Clifford Disentanglers for Entanglement Reduction in Molecular Electronic Structure Simulations

Abstract

Entanglement is a key bottleneck limiting the efficiency of tensor-network and quantum simulations of molecular electronic structure. Here, we systematically assess and extend Clifford disentanglers as a structure-preserving approach to entanglement reduction: they can modify the entanglement structure of qubit wave functions while retaining the Pauli-string form of qubit Hamiltonians. To enable a practical search over Clifford transformations, we classify Clifford operators by their action on the Schmidt spectrum across a bipartition, reducing the two- and four-qubit search spaces to 20 and 91392 representatives, respectively. Embedded in an iterative Clifford-augmented matrix product state framework, these transformations reduce the energy errors at fixed bond dimension for the molecular test cases studied and mitigate the dependence on orbital ordering and Fermion-to-qubit mappings. We further show that Clifford disentanglers can also benefit quantum simulations such as shallow-circuit variational quantum eigensolver calculations. Together, these results establish Clifford disentanglers as a useful structure-preserving entanglement-engineering tool for tensor-network and quantum simulations of molecular electronic structure, while also clarifying their dependence on correlation and motivating future developments.