  Quantum tunneling, a phenomenon in which a quantum state traverses energy
barriers above the energy of the state itself, has been hypothesized as an
advantageous physical resource for optimization. Here we show that multiqubit
tunneling plays a computational role in a currently available, albeit noisy,
programmable quantum annealer. We develop a non-perturbative theory of open
quantum dynamics under realistic noise characteristics predicting the rate of
many-body dissipative quantum tunneling. We devise a computational primitive
with 16 qubits where quantum evolutions enable tunneling to the global minimum
while the corresponding classical paths are trapped in a false minimum.
Furthermore, we experimentally demonstrate that quantum tunneling can
outperform thermal hopping along classical paths for problems with up to 200
qubits containing the computational primitive. Our results indicate that
many-body quantum phenomena could be used for finding better solutions to hard
optimization problems.
