Statistical Analysis Of Quantum Annealing Models And Density Matrix Estimation In Quantum Homodyne Tomography PDF Download

Abstract: We investigate the impact of disorder on the annealing process in state-of-the-art, tunable quantum annealing devices, using as an example the D-Wave 2000Q architecture. Recent rapid progress in this area has brought quantum computing technologies from proof-of-principle experiments to commercial availability already, triggering passionate debates in both the scientific community and in society in general. Facing these developments, the physical description of quantum annealing is challenged to keep track of the transition from well-controlled few-particle experiments to extremely complicated and potentially disordered complex systems. In contrast to this requirements, the most recent physical models for adiabatic quantum computing still assume perfect control over thousands of control parameters in these complex systems, which is far from being reached in the latest experimental setups. To resolve the above discrepancy is the main purpose of the present thesis. We introduce the customary description of quantum annealing in terms of the annealing Hamiltonian, which is commonly used to describe the general behavior and in particular the output statistics of quantum annealing devices. This description lacks the features mentioned above, since it assumes precise control over all parameters of the Hamiltonian, and is therefore unsuitable to treat the potentially statistical behavior of complex quantum systems. For this reason, we introduce a generalized and statistical model for the description of quantum annealing devices, taking into account the finite precision of the experimental realization by introducing \emph{disorder} on top of the quantum mechanical description. In this model, we explicitly take into account setup-specific features of D-Wave 2000Q, like the precision of the tuning parameters, their available tuning range and the structure of couplings between the qubits. These specifications can easily be adjusted to other experimental realizations, allowing a situation-dependent, device-specific treatment. This generalized model of quantum annealing in the presence of disorder allows quantitative predictions on the output statistics of D-Wave 2000Q, which was impossible so far. We compare these predictions to real experimental data and find good agreement, for both, small systems consisting of up to 15 active qubits in a discrete treatment, and for large systems with 2048 active qubits, by use of a continuous version of our statistical model. These results suggest the interpretation that disorder is the dominant source for the non-trivial output statistics observed from state-of-the-art tunable quantum annealers, and that therefore disorder is the main limitation for the quality of computational results obtained from those devices. The precise characterization of the output distributions from quantum annealers has only recently gained additional attention not only from physicists, but also from the machine learning community, since one possible application is the efficient sampling from annealing devices as random number generators. Important questions in this context are whether the resulting output distributions are Boltzmann distributions and how the best-fitting effective inverse temperature can be estimated. In this context, we investigate and discuss the emergence of Boltzmann-like output distributions from disorder. We find the same similarities to and deviations from Boltzmann distributions that already have been observed experimentally, again suggesting disorder as the dominant process in state-of-the-art quantum annealing devices. Furthermore, we provide the arguably first analytical treatment which explains the observed, Boltzmann-like features quantitatively