.
  arXiv  Detail & Related papers  (2024-06-01T08:50:26Z)
• Variational quantum simulation using non-Gaussian continuous-variable systems [39.58317527488534]
  We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space.
  arXiv  Detail & Related papers  (2023-10-24T15:20:07Z)
• Quantum Signal Processing with the one-dimensional quantum Ising model [0.0]
  Quantum Signal Processing (QSP) has emerged as a promising framework to manipulate and determine properties of quantum systems. We provide examples and applications of our approach in diverse fields ranging from space-time dual quantum circuits and quantum simulation, to quantum control.
  arXiv  Detail & Related papers  (2023-09-08T18:01:37Z)
• Quantum Davidson Algorithm for Excited States [42.666709382892265]
  We introduce the quantum Krylov subspace (QKS) method to address both ground and excited states. By using the residues of eigenstates to expand the Krylov subspace, we formulate a compact subspace that aligns closely with the exact solutions. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems.
  arXiv  Detail & Related papers  (2022-04-22T15:03:03Z)
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator [41.74498230885008]
  We demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms. We benchmark the system by creating and characterizing high-fidelity antiferromagnetically ordered states. We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation.
  arXiv  Detail & Related papers  (2020-12-22T19:00:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.