  Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute
high quality solutions of NP-hard problems. This is done by mapping a problem
onto the physical qubits of the quantum chip, from which a solution is obtained
after quantum annealing. However, since the connectivity of the physical qubits
on the chip is limited, a minor embedding of the problem structure onto the
chip is required. In this process, and especially for smaller problems, many
qubits will stay unused. We propose a novel method, called parallel quantum
annealing, to make better use of available qubits, wherein either the same or
several independent problems are solved in the same annealing cycle of a
quantum annealer, assuming enough physical qubits are available to embed more
than one problem. Although the individual solution quality may be slightly
decreased when solving several problems in parallel (as opposed to solving each
problem separately), we demonstrate that our method may give dramatic speed-ups
in terms of Time-to-Solution (TTS) for solving instances of the Maximum Clique
problem when compared to solving each problem sequentially on the quantum
annealer. Additionally, we show that solving a single Maximum Clique problem
using parallel quantum annealing reduces the TTS significantly.
