Circumventing Traps in Analog Quantum Machine Learning Algorithms Through Co-Design

TL;DR

This paper investigates the landscape properties of analog quantum machine learning algorithms, revealing trap issues and proposing a co-design methodology using Magnus expansion to improve their effectiveness in simulating quantum dynamics.

Contribution

It systematically studies AQML landscapes, identifies trap conditions, and introduces a co-design approach with Magnus expansion to enhance simulation accuracy.

Findings

Black-boxed models exhibit local traps in their landscapes.

Tailored models are trap-free according to numerical results.

Co-design with Magnus expansion improves convergence in quantum simulations.

Abstract

Quantum machine learning QML algorithms promise to deliver near-term, applicable quantum computation on noisy, intermediate-scale systems. While most of these algorithms leverage quantum circuits for generic applications, a recent set of proposals, called analog quantum machine learning (AQML) algorithms, breaks away from circuit-based abstractions and favors leveraging the natural dynamics of quantum systems for computation, promising to be noise-resilient and suited for specific applications such as quantum simulation. Recent AQML studies have called for determining best ansatz selection practices and whether AQML algorithms have trap-free landscapes based on theory from quantum optimal control (QOC). We address this call by systematically studying AQML landscapes on two models: those admitting black-boxed expressivity and those tailored to simulating a specific unitary evolution. Numerically, the first kind exhibits local traps in their landscapes, while the second kind is trap-free. However, both kinds violate QOC theory's key assumptions for guaranteeing trap-free landscapes. We propose a methodology to co-design AQML algorithms for unitary evolution simulation using the ansatz's Magnus expansion. We show favorable convergence in simulating dynamics with applications to metrology and quantum chemistry. We conclude that such co-design is necessary to ensure the applicability of AQML algorithms.