Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions

Abstract

Accurate determination of ground-state energies for molecules remains a challenge in quantum chemistry and a cornerstone for progress in fields such as drug discovery and materials design. The Variational Quantum Eigensolver (VQE) represents a leading hybrid quantum-classical paradigm for addressing this challenge; however, its widespread realization is limited by noise and the restricted scalability of current quantum hardware. Achieving efficient simulations on Noisy Intermediate-Scale Quantum (NISQ) devices and forthcoming Fault-Tolerant Application-Scalable Quantum (FASQ) systems demands a detailed understanding of how computational resources scale with molecular complexity and fermion-to-qubit encodings. In this study, resource requirements for VQE implementations employing the Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz are systematically analyzed. The molecular Hamiltonian is formulated in second quantization and mapped to qubit operators through the Jordan-Wigner (JW), Bravyi-Kitaev (BK), and Parity (Pa) transformations. Hamiltonian reduction strategies, including ${\mathbb{Z}}_2$ tapering and frozen-core approximations, are examined to assess their effect on quantum resource scaling. The analysis reveals that appropriate transformations, when combined with symmetry-based reductions, can substantially reduce qubit counts by up to $\approx 50\%$ and quantum gate counts by up to $\approx 27.5\times$ and Hamiltonian Pauli string counts by up to $\approx 2.75\times$, relative to the corresponding unreduced Hamiltonian representations within the same active-space configuration for the representative set of molecular systems under study. These findings provide practical circuit-level insights for executing chemically relevant simulations on NISQ hardware, while establishing physical-resource baselines that may inform future logical-level analyses targeting FASQ systems.

41 pages, 4 figures. Major revision

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