Proposal for Estimating the Energy Gap of the Transverse-Field Ising Hamiltonian Using a D-Wave Quantum Annealer

Abstract

The transverse-field Ising model is a fundamental quantum spin system that captures the competition between quantum fluctuations and interactions, playing a central role in studies of quantum phase transitions and non-equilibrium dynamics. However, classical computations of ground and excited states in large-scale or high-dimensional systems are severely limited by the exponential growth of the Hilbert space. Here, we propose a novel approach using a D-Wave quantum annealer, where a triangular-wave oscillating magnetic field is applied to induce Rabi oscillations, allowing the estimation of energy gaps between the ground and excited states. Unlike conventional quantum annealing methods limited to ground-state searches, this approach can directly access excited-state information. It is potentially applicable to larger systems, providing a new avenue for quantum-device-based simulation. The validity of the method is demonstrated through numerical simulations of relatively small systems.