Abstract
We investigate the problem of determining the Hamiltonian of a locally interacting open-quantum system. To do so, we construct model estimators based on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations of motion which rely on a polynomial number of measurements and parameters. We validate our Hamiltonian assignment methods by numerically simulating one-dimensional XX-interacting spin chains coupled to thermal reservoirs. We study Hamiltonian learning in the presence of systematic noise and find that, in certain time dependent cases, the Hamiltonian estimator accuracy increases when relaxing the environment's physicality constraints.
Highlights
Fault tolerant quantum computation provides a framework for digitally decomposing unitary operators using a polynomial number of one- and two-qubit operations drawn from a universal gate set [1]
For noisy intermediate scale quantum (NISQ) hardware, characterized by fixed gate fidelities and limited coherence times, digitizing a quantum simulation unitary is too costly in terms of the polynomial scaling circuit depth
Learning [5]), for scalable methods the estimation task is complicated by interactions coupling the principle system of interest to unwanted environmental degrees of freedom
Summary
Fault tolerant quantum computation provides a framework for digitally decomposing unitary operators using a polynomial number of one- and two-qubit operations drawn from a universal gate set [1]. It has been proposed that, in such a case, the target unitary can be decomposed as a sequence of native analog unitaries U = exp(−iHt ) interleaved with programmable singlequbit operations For certain applications, such as many-body simulations [3], the gate complexity, quantified by the total number of applications of the many-body evolution operator U and local rotations, may be significantly smaller than that of the digitized decomposition. Learning [5]), for scalable methods (local Hamiltonian tomography [6]) the estimation task is complicated by interactions coupling the principle system of interest to unwanted environmental degrees of freedom To address this outstanding issue, we study the problem of assigning a Hamiltonian to an open quantum system, provided the principle system and environmental interactions are both geometrically local. We conclude by discussing generalizations, practical constraints, and future directions for Hamiltonian learning
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