Hamiltonian assignment for open quantum systems

Abstract

We investigate the problem of determining the Hamiltonian of a locally interacting open quantum system. To do so, we construct Hamiltonian estimators based on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations of motion which rely on a polynomial number of measurements and model parameters. To validate our Hamiltonian assignment methods we numerically simulate one-dimensional X X-interacting spin chains coupled to thermal reservoirs. We provide general bounds on the scalability and assignment error in the presence of noise. In addition to discussing some details of practical implementations we find that, in a dynamical setting, the Hamiltonian estimator's accuracy increases when relaxing the environment's physicality constraints.

Toward pricing financial derivatives with an IBM quantum computer

“…where we have used the fact that S i−1 • S i × S i+1 contains 6 Pauli terms. For a 1D Heisenberg chain, the total commutator is bounded by 12J [122,123]. Additionally, Bayesian Hamiltonian learning [124] techniques may also be considered, although efficient importance sampling is required to adequately update models in this case.…”

Optimal parent Hamiltonians for time-dependent states

“…This matrix encodes the covariances of the local operators in the stationary state and its kernel contains all the possible local parent Hamiltonians. This approach has been extended in several ways, as the search for a stationary parent Hamiltonian associated to a state after a quantum quench 11 , to open quantum systems governed by a Lindblad dynamics 12,13 and the determination of a parent Hamiltonian of a Matrix Product State 14 . The non-uniqueness of the parent Hamiltonian is reflected in the degeneracy of the kernel of the QCM.…”