Efficient estimation of trainability for variational quantum circuits

TL;DR

This paper introduces an efficient classical method to evaluate the trainability of variational quantum circuits by mapping them to Clifford circuits, enabling the analysis of large systems and addressing barren plateau issues.

Contribution

It presents a novel exact mapping from random quantum circuits to classically simulable Clifford circuits for trainability assessment.

Findings

Method scales to 100 qubits

Can certify trainability of variational circuits

Helps design strategies to overcome barren plateaus

Abstract

Parameterized quantum circuits used as variational ans\"atze are emerging as promising tools to tackle complex problems ranging from quantum chemistry to combinatorial optimization. These variational quantum circuits can suffer from the well-known curse of barren plateaus, which is characterized by an exponential vanishing of the cost-function gradient with the system size, making training unfeasible for practical applications. Since a generic quantum circuit cannot be simulated efficiently, the determination of its trainability is an important problem. Here we find an efficient method to compute the gradient of the cost function and its variance for a wide class of variational quantum circuits. Our scheme relies on our proof of an exact mapping from randomly initialized circuits to a set of Clifford circuits that can be efficiently simulated on a classical computer by virtue of the celebrated Gottesmann-Knill theorem. This method is scalable and can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren plateau problem. As illustrative examples, we show results with up to 100 qubits.