Quantum Algorithm for a Convergent Series of Approximations towards the Exact Solution of the Lowest Eigenstates of a Hamiltonian

• URL: http://arxiv.org/abs/2009.03537v1
• Date: Tue, 8 Sep 2020 06:16:07 GMT
• Title: Quantum Algorithm for a Convergent Series of Approximations towards the Exact Solution of the Lowest Eigenstates of a Hamiltonian
• Authors: Zhiyong Zhang
• Abstract summary: We present quantum algorithms for Hamiltonians of linear combinations of local unitary operators. The algorithms implement a convergent series of approximations towards the exact solution of the full CI (configuration interaction) problem.
• Score: 1.8895156959295205
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to the diagonal matrix elements only. The algorithms implement a convergent series of approximations towards the exact solution of the full CI (configuration interaction) problem. The algorithm scales with O(m^5 ), with m the number of one-electron orbitals in the case of molecular electronic structure calculations. Full CI results can be obtained with a scaling of O(nm^5 ), with n the number of electrons and a prefactor on the order of 10 to 20. With low orders of Hamiltonian matrix-vector products, a whole repertoire of approximations widely used in modern electronic structure theory, including various orders of perturbation theory and/or truncated CI at different orders of excitations can be implemented for quantum computing for both routine and benchmark results at chemical accuracy. The lowest order matrix-vector product with preconditioning, basically the second-order perturbation theory, is expected to be a leading algorithm for demonstrating quantum supremacy for Ab Initio simulations, one of the most anticipated real world applications. The algorithm is also applicable for the hybrid variational quantum eigensolver.

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