# VanQver: The Variational and Adiabatically Navigated Quantum Eigensolver. (arXiv:1810.11511v2 [quant-ph] UPDATED)

The accelerated progress in manufacturing noisy intermediate-scale quantum

(NISQ) computing hardware has opened the possibility of exploring its

application in transforming approaches to solving computationally challenging

problems. The important limitations common among all NISQ computing

technologies are the absence of error correction and the short coherence time,

which limit the computational power of these systems. Shortening the required

time of a single run of a quantum algorithm is essential for reducing

environment-induced errors and for the efficiency of the computation. We have

investigated the ability of a variational version of adiabatic quantum

computation (AQC) to generate an accurate state more efficiently compared to

existing adiabatic methods. The standard AQC method uses a time-dependent

Hamiltonian, connecting the initial Hamiltonian with the final Hamiltonian. In

the current approach, a navigator Hamiltonian is introduced which has a

non-zero amplitude only in the middle of the annealing process. Both the

initial and navigator Hamiltonians are determined using variational methods. A

hermitian cluster operator, inspired by coupled-cluster theory and truncated to

single and double excitations/de-excitations, is used as a navigator

Hamiltonian. A comparative study of our variational algorithm (VanQver) with

that of standard AQC, starting with a Hartree--Fock Hamiltonian, is presented.

The results indicate that the introduction of the navigator Hamiltonian

significantly improves the annealing time required to achieve chemical accuracy

by two to three orders of magnitude. The efficiency of the method is

demonstrated in the ground-state energy estimation of molecular systems,

namely, H$_2$, P4, and LiH.