Jordan-Wigner mapping for nonorthogonal spin orbitals

Quantum computing offers a promising platform to address the computational challenges inherent in quantum chemistry, and particularly in valence bond (VB) methods, which are chemically appealing but suffer from high computational cost due to the use of nonorthogonal orbitals. While various fermionic-to-spin mappings exist for orthonormal spin orbitals, such as the widely used Jordan–Wigner transformations, an analogous framework for nonorthogonal spin orbitals remains undeveloped. In this work, we propose an alternative Jordan–Wigner-type mapping tailored for the nonorthogonal case, with the goal of enabling efficient quantum simulations of VB-type wavefunctions. Our approach paves the way towards the development of chemically interpretable and computationally feasible valence bond algorithms on near-term quantum devices.