4,084 research outputs found
Probabilistically Accurate Program Transformations
18th International Symposium, SAS 2011, Venice, Italy, September 14-16, 2011. ProceedingsThe standard approach to program transformation involves the use of discrete logical reasoning to prove that the transformation does not change the observable semantics of the program. We propose a new approach that, in contrast, uses probabilistic reasoning to justify the application of transformations that may change, within probabilistic accuracy bounds, the result that the program produces.
Our new approach produces probabilistic guarantees of the form ℙ(|D| ≥ B) ≤ ε, ε ∈ (0, 1), where D is the difference between the results that the transformed and original programs produce, B is an acceptability bound on the absolute value of D, and ε is the maximum acceptable probability of observing large |D|. We show how to use our approach to justify the application of loop perforation (which transforms loops to execute fewer iterations) to a set of computational patterns.National Science Foundation (U.S.) (Grant CCF-0811397)National Science Foundation (U.S.) (Grant CCF-0905244)National Science Foundation (U.S.) (Grant CCF-1036241)National Science Foundation (U.S.) (Grant IIS-0835652)United States. Dept. of Energy (Grant DE-SC0005288
A single-shot measurement of the energy of product states in a translation invariant spin chain can replace any quantum computation
In measurement-based quantum computation, quantum algorithms are implemented
via sequences of measurements. We describe a translationally invariant
finite-range interaction on a one-dimensional qudit chain and prove that a
single-shot measurement of the energy of an appropriate computational basis
state with respect to this Hamiltonian provides the output of any quantum
circuit. The required measurement accuracy scales inverse polynomially with the
size of the simulated quantum circuit. This shows that the implementation of
energy measurements on generic qudit chains is as hard as the realization of
quantum computation. Here a ''measurement'' is any procedure that samples from
the spectral measure induced by the observable and the state under
consideration. As opposed to measurement-based quantum computation, the
post-measurement state is irrelevant.Comment: 19 pages, transition rules for the CA correcte
Quantum Algorithms for Fermionic Simulations
We investigate the simulation of fermionic systems on a quantum computer. We
show in detail how quantum computers avoid the dynamical sign problem present
in classical simulations of these systems, therefore reducing a problem
believed to be of exponential complexity into one of polynomial complexity. The
key to our demonstration is the spin-particle connection (or generalized
Jordan-Wigner transformation) that allows exact algebraic invertible mappings
of operators with different statistical properties. We give an explicit
implementation of a simple problem using a quantum computer based on standard
qubits.Comment: 38 pages, 2 psfigur
Relational Quantum Mechanics
I suggest that the common unease with taking quantum mechanics as a
fundamental description of nature (the "measurement problem") could derive from
the use of an incorrect notion, as the unease with the Lorentz transformations
before Einstein derived from the notion of observer-independent time. I suggest
that this incorrect notion is the notion of observer-independent state of a
system (or observer-independent values of physical quantities). I reformulate
the problem of the "interpretation of quantum mechanics" as the problem of
deriving the formalism from a few simple physical postulates. I consider a
reformulation of quantum mechanics in terms of information theory. All systems
are assumed to be equivalent, there is no observer-observed distinction, and
the theory describes only the information that systems have about each other;
nevertheless, the theory is complete.Comment: Substantially revised version. LaTeX fil
Randomized accuracy-aware program transformations for efficient approximate computations
Despite the fact that approximate computations have come to dominate many areas of computer science, the field of program transformations has focused almost exclusively on traditional semantics-preserving transformations that do not attempt to exploit the opportunity, available in many computations, to acceptably trade off accuracy for benefits such as increased performance and reduced resource consumption.
We present a model of computation for approximate computations and an algorithm for optimizing these computations. The algorithm works with two classes of transformations: substitution transformations (which select one of a number of available implementations for a given function, with each implementation offering a different combination of accuracy and resource consumption) and sampling transformations (which randomly discard some of the inputs to a given reduction). The algorithm produces a (1+ε) randomized approximation to the optimal randomized computation (which minimizes resource consumption subject to a probabilistic accuracy specification in the form of a maximum expected error or maximum error variance).National Science Foundation (U.S.). (Grant number CCF-0811397)National Science Foundation (U.S.). (Grant number CCF-0905244)National Science Foundation (U.S.). (Grant number CCF-0843915)National Science Foundation (U.S.). (Grant number CCF-1036241)National Science Foundation (U.S.). (Grant number IIS-0835652)United States. Dept. of Energy. (Grant Number DE-SC0005288)Alfred P. Sloan Foundation. Fellowshi
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