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For many optimization algorithms the time-to-solution depends not only on the problem size but also on the specific problem instance and may vary by many orders of magnitude. It is then necessary to investigate the full distribution and especially its tail. Here we analyze the distributions of annealing times for simulated annealing and simulated quantum annealing (by path integral quantum Monte Carlo) for random Ising spin glass instances. We find power-law distributions with very heavy tails, corresponding to extremely hard instances, but far broader distributions - and thus worse performance for hard instances - for simulated quantum annealing than for simulated annealing. Fast, non-adiabatic, annealing schedules can improve the performance of simulated quantum annealing for very hard instances by many orders of magnitude.
The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuations theorems. Here we develop a semiclassical approximation to the work distribution for a quench process in chaotic systems.
In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of multiple simult
In this letter we present an efficient gap-independent cooling scheme for a quantum annealer that benefits from finite temperatures. We choose a system based on superconducting flux qubits as a prominent example of current quantum annealing platforms
We show that space- and time-correlated single-qubit rotation errors can lead to high-weight errors in a quantum circuit when the rotation angles are drawn from heavy-tailed distributions. This leads to a breakdown of quantum error correction, yieldi
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Simulated annealing is a computational technique which explores the configuration space by mimicking therma