The effects of the problem Hamiltonian parameters on the minimum spectral gap in adiabatic quantum optimization We study the relation between the Ising problem Hamiltonian parameters and the minimum spectral gap (mingap) of the system Hamiltonian in the Isingbased quantum annealer. The main criterion we use in this paper to assess the performance of a QA algorithm is the presence or absence of an anticrossing during quantum evolution. For this purpose, we introduce a new parametrization definition of the anticrossing. Using the Maximumweighted Independent Set (MIS) problem in which there are flexible parameters (energy penalties J between pairs of edges) in an Ising formulation as the model problem, we construct examples to show that by changing the value of J, we can change the quantum evolution from one that has an anticrossing (that results in an exponential small mingap) to one that does not have, or the other way around, and thus drastically change (increase or decrease) the mingap. However, we also show that by changing the value of J alone, one can not avoid the anticrossing. We recall a polynomial reduction from an Ising problem to an MIS problem to show that the flexibility of changing parameters without changing the problem to be solved can be applied to any Ising problem. As an example, we show that by such a reduction alone, it is possible to remove the anticrossing and thus increase the mingap. Our anticrossing definition is necessarily scaling invariant as scaling the problem Hamiltonian does not change the nature (i.e., presence or absence) of an anticrossing. As a side note, we show exactly how the mingap is scaled if we scale the problem Hamiltonian by a constant factor.

Solving Quantum Chemistry Problems with a DWave Quantum Annealer Quantum annealing devices have been subject to various analyses in order to classify their usefulness for practical applications. While it has been successfully proven that such systems can in general be used for solving combinatorial optimization problems, they have not been used to solve chemistry applications. In this paper we apply a mapping, put forward by Xia et al. (The Journal of Physical Chemistry B 122.13 (2017): 33843395.), from a quantum chemistry Hamiltonian to an Ising spin glass formulation and find the ground state energy with a quantum annealer. Additionally we investigate the scaling in terms of needed physical qubits on a quantum annealer with limited connectivity. To the best of our knowledge, this is the first experimental study of quantum chemistry problems on quantum annealing devices.