Quantum Hamiltonian Identification from Measurement Time Traces

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

Figure 1

A spin (or qubit) lattice as an example illustrating the type of system considered in this work. The spins interact with each other through nearest-neighbor or long-range couplings and certain local observables are measurable for a subset of the spins (circled above). The task is to identify the parameters defining the Hamiltonian of the interconnected system from a time trace of expectation values of these observables.

Figure 2

Assessing the robustness of the parameter estimation algorithm. The $x$ axis in both figures is the standard deviation of the measurement noise, $\sigma$. (a) Percentage relative error in mean of estimates. (b) Standard deviation of estimates.