5,802 research outputs found
Expected Runtime of Quantum Programs
Building upon recent work on probabilistic programs, we formally define the
notion of expected runtime for quantum programs. A representation of the
expected runtimes of quantum programs is introduced with an interpretation as
an observable in physics. A method for computing the expected runtimes of
quantum programs in finite-dimensional state spaces is developed. Several
examples are provided as applications of this method; in particular, an open
problem of computing the expected runtime of quantum random walks is solved
using our method
Quantum walk speedup of backtracking algorithms
We describe a general method to obtain quantum speedups of classical
algorithms which are based on the technique of backtracking, a standard
approach for solving constraint satisfaction problems (CSPs). Backtracking
algorithms explore a tree whose vertices are partial solutions to a CSP in an
attempt to find a complete solution. Assume there is a classical backtracking
algorithm which finds a solution to a CSP on n variables, or outputs that none
exists, and whose corresponding tree contains T vertices, each vertex
corresponding to a test of a partial solution. Then we show that there is a
bounded-error quantum algorithm which completes the same task using O(sqrt(T)
n^(3/2) log n) tests. In particular, this quantum algorithm can be used to
speed up the DPLL algorithm, which is the basis of many of the most efficient
SAT solvers used in practice. The quantum algorithm is based on the use of a
quantum walk algorithm of Belovs to search in the backtracking tree. We also
discuss how, for certain distributions on the inputs, the algorithm can lead to
an exponential reduction in expected runtime.Comment: 23 pages; v2: minor changes to presentatio
Quantum SDP-Solvers: Better upper and lower bounds
Brand\~ao and Svore very recently gave quantum algorithms for approximately
solving semidefinite programs, which in some regimes are faster than the
best-possible classical algorithms in terms of the dimension of the problem
and the number of constraints, but worse in terms of various other
parameters. In this paper we improve their algorithms in several ways, getting
better dependence on those other parameters. To this end we develop new
techniques for quantum algorithms, for instance a general way to efficiently
implement smooth functions of sparse Hamiltonians, and a generalized
minimum-finding procedure.
We also show limits on this approach to quantum SDP-solvers, for instance for
combinatorial optimizations problems that have a lot of symmetry. Finally, we
prove some general lower bounds showing that in the worst case, the complexity
of every quantum LP-solver (and hence also SDP-solver) has to scale linearly
with when , which is the same as classical.Comment: v4: 69 pages, small corrections and clarifications. This version will
appear in Quantu
Computation with narrow CTCs
We examine some variants of computation with closed timelike curves (CTCs),
where various restrictions are imposed on the memory of the computer, and the
information carrying capacity and range of the CTC. We give full
characterizations of the classes of languages recognized by polynomial time
probabilistic and quantum computers that can send a single classical bit to
their own past. Such narrow CTCs are demonstrated to add the power of limited
nondeterminism to deterministic computers, and lead to exponential speedup in
constant-space probabilistic and quantum computation. We show that, given a
time machine with constant negative delay, one can implement CTC-based
computations without the need to know about the runtime beforehand.Comment: 16 pages. A few typo was correcte
SICStus MT - A Multithreaded Execution Environment for SICStus Prolog
The development of intelligent software agents and other
complex applications which continuously interact with their
environments has been one of the reasons why explicit concurrency has
become a necessity in a modern Prolog system today. Such applications
need to perform several tasks which may be very different with respect
to how they are implemented in Prolog. Performing these tasks
simultaneously is very tedious without language support.
This paper describes the design, implementation and evaluation of a
prototype multithreaded execution environment for SICStus Prolog. The
threads are dynamically managed using a small and compact set of
Prolog primitives implemented in a portable way, requiring almost no
support from the underlying operating system
Experimental Realization of a One-way Quantum Computer Algorithm Solving Simon's Problem
We report an experimental demonstration of a one-way implementation of a
quantum algorithm solving Simon's Problem - a black box period-finding problem
which has an exponential gap between the classical and quantum runtime. Using
an all-optical setup and modifying the bases of single-qubit measurements on a
five-qubit cluster state, key representative functions of the logical two-qubit
version's black box can be queried and solved. To the best of our knowledge,
this work represents the first experimental realization of the quantum
algorithm solving Simon's Problem. The experimental results are in excellent
agreement with the theoretical model, demonstrating the successful performance
of the algorithm. With a view to scaling up to larger numbers of qubits, we
analyze the resource requirements for an n-qubit version. This work helps
highlight how one-way quantum computing provides a practical route to
experimentally investigating the quantum-classical gap in the query complexity
model.Comment: 9 pages, 5 figure
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