Non-adiabatic LHZ
Abstract
We present a coherent counter-diabatic quantum protocol to prepare ground states in the lattice gauge mapping of all-to-all Ising models (LHZ) with considerably enhanced final ground state fidelity compared to a quantum annealing protocol.
We make use of a variational method to find approximate counter-diabatic Hamiltonians that has recently been introduced by Sels and Polkovnikov (2017 Proc. Natl. Acad. Sci.114 3909). The resulting additional terms in our protocol are time-dependent local on-site y-magnetic fields. These additional Hamiltonian terms do not increase the minimal energy gap, but instead compensate for the Berry curvature. A single free parameter is introduced which is optimized via classical updates.
The protocol consists only of local and nearest-neighbor terms which makes it attractive for implementation in near term experiments.