Improved variational quantum eigensolver via quasi-dynamical evolution
The variational quantum eigensolver (VQE) is a hybrid quantum-classical
algorithm designed for current and near-term quantum devices. Despite its
initial success, there is a lack of understanding involving several of its key
aspects. There are problems with VQE that forbid a favourable scaling towards
quantum advantage. In order to alleviate the problems, we propose and
extensively test a quantum annealing inspired heuristic that supplements VQE.
The improved VQE enables an efficient initial state preparation mechanism, in a
recursive manner, for a quasi-dynamical unitary evolution. We conduct an
in-depth scaling analysis of finding the ground state energies with increasing
lattice sizes of the Heisenberg model, employing simulations of up to $40$
qubits that manipulate the complete state vector. For the current devices, we
further propose a benchmarking toolkit using a mean-field model and test it on
IBM Q devices. The improved VQE avoids barren plateaus, exits local minima, and
works with low-depth circuits. Realistic gate execution times estimate a longer
computational time to complete the same computation on a fully functional
error-free quantum computer than on a quantum computer emulator implemented on
a classical computer. However, our proposal can be expected to help accurate
estimations of the ground state energies beyond $50$ qubits when the complete
state vector can no longer be stored on a classical computer, thus enabling
quantum advantage.
Manpreet Singh Jattana Fengping Jin Hans De Raedt Kristel Michielsen