We introduce a novel hybrid quantum-classical quantum algorithm for solving many-body systems. An alternative to the well-known variational quantum eigensolver, the contracted quantum eigensolver (CQE) minimizes the residual of a contraction (or projection) of the Schrödinger equation onto the space of two (or more) electrons. The CQE is the quantum analog of classical methods for solving the anti-Hermitian contracted Schrödinger equation for the energies and two-electron reduced density matrices of ground and excited states without the many-electron wave function. The solver does not require deep circuits or difficult classical optimization and achieves a potentially exponential speed-up over its classical counterpart. The algorithm is demonstrated though computations on both a quantum simulator and two IBM quantum processing units. We apply the CQE with novel error-mitigation strategies on an IBM quantum computer to resolve the ground-state energies of the ortho-, meta-, and para- isomers of benzyne. We also show that the statically correlated active-space energy and two-electron reduced density matrix (2-RDM) from the CQE can be corrected to reflect the total electronic energies through a novel use of 2-RDM methods on the classical computer. Total energies are presented for two different 2-RDM methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multi-component pair density functional (MC-PDFT) theories.

Contracted quantum eigensolver for the quantum simulation of many-electron systems

ACS Spring 2022

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