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Quantum annealing has recently been used to determine the Ramsey numbersR(m,2) for 3 < m < 9 and R(3,3) [Bian et al. (2013) PRL 111, 130505]. This wasgreatly celebrated as the largest experimental implementation of an adiabaticevolution algorithm to that date. However, in that computation, more than 66%of the qubits used were auxiliary qubits, so the sizes of the Ramsey numberHamiltonians used were tremendously smaller than the full 128-qubit capacity ofthe device used. The reason these auxiliary qubits were needed was because thebest quantum annealing devices at the time (and still now) cannot implementmulti-qubit interactions beyond 2-qubit interactions, and they are also limitedin their capacity for 2-qubit interactions. We present a method which allowsthe full qubit capacity of a quantum annealing device to be used, by reducingmulti-qubit and 2-qubit interactions. With our method, the device used in the2013 Ramsey number quantum computation could have determined R(16,2) and R(4,3)with under 10 minutes of runtime.

Reducing multi-qubit interactions in adiabatic quantum computation  without adding auxiliary qubits. Part 2: The "split-reduc" method and its  application to quantum determination of Ramsey numbers