46 research outputs found
A Complexity Measure for Continuous Time Quantum Algorithms
We consider unitary dynamical evolutions on n qubits caused by time dependent
pair-interaction Hamiltonians and show that the running time of a parallelized
two-qubit gate network simulating the evolution is given by the time integral
over the chromatic index of the interaction graph. This defines a complexity
measure of continuous and discrete quantum algorithms which are in exact
one-to-one correspondence. Furthermore we prove a lower bound on the growth of
large-scale entanglement depending on the chromatic index.Comment: 6 pages, Revte
Quantum Trajectory method for the Quantum Zeno and anti-Zeno effects
We perform stochastic simulations of the quantum Zeno and anti-Zeno effects
for two level system and for the decaying one. Instead of simple projection
postulate approach, a more realistic model of a detector interacting with the
environment is used. The influence of the environment is taken into account
using the quantum trajectory method. The simulation of the measurement for a
single system exhibits the probabilistic behavior showing the collapse of the
wave-packet. When a large ensemble is analysed using the quantum trajectory
method, the results are the same as those produced using the density matrix
method. The results of numerical calculations are compared with the analytical
expressions for the decay rate of the measured system and a good agreement is
found. Since the analytical expressions depend on the duration of the
measurement only, the agreement with the numerical calculations shows that
otherparameters of the model are not important.Comment: 12 figures, accepted for publication in Phys. Rev. A replaced with
single-spaced versio
Optical discrimination between spatial decoherence and thermalization of a massive object
We propose an optical ring interferometer to observe environment-induced
spatial decoherence of massive objects. The object is held in a harmonic trap
and scatters light between degenerate modes of a ring cavity. The output signal
of the interferometer permits to monitor the spatial width of the object's wave
function. It shows oscillations that arise from coherences between energy
eigenstates and that reveal the difference between pure spatial decoherence and
that coinciding with energy transfer and heating. Our method is designed to
work with a wide variety of masses, ranging from the atomic scale to
nano-fabricated structures. We give a thorough discussion of its experimental
feasibility.Comment: 2 figure
Decoherence Rates in Large Scale Quantum Computers and Macroscopic Systems
Markovian regime decoherence effects in quantum computers are studied in
terms of the fidelity for the situation where the number of qubits N becomes
large. A general expression giving the decoherence time scale in terms of
Markovian relaxation elements and expectation values of products of system
fluctuation operators is obtained, which could also be applied to study
decoherence in other macroscopic systems such as Bose condensates and
superconductors. A standard circuit model quantum computer involving
three-state lambda system ionic qubits is considered, with qubits localised
around well-separated positions via trapping potentials. The centre of mass
vibrations of the qubits act as a reservoir. Coherent one and two qubit gating
processes are controlled by time dependent localised classical electromagnetic
fields that address specific qubits, the two qubit gating processes being
facilitated by a cavity mode ancilla, which permits state interchange between
qubits. With a suitable choice of parameters, it is found that the decoherence
time can be made essentially independent of N.Comment: Minor revisions. To be published in J Mod Opt. One figur
Decoherence in Bose-Einstein Condensates: towards Bigger and Better Schroedinger Cats
We consider a quantum superposition of Bose-Einstein condensates in two
immiscible internal states. A decoherence rate for the resulting Schroedinger
cat is calculated and shown to be a significant threat to this macroscopic
quantum superposition of BEC's. An experimental scenario is outlined where the
decoherence rate due to the thermal cloud is dramatically reduced thanks to
trap engineering and "symmetrization" of the environment which allow for the
Schroedinger cat to be an approximate pointer states.Comment: 12 pages in RevTex; improved presentation; a new comment on
decoherence-free pointer subspaces in BEC; accepted in Phys.Rev.
Macroscopic Quantum Phenomena from the Correlation, Coupling and Criticality Perspectives
In this sequel paper we explore how macroscopic quantum phenomena can be
measured or understood from the behavior of quantum correlations which exist in
a quantum system of many particles or components and how the interaction
strengths change with energy or scale, under ordinary situations and when the
system is near its critical point. We use the nPI (master) effective action
related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equations as a
tool for systemizing the contributions of higher order correlation functions to
the dynamics of lower order correlation functions. Together with the large N
expansion discussed in our first paper(MQP1) we explore 1) the conditions
whereby an H-theorem is obtained, which can be viewed as a signifier of the
emergence of macroscopic behavior in the system. We give two more examples from
past work: 2) the nonequilibrium dynamics of N atoms in an optical lattice
under the large (field components), 2PI and second order perturbative
expansions, illustrating how N and enter in these three aspects of
quantum correlations, coherence and coupling strength. 3) the behavior of an
interacting quantum system near its critical point, the effects of quantum and
thermal fluctuations and the conditions under which the system manifests
infrared dimensional reduction. We also discuss how the effective field theory
concept bears on macroscopic quantum phenomena: the running of the coupling
parameters with energy or scale imparts a dynamical-dependent and an
interaction-sensitive definition of `macroscopia'.Comment: For IARD 2010 meeting, Hualien, Taiwan. Proceedings to appear in J.
Physics (Conf. Series
Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom
Published versio
Background Independent Quantum Gravity: A Status Report
The goal of this article is to present an introduction to loop quantum
gravity -a background independent, non-perturbative approach to the problem of
unification of general relativity and quantum physics, based on a quantum
theory of geometry. Our presentation is pedagogical. Thus, in addition to
providing a bird's eye view of the present status of the subject, the article
should also serve as a vehicle to enter the field and explore it in detail. To
aid non-experts, very little is assumed beyond elements of general relativity,
gauge theories and quantum field theory. While the article is essentially
self-contained, the emphasis is on communicating the underlying ideas and the
significance of results rather than on presenting systematic derivations and
detailed proofs. (These can be found in the listed references.) The subject can
be approached in different ways. We have chosen one which is deeply rooted in
well established physics and also has sufficient mathematical precision to
ensure that there are no hidden infinities. In order to keep the article to a
reasonable size, and to avoid overwhelming non-experts, we have had to leave
out several interesting topics, results and viewpoints; this is meant to be an
introduction to the subject rather than an exhaustive review of it.Comment: 125 pages, 5 figures (eps format), the final version published in CQ