Dynamical Self-energy mapping for Quantum Computing.*

For noisy intermediate-scale quantum (NISQ) devices only a moderate number of qubits with alimited coherence is available thus enabling only shallow circuits and a few time evolution stepsin the currently performed quantum computations. Here, we present how to bypass this challengein practical molecular chemistry simulations on NISQ devices by employing a quantum–classicalhybrid algorithm allowing us to produce a sparse Hamiltonian which contains onlyO(n2) terms in aGaussian orbital basis when compared to theO(n4) terms of a standard Hamiltonian, wherenis thenumber of orbitals in the system. Classical part of this hybrid entails parametrization of the sparse,fictitious Hamiltonian in such a way that it recovers the self-energy of the original molecular system.Quantum machine then uses this fictitious Hamiltonian to calculate the self-energy of the system.We show that the developed hybrid algorithm yields very good total energies for small moleculartest cases while reducing the depth of the quantum circuit by at least an order of magnitude whencompared with simulations involving a full Hamiltonian.

arXiv:2010.05441