Fragmentation of Virtual Orbitals for Quantum Computing: Reducing Qubit Requirements through Many-Body Expansion

Abstract: The development of quantum computing for molecular simulations is constrained by the limited number of qubits available on current Noisy Intermediate-Scale Quantum (NISQ) devices. The present work introduces the Virtual Orbital Fragmentation (FVO) method, a systematic approach that reduces qubit requirements by 40--66\% while maintaining chemical accuracy. The method partitions the virtual orbital space into chemically intuitive fragments and employs many-body expansion techniques analogous to spatial fragmentation methods. Applications to six molecular systems demonstrate that the 2-body FVO expansion achieves errors below 3 kcal/mol, while the 3-body expansion provides sub-kcal/mol accuracy. When integrated with the Variational Quantum Eigensolver (VQE) and combined with the Effective Fragment Molecular Orbital (EFMO) method for multi-molecular systems, the hierarchical Q-EFMO-FVO approach achieves 96--100\% accuracy relative to full calculations. The method provides a practical pathway for quantum chemical calculations on current 50--100 qubit processors and establishes virtual orbital fragmentation as a complementary strategy to spatial fragmentation for managing quantum computational complexity.