Parametric Quantum State Tomography with HyperRBMs
This work addresses the scalability challenge in quantum state tomography for validating quantum devices, offering an efficient method for reconstructing phase diagrams, though it is incremental as it builds on existing neural-network quantum state approaches.
The authors tackled the problem of exponential scaling in quantum state tomography by introducing a hypernetwork-based parametric framework that conditions a Restricted Boltzmann Machine on Hamiltonian parameters, enabling reconstruction of entire families of quantum ground states from local Pauli measurements. Their HyperRBM achieved high-fidelity reconstructions in 1D and 2D transverse-field Ising models, accurately reproducing fidelity susceptibility and identifying quantum phase transitions without prior knowledge.
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.