Randomized adaptive quantum state preparation

TL;DR

This paper introduces an adaptive quantum state preparation method that leverages randomness and feedback from gradient measurements, avoiding classical optimization, and demonstrates its effectiveness through theoretical and numerical analysis.

Contribution

It presents a novel randomized adaptive approach for quantum state preparation that does not rely on classical optimization, with proven convergence and applicability to large-scale problems.

Findings

Convergence to the target state is achievable for almost all initial states.

Different randomization procedures impact the efficiency and success of the method.

Lower bounds on expected cost function change relate to barren plateaus and large-scale applicability.

Abstract

We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state through an adaptively constructed quantum circuit, where each adaptive step is informed by feedback from gradient measurements in which the associated tangent space directions are randomized. We provide theoretical arguments and numerical evidence that convergence to the target state can be achieved for almost all initial states. We investigate different randomization procedures and develop lower bounds on the expected cost function change, which allows for drawing connections to barren plateaus and for assessing the applicability of the algorithm to large-scale problems.