Iterative Qubit Coupled Cluster method with involutory linear combinations of Pauli products.

Application of current and near-term quantum hardware to the electronic structure problem is highly limited by coherence times and gate fidelities. To address these restrictions within the variational quantum eigensolver (VQE) framework, the iterative qubit coupled-cluster (iQCC) procedure [I.G.Ryabinkin $et$ $al.$, arXiv:1906.11192] includes a portion of the ansatz not as quantum circuit elements but by unitarily transforming the Hamiltonian. iQCC has demonstrated systematic convergence towards ground state energies capable with arbitrarily shallow circuits, at the expense of exponential growth of the number of required measurements per VQE step. To reduce the growth of measurement requirements in iQCC, we present a scheme where the Hamiltonian is sequentially transformed via the unitary exponential of involutory linear combinations (ILC) of Pauli products. The ILC transformation results in quadratic growth in the number of Hamiltonian terms with the number of Pauli products included in ILC. The iQCC-ILC procedure is systematically improvable, variational, and hardware tailorable through modulation of computational cost between classical computation, number of measurements required per VQE step, and quantum circuit depths. We demonstrated that iQCC-ILC can provide chemically accurate potential energy curves for symmetric bond dissociation of H$_2$O and LiH.