Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm

TL;DR

This paper introduces Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer, advancing quantum generative modeling and thermal state preparation with numerical demonstrations on various quantum systems.

Contribution

It presents a new class of quantum-neural-network models and a thermalizer algorithm, enhancing hybrid quantum-classical learning and thermal state generation capabilities.

Findings

QHBMs effectively model classical and quantum correlations.

VQT converges to VQE at zero temperature.

Numerical results demonstrate successful application to spin, Bosonic, and Fermionic systems.

Abstract

We introduce a new class of generative quantum-neural-network-based models called Quantum Hamiltonian-Based Models (QHBMs). In doing so, we establish a paradigmatic approach for quantum-probabilistic hybrid variational learning, where we efficiently decompose the tasks of learning classical and quantum correlations in a way which maximizes the utility of both classical and quantum processors. In addition, we introduce the Variational Quantum Thermalizer (VQT) for generating the thermal state of a given Hamiltonian and target temperature, a task for which QHBMs are naturally well-suited. The VQT can be seen as a generalization of the Variational Quantum Eigensolver (VQE) to thermal states: we show that the VQT converges to the VQE in the zero temperature limit. We provide numerical results demonstrating the efficacy of these techniques in illustrative examples. We use QHBMs and the VQT on Heisenberg spin systems, we apply QHBMs to learn entanglement Hamiltonians and compression codes in simulated free Bosonic systems, and finally we use the VQT to prepare thermal Fermionic Gaussian states for quantum simulation.