We argue that a quantum annealer at very long annealing times is likely to experience a quasistatic evolution, returning a final population that is close to a Boltzmann distributionof the Hamiltonian at a single (freeze-out) point during the annealing. Such a system is expected to correlate well with a proper quantum Monte Carlo simulation. It may also correlate with simulated annealing if at the freeze-out point the quantum energy eigenvalues are close to the classical ones. These correlations are just signatures of equilibration and do not mean that the evolution of the quantum annealer is classical or can be simulated by quantum Monte Carlo. The computation time extracted from such a distribution reflects the equilibrium behavior and therefore provides no information about the underlying quantum dynamics. This makes the search for quantum speedup in suboptimal quantum annealers problematic. We use an open quantum master equation with realistic parameters to illustrate quasistatic evolution in a 16 qubit quantum annealer and discuss its implication for quantum speedup.
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 foroptimization. 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.
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 physicalresource 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, the simplest non-convex optimization problem consisting of just one global and one local 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.