Recent advances in selected CI, including the adaptive sampling configuration interaction (ASCI) algorithm and its heat bath extension, have made the ASCI approach competitive with the most accurate techniques available, and hence an increasingly powerful tool in solving quantum Hamiltonians. In this work, we show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques we present ASCI results applied to a large range of systems and basis sets in order to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double-and triple-zeta benchmark data for the G1 dataset. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets. arXiv:1807.00821v1 [physics.comp-ph]

We present analytical expressions relating the bipolar moment β(Q)(K)(k(1)k(2)) parameters of Dixon to the measured anisotropy parameters of different pump/probe geometry sliced ion images. In the semi-classical limit, when there is no significant coherent contribution from multiple excited states to fragment angular momentum polarization, the anisotropy of the images alone is sufficient to extract the β(Q)(K)(k(1)k(2)) parameters with no need to reference relative image intensities. The analysis of sliced images is advantageous since the anisotropy can be directly obtained from the image at any radius without the need for 3D-deconvolution, which is not applicable for most pump/probe geometries. This method is therefore ideally suited for systems which result in a broad distribution of fragment velocities. The bipolar moment parameters are obtained for NO(2) dissociation at 355 nm using these equations, and are compared to the bipolar moment parameters obtained from a proven iterative fitting technique for crushed ion images. Additionally, the utility of these equations in extracting speed-dependent bipolar moments is demonstrated on the recently investigated NO(3) system.

We present an analysis of the relaxation dynamics of finite-size topological qubits in contact with a thermal bath. Using a continuous-time Monte Carlo method, we explicitly compute the low-temperature nonequilibrium dynamics of the toric code on finite lattices. In contrast to the size-independent bound predicted for the toric code in the thermodynamic limit, we identify a lowtemperature regime on finite lattices below a size-dependent crossover temperature with nontrivial finite-size and temperature scaling of the relaxation time. We demonstrate how this nontrivial finite-size scaling is governed by the scaling of topologically nontrivial two-dimensional classical random walks. The transition out of this low-temperature regime defines a dynamical finite-size crossover temperature that scales inversely with the log of the system size, in agreement with a crossover temperature defined from equilibrium properties. We find that both the finite-size and finite-temperature scaling are stronger in the low-temperature regime than above the crossover temperature. Since this finite-temperature scaling competes with the scaling of the robustness to unitary perturbations, this analysis may elucidate the scaling of memory lifetimes of possible physical realizations of topological qubits.