Noise amplification at spin-glass bottlenecks of quantum annealing: A solvable model
David C K Roberts, Łukasz Cincio, Avadh Saxena, A. G. Petukhov, Sergey Knysh · Physical Review A · 2020
To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult optimization problems. We uncover a noise amplification effect at these bottlenecks, whereby tunneling rates caused by flux-qubit noise scale in proportion to the number of qubits $\mathcal{N}$ in the limit that $\mathcal{N}\ensuremath{\rightarrow}\ensuremath{\infty}$. By solving the incoherent annealing dynamics exactly, we find a wide range of regimes where the probability that a quantum annealer remains in the ground state upon exiting the bottleneck is close to one-half. We corroborate our analysis with detailed simulations of the performance of the D-Wave 2X quantum annealer on our class of computational problems.