Demonstration of Error-Suppressed Quantum Annealing Via Boundary Cancellation

The boundary-cancellation theorem for open systems extends the standard quantum adiabatic theorem: assuming the gap of the Liouvillian does not vanish, the distance between a state prepared by a boundary -cancelling adiabatic protocol and the steady state of the system shrinks as a power of the number of vanishing time derivatives of the Hamiltonian at the end of the preparation. Here we generalize the boundary-cancellation theorem so that it applies also to the case where the Liouvillian gap vanishes, and consider the effect of dynamical freezing of the evolution. We experimentally test the predictions of the boundary-cancellation theorem using quantum annealing hardware, and find qualitative agree-ment with the predicted error suppression despite using annealing schedules that only approximate the required smooth schedules. Performance is further improved by using quantum annealing correction, and we demonstrate that the boundary-cancellation protocol is significantly more robust to parameter variations than protocols that employ pausing to enhance the probability of finding the ground state.

Automated summary

The boundary-cancellation theorem extends the standard quantum adiabatic theorem and shows that the distance between a state prepared by a boundary-cancelling adiabatic protocol and the steady state of the system shrinks as a power of the number of vanishing time derivatives of the Hamiltonian. This theorem is further generalized to apply to cases where the Liouvillian gap vanishes, and the effect of dynamical freezing of the evolution is considered. Experimental tests using quantum annealing hardware confirm the predictions of the boundary-cancellation theorem and demonstrate its robustness compared to other protocols.