Quantum Annealing with Non-stoquastic Hamiltonians
We study the role of Hamiltonian complexity in the performance of quantum annealers. It is well-known that non-stoquastic Hamiltonians are more complex than stoquastic Hamiltonians and universal adiabatic quantum computing is possible when they are employed. Here we ask whether utilizing non-stoquastic Hamiltonians in quantum annealers can lead to a better performance in solving optimization problems. We simulate the process of quantum annealing with both stoquastic and non-stoquastic Hamiltonians and compare their performance in finding the groundstate of a long-range Ising spin glass. We find that, for a small percentage of mostly harder instances, quantum annealers with non-stoquastic Hamiltonians greatly outperform their stoquastic counterparts and this superior performance persists as the system size grows. We conjecture that the observed advantage is closely related to the frustrated nature of our non-stoquastic Hamiltonians. This work is based on Phys. Rev. B 95, 184416 (2017).