Quantum Hamiltonian identification from measurement time traces

Abstract

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this work we consider a setting where system evolution is determined by a parameterized 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.

5 pages + Supplementary Information. Modified estimation algorithm to be robust to measurement noise. New results on noise robustness. Published version

References in corpus (7)

• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Quantum Process Tomography: Resource Analysis of Different Strategies
• Robust Online Hamiltonian Learning
• Coupling strength estimation for spin chains despite restricted access
• Hamiltonian tomography in an access-limited setting without state initialization
• Identifying an Experimental Two-State Hamiltonian to Arbitrary Accuracy
• Indirect Hamiltonian Identification through a small gateway

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