Scalable reconstruction of unitary processes and Hamiltonians

TL;DR

This paper introduces a scalable quantum process tomography method that efficiently reconstructs unitary processes and local Hamiltonians using linearly many measurements and states, significantly reducing resource requirements.

Contribution

The authors develop a scalable tomography technique for unitary processes and Hamiltonians that requires only linearly many measurements and states, improving over exponential scaling methods.

Findings

Numerical simulations show polynomial scaling of measurements and processing.

Method successfully reconstructs quantum circuits and local Hamiltonians.

Requires only local measurements and eigenstate preparations or ancilla-based entanglement.

Abstract

Based on recently introduced efficient quantum state tomography schemes, we propose a scalable method for the tomography of unitary processes and the reconstruction of one-dimensional local Hamiltonians. As opposed to the exponential scaling with the number of subsystems of standard quantum process tomography, the method relies only on measurements of linearly many local observables and either (a) the ability to prepare eigenstates of locally informationally complete operators or (b) access to an ancilla of the same size as the to-be-characterized system and the ability to prepare a maximally entangled state on the combined system. As such, the method requires at most linearly many states to be prepared and linearly many observables to be measured. The quality of the reconstruction can be quantified with the same experimental resources that are required to obtain the reconstruction in the first place. Our numerical simulations of several quantum circuits and local Hamiltonians suggest a polynomial scaling of the total number of measurements and post-processing resources.