Benchmarking Variational Quantum Eigensolvers for Entanglement Detection in Many-Body Hamiltonian Ground States

TL;DR

This paper benchmarks variational quantum eigensolvers (VQEs) for detecting entanglement in many-body ground states, showing that Hamiltonian-inspired circuits outperform generic ones in cost function estimation.

Contribution

It provides a systematic comparison of VQEs with different circuit structures for entanglement detection in many-body systems.

Findings

Hamiltonian-inspired circuits yield better cost function estimates.

Performance varies with the number of qubits and shots.

VQEs can effectively detect entanglement in many-body ground states.

Abstract

Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. These task-oriented algorithms work in a hybrid loop combining a quantum processor and classical optimization. Using a specific class of VQA named variational quantum eigensolvers (VQEs), we choose some parameterized quantum circuits to benchmark them at entanglement witnessing and entangled ground state detection for many-body systems described by Heisenberg Hamiltonian, varying the number of qubits and shots. Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.