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

TL;DR

This work tackles the qubit bottleneck in NISQ quantum chemistry by introducing Virtual Orbital Fragmentation (FVO), a method that partitions the virtual orbital space and uses a many-body expansion to recover full correlation with significantly fewer qubits. When coupled with VQE and EFMO in a hierarchical Q-EFMO-FVO framework, the approach achieves 40–66% qubit reductions and sub-kcal/mol accuracy across diverse molecular systems, with 2-body expansions capturing 96–99.5% of the full correlation and 3-body expansions delivering even higher precision. The results show substantial circuit-depth reductions in VQE and demonstrate that multi-scale fragmentation can render otherwise intractable molecular clusters feasible on 50–100 qubit devices. This work establishes virtual orbital fragmentation as a robust, complementary strategy to spatial fragmentation, providing a scalable path toward practical quantum-chemical calculations on near-term hardware and beyond.

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.

Figures (4)

• Figure 1: Schematic illustration of the Virtual Orbital Fragmentation (FVO) approach. Left: Full molecular orbital space showing occupied orbitals (OO, blue) and complete set of virtual orbitals (VO$_1$--VO$_N$, gray). Center: Fragmentation of virtual orbitals into chemically intuitive subsets (VO$_1$--VO$_3$, colored regions). Right: Many-body expansion calculations showing 1-body (individual fragments), 2-body (pairwise interactions), and 3-body (three-way interactions) terms that recover the full correlation energy while requiring fewer qubits per calculation.
• Figure 2: FVO monomer energy calculations in the many-body expansion. Each monomer calculation combines the complete occupied orbital space (blue) with a single virtual orbital fragment (colored), enabling parallel computation of individual fragment contributions.
• Figure 3: FVO dimer correction calculations in the many-body expansion. Each dimer calculation combines the complete occupied orbital space with two virtual orbital fragments to capture pairwise interaction corrections.
• Figure 4: Spatial fragmentation schemes for molecular clusters in the Q-EFMO-FVO framework. Top left: Water trimer (3H$_2$O) with three spatial fragments. Top right: Water tetramer (4H$_2$O) with four spatial fragments. Bottom left: Ammonia trimer (3NH$_3$) with three spatial fragments. Bottom right: Mixed system (H$_2$O + NH$_3$ + CH$_2$O) with three different molecular species. Each cluster is decomposed at the spatial level (EFMO), with each fragment then undergoing virtual orbital fragmentation (FVO).