Direct Energy Gap Calculations in Heisenberg Spin Systems Using Superconducting Quantum Devices

Accurate calculation of spin-state energy gaps is central to spin chemistry. The novel Quantum Phase Difference Estimation (QPDE) algorithm enables direct computation of energy gaps on a quantum computer. However, the required quantum circuits are typically too deep for noisy intermediate-scale quantum (NISQ) devices. In this study, as an initial step toward practical calculations for strongly correlated molecular multi-spin systems, we applied QPDE to two- and three-spin Heisenberg Hamiltonians with various geometries and coupling strengths, including symmetric, asymmetric, spin-frustrated, and non-frustrated configurations. We found that the quantum circuit for the time-evolution operator achieves constant depth due to its match gate-like structure, making it well-suited for NISQ implementation. Proof-of-principle hardware demonstrations using an IBM quantum processor yielded 85%-96% accuracy in determining spin-state energy gaps.