  Quantum tunneling is a phenomenon in which a quantum state traverses energy
barriers above the energy of the state itself. Tunneling has been hypothesized
as an advantageous physical resource for optimization. Here we present the
first experimental evidence of a computational role of multiqubit quantum
tunneling in the evolution of a programmable quantum annealer. We develop a
theoretical model based on a NIBA Quantum Master Equation to describe the
multiqubit dissipative tunneling effects under the complex noise
characteristics of such quantum devices. We start by considering a
computational primitive, an optimization problem consisting of just one global
and one false minimum. The quantum evolutions enable tunneling to the global
minimum while the corresponding classical paths are trapped in a false minimum.
In our study the non-convex potentials are realized by frustrated networks of
qubit clusters with strong intra-cluster coupling. We show that the collective
effect of the quantum environment is suppressed in the "critical" phase during
the evolution where quantum tunneling "decides" the right path to solution. In
a later stage dissipation facilitates the multiqubit tunneling leading to the
solution state. The predictions of the model accurately describe the
experimental data from the D-Wave Two quantum annealer at NASA Ames. In our
computational primitive the temperature dependence of the probability of
success in the quantum model is opposite to that of the classical paths with
thermal hopping. Specifically, we provide an analysis of an optimization
problem with sixteen qubits, demonstrating eight qubit tunneling that increases
success probabilities. Furthermore, we report results for larger problems with
up to 200 qubits that contain the primitive as subproblems.
