Quantum Wasserstein Compilation: Unitary Compilation using the Quantum Earth Mover's Distance

TL;DR

This paper introduces a novel variational quantum circuit compilation method using the quantum Wasserstein distance, which improves optimization and reduces barren plateaus in deep quantum circuits.

Contribution

It proposes the quantum Wasserstein compilation (QWC) cost function for VQCC, demonstrating its advantages over existing metrics like LET and HST.

Findings

QWC upper bounds average infidelity of circuits.

QWC is less affected by barren plateaus.

QWC improves deep circuit compilation performance.

Abstract

Despite advances in the development of quantum computers, the practical application of quantum algorithms requiring deep circuit depths or high-fidelity transformations remains outside the current range of the so-called noisy intermediate-scale quantum devices. Now and beyond, quantum circuit compilation (QCC) is a crucial component of any quantum algorithm execution. Besides translating a circuit into hardware-specific gates, it can optimize circuit depth and adapt to noise. Variational quantum circuit compilation (VQCC) optimizes the parameters of an ansatz according to the goal of reproducing a given unitary transformation. In this work, we present a VQCC-objective function called the quantum Wasserstein compilation (QWC) cost function based on the quantum Wasserstein distance of order 1. We show that the QWC cost function upper bounds the average infidelity of two circuits. An estimation method based on measurements of local Pauli-observable is utilized in a generative adversarial network to learn a given quantum circuit. We demonstrate the efficacy of the QWC cost function by compiling hardware efficient ansatz (HEA) as both the target and the ansatz and comparing to cost functions such as the Loschmidt echo test (LET) and the Hilbert-Schmidt test (HST). Finally, our experiments demonstrate that QWC as a cost function is the least affected by barren plateaus when compared to LET and HST for deep enough circuits.