Automated searching for quantum subsystem codes

Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to active quantum error correcting schemes as well as to the design of self-correcting quantum memories. Previous approaches for investigating these codes have focused on applying theoretical analysis to look for interesting codes and to investigate their properties. In this paper we present an alternative approach that uses computational analysis to accomplish the same goals. Specifically, we present an algorithm that computes the optimal quantum subsystem code that can be implemented given an arbitrary set of measurement operators that are tensor products of Pauli operators. We then demonstrate the utility of this algorithm by performing a systematic investigation of the quantum subsystem codes that exist in the setting where the interactions are limited to 2-body interactions between neighbors on lattices derived from the convex uniform tilings of the plane.Comment: 38 pages, 15 figure, 10 tables. The algorithm described in this paper is available as both library and a command line program (including full source code) that can be downloaded from http://github.com/gcross/CodeQuest/downloads. The source code used to apply the algorithm to scan the lattices is available upon request. Please feel free to contact the authors with question

Finite automata for caching in matrix product algorithms

A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can proceed in the opposite direction: writing an automaton that ``generates'' an operator gives one an immediate matrix product factorization of it. Matrix product factorizations have the advantage of reducing the cost of computing expectation values by facilitating caching of intermediate calculations. Thus our connection to complex weighted finite state automata yields insight into what allows for efficient caching in matrix product algorithms. Finally, these techniques are generalized to the case of multiple dimensions.Comment: 18 pages, 19 figures, LaTeX; numerous improvements have been made to the manuscript in response to referee feedbac

Chasing infinity with matrix product states by embracing divergences

In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products, expectations, etc, as maps from natural numbers to complex numbers which contain information about how these quantities diverge, and in particular whether they scale linearly, quadratically, exponentially, etc with the size of the system. We build our formalism on a variant of matrix product states, as this class of states has a structure that naturally provides a way to obtain the scaling function. We show that the states in our formalism form a module over the ring of functions that are made up of sums of exponentials times polynomials and delta functions. We analyze properties of this formalism and show how it works for selected systems. Finally, we discuss how our formalism relates to other work

Development of an electrophoretic display technology for selectively retroreflective signs and pavement markers

This paper describes an enabling technology that could be used to develop electronic roadway signs and markers whose display content can be changed and that are selectively retroreflective. This would give them the good visibility of retroreflective signs at night, coupled with invisibility under circumstances where they are not meant to be seen, thereby reducing both confusion and light pollution. This paper describes how the half-silvered and blackened glass beads that constitute the visible components of the display were fabricated in the lab and derives their geometric optics, demonstrating their retroreflective capabilities. The paper also describes the construction of a transparent top electrode necessary to establish the electric field for changing the displays and derives some of the electric properties of the electrode and the resulting capacitorlike display. The work is in an early developmental stage, and the paper concludes with an outline of some of the remaining issues that need to be solved before a working device could be constructed