01529nas a2200109 4500008004100000245005800041210005700099520118800156100002101344700001701365856003701382 2018 eng d00aMathematical methods for resource-based type theories0 aMathematical methods for resourcebased type theories3 a

With the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a quantum program. In this work, we make progress towards a program verification approach using the formalism of operational quantum mechanics and resource theories. We present a logical framework that captures two mathematical approaches to resource theory based on monoids (algebraic) and monoidal categories (categorical). We develop the syntax of this framework as an intuitionistic sequent calculus, and prove soundness and completeness of an algebraic and categorical semantics that recover these approaches. We also provide a cut-elimination theorem, normal form, and analogue of Lambek's lifting theorem for polynomial systems over the logics. Using these approaches along with the Curry-Howard-Lambek correspondence for programs, proofs and categories, this work lays the mathematical groundwork for a type checker for some resource theory based frameworks, with the possibility of extending it other quantum programming languages.

1 aSundaram, Aarthi1 aLackey, Brad uhttps://arxiv.org/abs/1812.0872600683nas a2200109 4500008004100000245004600041210004600087520036300133100001700496700002300513856003700536 2018 eng d00aMorphisms in categories of nonlocal games0 aMorphisms in categories of nonlocal games3 a

Synchronous correlations provide a class of nonlocal games that behave like functions between finite sets. In this work we examine categories whose morphisms are games with synchronous classical, quantum, or general nonsignaling correlations. In particular, we characterize when morphisms in these categories are monic, epic, sections, or retractions.

1 aLackey, Brad1 aRodrigues, Nishant uhttps://arxiv.org/abs/1810.1007403037nas a2200193 4500008004100000245010200041210006900143260001500212300000700227490000600234520240900240100002002649700001902669700002602688700001702714700002502731700001502756856007202771 2016 eng d00aMapping contrained optimization problems to quantum annealing with application to fault diagnosis0 aMapping contrained optimization problems to quantum annealing wi c2016/07/28 a140 v33 a

Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping Boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular, we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. By contrast, global embedding techniques generate a hardware-independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of the D-Wave hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D- Wave’s QA hardware to circuit-based fault diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000 N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Furthermore, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.

1 aBian, Zhengbing1 aChudak, Fabian1 aIsrael, Robert, Brian1 aLackey, Brad1 aMacready, William, G1 aRoy, Aiden uhttp://journal.frontiersin.org/article/10.3389/fict.2016.00014/full00986nas a2200121 4500008004100000245003800041210003800079260001500117490000600132520063500138100001700773856007400790 2000 eng d00aMetric Equivalence of Path Spaces0 aMetric Equivalence of Path Spaces c2000/01/010 v73 aLocal equivalence and the invariants of systems of second order differential equations were studied in a series of papers by Kosambi, Cartan, and Chern. The resulting theory, deemed KCC-theory, is a rich geometric study which in many ways generalizes Riemannian and Finsler geometry. Yet, in many applications one requires a metric structure in addition to the systems of second order differential equations. We pose a geometry which is equipped with both of these structures, and solve the problem of local equivalence and thus determining a preferred connection and finding a generating set for all the invariants of the theory.1 aLackey, Brad uhttps://www.quics.umd.edu/publications/metric-equivalence-path-spaces00346nas a2200121 4500008004100000245003000041210002800071260002500099300001200124490000700136100001700143856006400160 1999 eng d00aA model of trophodynamics0 amodel of trophodynamics bPergamonc1999/01/01 a37–570 v351 aLackey, Brad uhttps://www.quics.umd.edu/publications/model-trophodynamics