21,117 research outputs found
Quantum compiling with diffusive sets of gates
Given a set of quantum gates and a target unitary operation, the most
elementary task of quantum compiling is the identification of a sequence of the
gates that approximates the target unitary to a determined precision
. Solovay-Kitaev theorem provides an elegant solution which is
based on the construction of successively tighter `nets' around the unity
comprised by successively longer sequences of gates. The procedure for the
construction of the nets, according to this theorem, requires accessibility to
the inverse of the gates as well. In this work, we propose a method for
constructing nets around unity without this requirement. The algorithmic
procedure is applicable to sets of gates which are diffusive enough, in the
sense that sequences of moderate length cover the space of unitary matrices in
a uniform way. We prove that the number of gates sufficient for reaching a
precision scales as
while the pre-compilation time is increased as compared to thatof the
Solovay-Kitaev algorithm by the exponential factor 3/2.Comment: 6 pages, several corrections in text, figures & bibliograph
A compiler approach to scalable concurrent program design
The programmer's most powerful tool for controlling complexity in program design is abstraction. We seek to use abstraction in the design of concurrent programs, so as to
separate design decisions concerned with decomposition, communication, synchronization, mapping, granularity, and load balancing. This paper describes programming and compiler techniques intended to facilitate this design strategy. The programming techniques are based on a core programming notation with two important properties: the ability to separate concurrent programming concerns, and extensibility with reusable programmer-defined
abstractions. The compiler techniques are based on a simple transformation system together with a set of compilation transformations and portable run-time support. The
transformation system allows programmer-defined abstractions to be defined as source-to-source transformations that convert abstractions into the core notation. The same
transformation system is used to apply compilation transformations that incrementally transform the core notation toward an abstract concurrent machine. This machine can be implemented on a variety of concurrent architectures using simple run-time support.
The transformation, compilation, and run-time system techniques have been implemented and are incorporated in a public-domain program development toolkit. This
toolkit operates on a wide variety of networked workstations, multicomputers, and shared-memory
multiprocessors. It includes a program transformer, concurrent compiler, syntax checker, debugger, performance analyzer, and execution animator. A variety of substantial
applications have been developed using the toolkit, in areas such as climate modeling and fluid dynamics
A, B, C's (and D)'s for Understanding VARs
The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A,B,C,D) that define a state space system. An associated state space system (A,K,C,Sigma) determines a vector autoregression for observables available to an econometrician. We review circumstances under which the impulse response of the VAR resembles the impulse response associated with the economic model. We give four examples that illustrate a simple condition for checking whether the mapping from VAR shocks to economic shocks is invertible. The condition applies when there are equal numbers of VAR and economic shocks.
A, B, C’s (And D’s) For Understanding VARS
The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A,B,C,D) that define a state space system. An associated state space system (A,K,C, Sigma) determines a vector autoregression for observables available to an econometrician. We review circumstances under which the impulse response of the VAR resembles the impulse response associated with the economic model. We give four examples that illustrate a simple condition for checking whether the mapping from VAR shocks to economic shocks is invertible. The condition applies when there are equal numbers of VAR and economic shocks.VARs , Invertibility, Estimation of Dynamic Equilibrium Models, economic shocks, innovations
A, B, C’s, (and D’s) for understanding VARs
The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A, B, C, D) that define a state-space system. An associated state space system (A, K, C, S) determines a vector autoregression (VAR) for observables available to an econometrician. We review circumstances in which the impulse response of the VAR resembles the impulse response associated with the economic model. We give four examples that illustrate a simple condition for checking whether the mapping from VAR shocks to economic shocks is invertible. The condition applies when there are equal numbers of VAR and economic shocks.
QuantumInformation.jl---a Julia package for numerical computation in quantum information theory
Numerical investigations are an important research tool in quantum
information theory. There already exists a wide range of computational tools
for quantum information theory implemented in various programming languages.
However, there is little effort in implementing this kind of tools in the Julia
language. Julia is a modern programming language designed for numerical
computation with excellent support for vector and matrix algebra, extended type
system that allows for implementation of elegant application interfaces and
support for parallel and distributed computing. QuantumInformation.jl is a new
quantum information theory library implemented in Julia that provides functions
for creating and analyzing quantum states, and for creating quantum operations
in various representations. An additional feature of the library is a
collection of functions for sampling random quantum states and operations such
as unitary operations and generic quantum channels.Comment: 32 pages, 8 figure
Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms
We consider optimal distributed computation of a given function of
distributed data. The input (data) nodes and the sink node that receives the
function form a connected network that is described by an undirected weighted
network graph. The algorithm to compute the given function is described by a
weighted directed acyclic graph and is called the computation graph. An
embedding defines the computation communication sequence that obtains the
function at the sink. Two kinds of optimal embeddings are sought, the embedding
that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes
cost of one instance of computation of function. This abstraction is motivated
by three applications---in-network computation over sensor networks, operator
placement in distributed databases, and module placement in distributed
computing.
We first show that obtaining minimum-delay and minimum-cost embeddings are
both NP-complete problems and that cost minimization is actually MAX SNP-hard.
Next, we consider specific forms of the computation graph for which polynomial
time solutions are possible. When the computation graph is a tree, a polynomial
time algorithm to obtain the minimum delay embedding is described. Next, for
the case when the function is described by a layered graph we describe an
algorithm that obtains the minimum cost embedding in polynomial time. This
algorithm can also be used to obtain an approximation for delay minimization.
We then consider bounded treewidth computation graphs and give an algorithm to
obtain the minimum cost embedding in polynomial time
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