Quantum Process Tomography of Unitary Maps from Time-Delayed Measurements

TL;DR

This paper introduces a novel quantum process tomography method that reconstructs unitary maps and Hamiltonians using only a few initial states and time-delayed measurements, leveraging Takens embedding theorem.

Contribution

It presents a new approach to quantum process tomography that reduces the need for multiple initial states by using time-delayed measurements and mathematical embedding techniques.

Findings

Successfully reconstructs single-qubit Hamiltonians from limited measurements.

Demonstrates feasibility for few-qubit and lattice systems with local interactions.

Enables Hamiltonian identification of a two-qubit system by observing only one qubit.

Abstract

Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known initial states together with time-delayed measurements for reconstructing the unitary map and corresponding Hamiltonian of the time dynamics. The overarching mathematical framework and feasibility guarantee of our method is provided by the Takens embedding theorem. We explain in detail how the reconstruction of a single qubit Hamiltonian works in this setting, and provide numerical methods and experiments for general few-qubit and lattice systems with local interactions. In particular, the method allows to find the Hamiltonian of a two qubit system by observing only one of the qubits.