The Questionable Influence of Entanglement in Quantum Optimisation Algorithms

TL;DR

This study investigates the role of entanglement in quantum optimization algorithms, finding that entanglement does not improve solution quality and may even hinder performance as circuit complexity increases.

Contribution

The paper provides empirical evidence questioning the effectiveness of entanglement in quantum optimization circuits, challenging assumptions about its benefits in quantum machine learning.

Findings

Entanglement shows no positive effect on solution quality.

Adding entanglement can lead to lower and worse results.

More circuit layers with entanglement deteriorate performance.

Abstract

The performance of the Variational Quantum Eigensolver (VQE) is promising compared to other quantum algorithms, but also depends significantly on the appropriate design of the underlying quantum circuit. Recent research by Bowles, Ahmend \& Schuld, 2024 [1] raises questions about the effectiveness of entanglement in circuits for quantum machine learning algorithms. In our paper we want to address questions about the effectiveness of state preparation via Hadamard gates and entanglement via CNOT gates in the realm of quantum optimisation. We have constructed a total of eight different circuits, varying in implementation details, solving a total of 100 randomly generated MaxCut problems. Our results show no improvement with Hadamard gates applied at the beginning of the circuits. Furthermore, also entanglement shows no positive effect on the solution quality in our small scale experiments. In contrast, the investigated circuits that used entanglement generally showed lower, as well as deteriorating results when the number of circuit layers is increased. Based on our results, we hypothesise that entanglement can play a coordinating role, such that changes in individual parameters are distributed across multiple qubits in quantum circuits, but that this positive effect can quickly be overdosed and turned negative. The verification of this hypothesis represents a challenge for future research and can have a considerable influence on the development of new hybrid algorithms.