Tomography of time-dependent quantum Hamiltonians with machine learning

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.

Quantum Machine Learning: from physics to software engineering

“…Applications of these data-driven learning and/or adaptation ML are not limited to quantum state tomography. Identification and estimation of quantum process tomography, Hamiltonian tomography, and quantum channel tomography, as well as quantum phase estimation, are also in progresses [357][358][359][360]. Moreover, ML in quantum tomography can be used for the quantum state preparation, for the general single-preparation quantum information processing (SIPQIP) framework [361].…”

Learning Quantum Systems

“…GAN-based approximations of the superoperator Λ have also been proposed as an efficient method for QPT [86]. Other methods exploit NNs to generalise QPT to the characterisation of time dependent spin systems [139], while yet another class reconstructs a unitary quantum process by inverting the dynamics using a variational algorithm [140,141]. RNNs have recently been shown to be useful in learning the non-equilibrium dynamics of a many-body quantum system from its nonlinear response under random driving [142].…”