Quantum Wasserstein Compilation: Unitary Compilation using the Quantum Earth Mover's Distance
Marvin Richter, Abhishek Y. Dubey, Axel Plinge, Christopher Mutschler,, Daniel D. Scherer, Michael J. Hartmann

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…
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Taxonomy
Topicsadvanced mathematical theories · Advanced Mathematical Theories and Applications
