Molecular Ground State Simulation by Subspace Restriction and Hund's Rule

2026-10-19 · arXiv Quantum Physics

arXiv:2404.03268v4 Announce Type: replace

Abstract: The Subspace Restriction Scheme (SRS) is presented to address the qubit and resource constraints of molecular simulation on near-term quantum hardware. SRS restricts a molecular Hamiltonian to a selected determinant subspace before qubit encoding, so a $D$-dimensional subspace requires only $q=\lceil\log_2D\rceil$ qubits. We apply SRS to the established seniority-resolved Multi-Hund Subspaces $\mathrm{MHS}(\Omega)$ and develop compact encodings for these sectors. At fixed seniority and filling fraction, MHS asymptotically uses about half as many qubits as a compact particle-conserving encoding. For the $\mathrm{H}_{22}$ chain, the register shrinks from $44$ to $20$ qubits. Compression can nevertheless increase Pauli-operator density and does not always reduce measurement cost. In noiseless VQE benchmarks, shallow circuits reach within $1.6$~mHa of the exact subspace minima using only $4$--$30$ CNOT gates. However, the corresponding subspace minima for LiH, HF, OH, and CH remain $4.39$--$9.73$~mHa above FCI. Full-space UCCSD reaches chemical accuracy but requires hundreds to thousands of CNOT gates. SRS therefore provides a controlled resource--accuracy trade-off when register width is the binding constraint and the target state is well represented within a selected seniority sector.

原文链接：https://arxiv.org/abs/2404.03268

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