Calibrating the Role of Entanglement in Variational Quantum Algorithms from a Geometric Perspective

TL;DR

This paper investigates how entanglement influences variational quantum algorithms by analyzing the geometric phases involved, revealing that entanglement acts as a dynamical resource in certain ansatzes.

Contribution

It introduces a geometric perspective on entanglement dynamics in quantum algorithms, highlighting the role of geometric phases and entanglement as a resource in HVA.

Findings

Quantum state evolution is mainly governed by geometric phase.

In HEA, entanglement dynamics are decoupled from state evolution.

In HVA, entanglement consumption correlates with faster evolution.

Abstract

Calibrating the role of entanglement in quantum algorithms is a crucial task in the development of quantum computing. Most existing studies have primarily focused on how the static properties of entanglement-such as its magnitude and phase-affect key performance metrics. In this work, we instead explore the relationship between the dynamical behaviors of entanglement and the execution of variational quantum algorithms from a geometric perspective. We find that, in contrast to conventional Hamiltonian dynamics where the evolution process is dominated by the dynamical phase, quantum state evolution in quantum algorithms is primarily governed by the geometric phase with the trajectory determined by the parameter-dependent Hilbert space geometry. In the problem-agnostic Hardware-Efficient Ansatz (HEA), entanglement dynamics and state evolution are decoupled. Conversely, in the problem-inspired Hamiltonian Variational Ansatz (HVA), the dynamical phase contribution is enhanced, allowing entanglement to function as a dynamical resource: more entanglement consumption correlates directly with faster quantum state evolution.