Parametric Quantum State Tomography with HyperRBMs

TL;DR

This paper introduces a hypernetwork-based neural quantum state model that efficiently performs quantum state tomography across entire phase diagrams, accurately capturing phase transitions without retraining.

Contribution

It presents a novel parametric QST method using hypernetworks to condition RBMs on Hamiltonian parameters, enabling comprehensive phase diagram reconstruction.

Findings

High-fidelity state reconstructions across phases

Accurate reproduction of fidelity susceptibility

Identification of quantum phase transitions

Abstract

Quantum state tomography (QST) is essential for validating quantum devices but suffers from exponential scaling in system size. Neural-network quantum states, such as Restricted Boltzmann Machines (RBMs), can efficiently parameterize individual many-body quantum states and have been successfully used for QST. However, existing approaches are point-wise and require retraining at every parameter value in a phase diagram. We introduce a parametric QST framework based on a hypernetwork that conditions an RBM on Hamiltonian control parameters, enabling a single model to represent an entire family of quantum ground states. Applied to the transverse-field Ising model, our HyperRBM achieves high-fidelity reconstructions from local Pauli measurements on 1D and 2D lattices across both phases and through the critical region. Crucially, the model accurately reproduces the fidelity susceptibility and identifies the quantum phase transition without prior knowledge of the critical point. These results demonstrate that hypernetwork-modulated neural quantum states provide an efficient and scalable route to tomographic reconstruction across full phase diagrams.