Adaptive Quantum Generative Training using an Unbounded Loss Function

TL;DR

This paper introduces Re9nyi-ADAPT, a quantum generative learning algorithm that employs an unbounded loss function to improve training efficiency and circuit depth, outperforming existing methods in learning thermal states.

Contribution

The paper presents a novel adaptive quantum training algorithm using the maximal quantum Re9nyi divergence as a loss function, mitigating barren plateaus and enabling efficient circuit construction.

Findings

Re9nyi-ADAPT constructs shallow circuits comparable to state-of-the-art methods.

The maximal Re9nyi divergence loss maintains favorable gradients during training.

Numerical experiments demonstrate effectiveness on systems up to 12 qubits.

Abstract

We propose a generative quantum learning algorithm, R\'enyi-ADAPT, using the Adaptive Derivative-Assembled Problem Tailored ansatz (ADAPT) framework in which the loss function to be minimized is the maximal quantum R\'enyi divergence of order two, an unbounded function that mitigates barren plateaus which inhibit training variational circuits. We benchmark this method against other state-of-the-art adaptive algorithms by learning random two-local thermal states. We perform numerical experiments on systems of up to 12 qubits, comparing our method to learning algorithms that use linear objective functions, and show that R\'enyi-ADAPT is capable of constructing shallow quantum circuits competitive with existing methods, while the gradients remain favorable resulting from the maximal R\'enyi divergence loss function.