Chemical structure matching using correlation matrix memories

This paper describes the application of the Relaxation By Elimination (RBE) method to matching the 3D structure of molecules in chemical databases within the frame work of binary correlation matrix memories. The paper illustrates that, when combined with distributed representations, the method maps well onto these networks, allowing high performance implementation in parallel systems. It outlines the motivation, the neural architecture, the RBE method and presents some results of matching small molecules against a database of 100,000 models

Supporting 64-bit global indices in Epetra and other Trilinos packages -- Techniques used and lessons learned

The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an object-oriented framework. It is intended for large-scale, complex multiphysics engineering and scientific applications. Epetra is one of its basic packages. It provides serial and parallel linear algebra capabilities. Before Trilinos version 11.0, released in 2012, Epetra used the C++ int data-type for storing global and local indices for degrees of freedom (DOFs). Since int is typically 32-bit, this limited the largest problem size to be smaller than approximately two billion DOFs. This was true even if a distributed memory machine could handle larger problems. We have added optional support for C++ long long data-type, which is at least 64-bit wide, for global indices. To save memory, maintain the speed of memory-bound operations, and reduce further changes to the code, the local indices are still 32-bit. We document the changes required to achieve this feature and how the new functionality can be used. We also report on the lessons learned in modifying a mature and popular package from various perspectives -- design goals, backward compatibility, engineering decisions, C++ language features, effects on existing users and other packages, and build integration

Quantum Error Correction on Linear Nearest Neighbor Qubit Arrays

A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations. Simulations of the circuit's performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.Comment: 4 pages, 5 figure

Closed-form expressions for the numerical dispersion and reflection in FEM simulations involving biaxial materials

Closed-form expressions for the numerical errors caused by finite-element discretization of problems involving materials of biaxial permittivity and permeability tensors are developed. In particular, we derive expressions for the numerical dispersion and reflection in both first-order node and edge basis function finite-element formulations in an equilateral triangular mesh. Results using these closed-form expressions are compared to practical numerical simulations. The application of these expressions to the analysis of the performance of the perfectly matched layer boundary is suggeste

Layered architecture for quantum computing

We develop a layered quantum computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface code quantum error correction. In doing so, we propose a new quantum computer architecture based on optical control of quantum dots. The timescales of physical hardware operations and logical, error-corrected quantum gates differ by several orders of magnitude. By dividing functionality into layers, we can design and analyze subsystems independently, demonstrating the value of our layered architectural approach. Using this concrete hardware platform, we provide resource analysis for executing fault-tolerant quantum algorithms for integer factoring and quantum simulation, finding that the quantum dot architecture we study could solve such problems on the timescale of days.Comment: 27 pages, 20 figure

Quantum response of weakly chaotic systems

Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical billiards with vibrating walls. The Hamiltonian matrix of the driven system does not look like one from a Gaussian ensemble, but rather it is very sparse. This sparsity can be characterized by parameters $s$ and $g$ that reflect the percentage of large elements, and their connectivity respectively. For $g$ we use a resistor network calculation that has direct relation to the semi-linear response characteristics of the system.Comment: 7 pages, 5 figures, expanded improved versio

Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics

Radiative corrections arising from Lorentz violation in the fermion sector induce a nonzero amplitude for vacuum photon splitting. At one loop, the on-shell amplitude acquires both CPT-even and CPT-odd contributions forbidden in conventional electrodynamics.Comment: 4 pages, minor wording changes, references added, accepted in Physical Review Letter