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

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.

arXiv:2404.03268 [quant-ph]

(or arXiv:2404.03268v4 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2404.03268 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.