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

TL;DR

This paper develops a phase-space formalism for multi-qubit quantum machine learning, enabling scalable classical simulations and new variational approaches by representing quantum states as quasi-probability functions.

Contribution

It introduces a novel phase-space dynamical framework for multi-qubit systems, replacing operator algebra with function dynamics on symplectic manifolds, facilitating scalable QML.

Findings

Formalism scales linearly with qubits

Replaces operator algebra with function dynamics

Enables variational modeling in phase-space

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.