5,839 research outputs found
Quantum measurements and the Abelian Stabilizer Problem
We present a polynomial quantum algorithm for the Abelian stabilizer problem
which includes both factoring and the discrete logarithm. Thus we extend famous
Shor's results. Our method is based on a procedure for measuring an eigenvalue
of a unitary operator. Another application of this procedure is a polynomial
quantum Fourier transform algorithm for an arbitrary finite Abelian group. The
paper also contains a rather detailed introduction to the theory of quantum
computation.Comment: 22 pages, LATE
Computer Simulation of Quantum Dynamics in a Classical Spin Environment
In this paper a formalism for studying the dynamics of quantum systems
coupled to classical spin environments is reviewed. The theory is based on
generalized antisymmetric brackets and naturally predicts open-path
off-diagonal geometric phases in the evolution of the density matrix. It is
shown that such geometric phases must also be considered in the
quantum-classical Liouville equation for a classical bath with canonical phase
space coordinates; this occurs whenever the adiabatics basis is complex (as in
the case of a magnetic field coupled to the quantum subsystem). When the
quantum subsystem is weakly coupled to the spin environment, non-adiabatic
transitions can be neglected and one can construct an effective non-Markovian
computer simulation scheme for open quantum system dynamics in classical spin
environments. In order to tackle this case, integration algorithms based on the
symmetric Trotter factorization of the classical-like spin propagator are
derived. Such algorithms are applied to a model comprising a quantum two-level
system coupled to a single classical spin in an external magnetic field.
Starting from an excited state, the population difference and the coherences of
this two-state model are simulated in time while the dynamics of the classical
spin is monitored in detail. It is the author's opinion that the numerical
evidence provided in this paper is a first step toward developing the
simulation of quantum dynamics in classical spin environments into an effective
tool. In turn, the ability to simulate such a dynamics can have a positive
impact on various fields, among which, for example, nano-science.Comment: To appear in Theoretical Chemistry Accounts (special issue in honor
of Professor Gregory Sion Ezra
Quantum Cellular Automata
Quantum cellular automata (QCA) are reviewed, including early and more recent
proposals. QCA are a generalization of (classical) cellular automata (CA) and
in particular of reversible CA. The latter are reviewed shortly. An overview is
given over early attempts by various authors to define one-dimensional QCA.
These turned out to have serious shortcomings which are discussed as well.
Various proposals subsequently put forward by a number of authors for a general
definition of one- and higher-dimensional QCA are reviewed and their properties
such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of
Complexity and Systems Scienc
Local Unitary Quantum Cellular Automata
In this paper we present a quantization of Cellular Automata. Our formalism
is based on a lattice of qudits, and an update rule consisting of local unitary
operators that commute with their own lattice translations. One purpose of this
model is to act as a theoretical model of quantum computation, similar to the
quantum circuit model. It is also shown to be an appropriate abstraction for
space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains
and others. Some results that show the benefits of basing the model on local
unitary operators are shown: universality, strong connections to the circuit
model, simple implementation on quantum hardware, and a wealth of applications.Comment: To appear in Physical Review
Cellular Automata as a Model of Physical Systems
Cellular Automata (CA), as they are presented in the literature, are abstract
mathematical models of computation. In this pa- per we present an alternate
approach: using the CA as a model or theory of physical systems and devices.
While this approach abstracts away all details of the underlying physical
system, it remains faithful to the fact that there is an underlying physical
reality which it describes. This imposes certain restrictions on the types of
computations a CA can physically carry out, and the resources it needs to do
so. In this paper we explore these and other consequences of our
reformalization.Comment: To appear in the Proceedings of AUTOMATA 200
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