One-Qubit Transverse-Field Ising Model and Variational Quantum Algorithms

Robson Giles

Ashutosh P. Tripathi, Nilmani Mathur A, Vikram Tripathi

The Variational Quantum Eigensolver (VQE) is a leading hybrid quantum-classical algorithm for simulating many-body systems in the NISQ era. Its effectiveness, however, depends on the faithful preparation of eigenstates, which becomes challenging in degenerate and strongly entangled regimes. We study this problem using the transverse-field Ising model (TFIM) with periodic boundary conditions in one, two, and three dimensions, considering systems of up to 27 qubits. We employ different ansatzes: the hardware-efficient EfficientSU2 from Qiskit, the physics-inspired Hamiltonian Variational Ansatz (HVA) and HVA with symmetry breaking, and benchmark their performance using energy variance, entanglement entropy, spin correlations, and magnetization.

Jun‐ichi Inoue

Ashutosh P. Tripathi, Nilmani Mathur, Vikram Tripathi

The Variational Quantum Eigensolver (VQE) is a leading hybrid quantum-classical algorithm for simulating many-body systems in the NISQ era. Its effectiveness, however, depends on the faithful preparation of eigenstates, which becomes challenging in degenerate and strongly entangled regimes. We study this problem using the transverse-field Ising model (TFIM) with periodic boundary conditions in one, two, and three dimensions, considering systems of up to 27 qubits. We employ different ansatzes: the hardware-efficient EfficientSU2 from Qiskit, the physics-inspired Hamiltonian Variational Ansatz (HVA) and HVA with symmetry breaking, and benchmark their performance using energy variance, entanglement entropy, spin correlations, and magnetization.

Babatunde M. Ayeni

Ashutosh P. Tripathi, Nilmani Mathur, Vikram Tripathi

We explore the application of the Variational Quantum Eigensolver (VQE) to investigate the ground state properties, particularly the entanglement entropy, of the Transverse Field Ising Model (TFIM) in one, two, and three dimensions, considering systems of up to 27 spins. By benchmarking VQE results against exact diagonalization and analyzing the entanglement properties across different system sizes, we assess the algorithm's effectiveness in capturing faithful ground state. Using results of TFIM, we also investigate how VQE's expressivity and optimization influence the simulation of highly entangled quantum states. We employ different ansätze: the hardware-efficient EfficientSU2 from Qiskit, the physics-inspired Hamiltonian Variational ansätz (HVA) and HVA with symmetry breaking, and benchmark their performance using energy variance, entanglement entropy, spin correlations, and magnetization. We further discuss the implications for scaling these methods to larger quantum systems.