The Questionable Influence of Entanglement in Quantum Optimisation Algorithms

2024-07-24

International Conference on Quantum Computing and Engineering

AI Summary

The impact of Hadamard state initialization and CNOT-based entanglement structure on the performance of the Variational Quantum Eigensolver (VQE) for solving MaxCut remains poorly understood. Method: We systematically evaluate eight parameterized quantum circuit variants across 100 random graph instances, isolating the effects of initial state preparation and entanglement depth. Contribution/Results: Contrary to common assumptions, Hadamard initialization yields no performance improvement; moreover, entanglement introduction does not enhance solution quality and consistently degrades performance as circuit depth increases. Crucially, we observe a non-monotonic entanglement effect—moderate entanglement may facilitate coordination among qubits, whereas excessive entanglement induces “overload,” leading to deterioration. This challenges the heuristic “more entanglement is better” in quantum optimization. Based on these findings, we propose the “coordination–overload” biphasic hypothesis of entanglement, offering empirical evidence and theoretical insight for the rational design of entanglement resources in VQE and related quantum algorithms.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The performance of the Variational Quantum Eigen-solver (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.

Problem

• Evaluating entanglement effectiveness in quantum optimization algorithms
• Assessing Hadamard and CNOT gates impact on solution quality
• Investigating entanglement's role in parameter coordination across qubits

Innovation

• Evaluating Hadamard and CNOT gate effectiveness
• Testing eight circuits on MaxCut problems
• Observing entanglement's negative impact on results