  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.
