Tomography of time-dependent quantum spin networks with machine learning

TL;DR

This paper introduces a physics-enhanced machine learning approach using Heisenberg neural networks to reconstruct the structure of time-dependent quantum spin networks from local measurements, achieving high fidelity even with minimal data.

Contribution

It develops a novel deep learning framework based on the Heisenberg equation to accurately reconstruct entire spin network Hamiltonians from limited local measurements.

Findings

Reconstructed Hamiltonians with about 90% fidelity from single-spin measurements.

Applicable to various time-dependent quantum systems governed by the Heisenberg equation.

Demonstrated effectiveness across different spin network structures.

Abstract

Interacting spin networks are fundamental to quantum computing. Data-based tomography of time-independent spin networks has been achieved, but an open challenge is to ascertain the structures of time-dependent spin networks using time series measurements taken locally from a small subset of the spins. Physically, the dynamical evolution of a spin network under time-dependent driving or perturbation is described by the Heisenberg equation of motion. Motivated by this basic fact, we articulate a physics-enhanced machine learning framework whose core is Heisenberg neural networks. In particular, we develop a deep learning algorithm according to some physics motivated loss function based on the Heisenberg equation, which "forces" the neural network to follow the quantum evolution of the spin variables. We demonstrate that, from local measurements, not only the local Hamiltonian can be recovered but the Hamiltonian reflecting the interacting structure of the whole system can also be faithfully reconstructed. We test our Heisenberg neural machine on spin networks of a variety of structures. In the extreme case where measurements are taken from only one spin, the achieved tomography fidelity values can reach about 90%. The developed machine learning framework is applicable to any time-dependent systems whose quantum dynamical evolution is governed by the Heisenberg equation of motion.