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.

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