3,032 research outputs found
An Introduction to Quantum Computing for Non-Physicists
Richard Feynman's observation that quantum mechanical effects could not be
simulated efficiently on a computer led to speculation that computation in
general could be done more efficiently if it used quantum effects. This
speculation appeared justified when Peter Shor described a polynomial time
quantum algorithm for factoring integers.
In quantum systems, the computational space increases exponentially with the
size of the system which enables exponential parallelism. This parallelism
could lead to exponentially faster quantum algorithms than possible
classically. The catch is that accessing the results, which requires
measurement, proves tricky and requires new non-traditional programming
techniques.
The aim of this paper is to guide computer scientists and other
non-physicists through the conceptual and notational barriers that separate
quantum computing from conventional computing. We introduce basic principles of
quantum mechanics to explain where the power of quantum computers comes from
and why it is difficult to harness. We describe quantum cryptography,
teleportation, and dense coding. Various approaches to harnessing the power of
quantum parallelism are explained, including Shor's algorithm, Grover's
algorithm, and Hogg's algorithms. We conclude with a discussion of quantum
error correction.Comment: 45 pages. To appear in ACM Computing Surveys. LATEX file. Exposition
improved throughout thanks to reviewers' comment
Adaptive Horizon Model Predictive Control and Al'brekht's Method
A standard way of finding a feedback law that stabilizes a control system to
an operating point is to recast the problem as an infinite horizon optimal
control problem. If the optimal cost and the optmal feedback can be found on a
large domain around the operating point then a Lyapunov argument can be used to
verify the asymptotic stability of the closed loop dynamics. The problem with
this approach is that is usually very difficult to find the optimal cost and
the optmal feedback on a large domain for nonlinear problems with or without
constraints. Hence the increasing interest in Model Predictive Control (MPC).
In standard MPC a finite horizon optimal control problem is solved in real time
but just at the current state, the first control action is implimented, the
system evolves one time step and the process is repeated. A terminal cost and
terminal feedback found by Al'brekht's methoddefined in a neighborhood of the
operating point is used to shorten the horizon and thereby make the nonlinear
programs easier to solve because they have less decision variables. Adaptive
Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon
length of Model Predictive Control (MPC) as needed. Its goal is to achieve
stabilization with horizons as small as possible so that MPC methods can be
used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861
A Multi-Exchange Neighborhood Search Heuristic for an Integrated Clustering and Machine Setup Model for PCB Manufacturing
In the manufacture of printed circuit boards, electronic components are attached to a blank board by one or more pick-and-place machines. Frequent machine setups, though time consuming, can reduce overall processing time. We consider the Integrated Clustering and Machine Setup (ICMS) model, which incorporates this tradeoff between processing time and setup time and seeks to minimize the sum of the two. Solving this model to optimality is intractable for very large-scale instances. We show that ICMS is NP-hard and consequently propose and test a heuristic based on multi-exchange neighborhood search structures. Initial numerical results are very encouraging. Keywords: Printed circuit board assembly, feeder slot assignment, product clustering, integer programming, computational complexity, heuristics
Local dissipation effects in two-dimensional quantum Josephson junction arrays with magnetic field
We study the quantum phase transitions in two-dimensional arrays of
Josephson-couples junctions with short range Josephson couplings (given by the
Josephson energy) and the charging energy. We map the problem onto the solvable
quantum generalization of the spherical model that improves over the mean-field
theory method. The arrays are placed on the top of a two-dimensional electron
gas separated by an insulator. We include effects of the local dissipation in
the presence of an external magnetic flux f in square lattice for several
rational fluxes f=0,1/2,1/3,1/4 and 1/6. We also have examined the T=0
superconducting-insulator phase boundary as function of a dissipation alpha for
two different geometry of the lattice: square and triangular. We have found
critical value of the dissipation parameter independent on geometry of the
lattice and presence magnetic field.Comment: accepted to PR
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