2,396 research outputs found
Efficient classical simulation of slightly entangled quantum computations
We present a scheme to efficiently simulate, with a classical computer, the
dynamics of multipartite quantum systems on which the amount of entanglement
(or of correlations in the case of mixed-state dynamics) is conveniently
restricted. The evolution of a pure state of n qubits can be simulated by using
computational resources that grow linearly in n and exponentially in the
entanglement. We show that a pure-state quantum computation can only yield an
exponential speed-up with respect to classical computations if the entanglement
increases with the size n of the computation, and gives a lower bound on the
required growth.Comment: 4 pages. Major changes. Significantly improved simulation schem
Encoding a qubit in an oscillator
Quantum error-correcting codes are constructed that embed a
finite-dimensional code space in the infinite-dimensional Hilbert space of a
system described by continuous quantum variables. These codes exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested
by Phys. Rev. A, minor correction
Quantum Teleportation is a Universal Computational Primitive
We present a method to create a variety of interesting gates by teleporting
quantum bits through special entangled states. This allows, for instance, the
construction of a quantum computer based on just single qubit operations, Bell
measurements, and GHZ states. We also present straightforward constructions of
a wide variety of fault-tolerant quantum gates.Comment: 6 pages, REVTeX, 6 epsf figure
Methodology for quantum logic gate constructions
We present a general method to construct fault-tolerant quantum logic gates
with a simple primitive, which is an analog of quantum teleportation. The
technique extends previous results based on traditional quantum teleportation
(Gottesman and Chuang, Nature {\bf 402}, 390, 1999) and leads to
straightforward and systematic construction of many fault-tolerant encoded
operations, including the and Toffoli gates. The technique can also be
applied to the construction of remote quantum operations that cannot be
directly performed.Comment: 17 pages, mypsfig2, revtex. Revised with a different title, a new
appendix for clarifying fault-tolerant preparation of quantum states, and
various minor change
Efficient Computations of Encodings for Quantum Error Correction
We show how, given any set of generators of the stabilizer of a quantum code,
an efficient gate array that computes the codewords can be constructed. For an
n-qubit code whose stabilizer has d generators, the resulting gate array
consists of O(n d) operations, and converts k-qubit data (where k = n - d) into
n-qubit codewords.Comment: 16 pages, REVTeX, 3 figures within the tex
Graph states in phase space
The phase space for a system of qubits is a discrete grid of points, whose axes are labeled in terms of the elements of the
finite field \Gal{2^n} to endow it with proper geometrical properties. We
analyze the representation of graph states in that phase space, showing that
these states can be identified with a class of non-singular curves. We provide
an algebraic representation of the most relevant quantum operations acting on
these states and discuss the advantages of this approach.Comment: 14 pages. 2 figures. Published in Journal of Physics
Dark Matter and the Chemical Evolution of Irregular Galaxies
We present three types of chemical evolution models for irregular galaxies:
closed-box with continuous star formation rates (SFRs), closed-box with
bursting SFRs, and O-rich outflow with continuous SFRs. We discuss the chemical
evolution of the irregular galaxies NGC 1560 and II Zw 33, and a ``typical''
irregular galaxy. The fraction of low-mass stars needed by our models is larger
than that derived for the solar vicinity, but similar to that found in globular
clusters. For our typical irregular galaxy we need a mass fraction of about 40%
in the form of substellar objects plus non baryonic dark matter inside the
Holmberg radius, in good agreement with the results derived for NGC 1560 and II
Zw 33 where we do have an independent estimate of the mass fraction in non
baryonic dark matter. Closed-box models are better than O-rich outflow models
in explaining the C/O and Z/O observed values for our typical irregular galaxy.Comment: 14 pages, 2 figure, uses emulateapj.sty package. ApJ in press. New
models were added. The order of Tables has been correcte
Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
For a quantum computer acting on d-dimensional systems, we analyze the
computational power of circuits wherein stabilizer operations are perfect and
we allow access to imperfect non-stabilizer states or operations. If the noise
rate affecting the non-stabilizer resource is sufficiently high, then these
states and operations can become simulable in the sense of the Gottesman-Knill
theorem, reducing the overall power of the circuit to no better than classical.
In this paper we find the depolarizing noise rate at which this happens, and
consequently the most robust non-stabilizer states and non-Clifford gates. In
doing so, we make use of the discrete Wigner function and derive facets of the
so-called qudit Clifford polytope i.e. the inequalities defining the convex
hull of all qudit Clifford gates. Our results for robust states are provably
optimal. For robust gates we find a critical noise rate that, as dimension
increases, rapidly approaches the the theoretical optimum of 100%. Some
connections with the question of qudit magic state distillation are discussed.Comment: 14 pages, 1 table; Minor changes vs. version
Preparing encoded states in an oscillator
Recently a scheme has been proposed for constructing quantum error-correcting
codes that embed a finite-dimensional code space in the infinite-dimensional
Hilbert space of a system described by continuous quantum variables. One of the
difficult steps in this scheme is the preparation of the encoded states. We
show how these states can be generated by coupling a continuous quantum
variable to a single qubit. An ion trap quantum computer provides a natural
setting for a continuous system coupled to a qubit. We discuss how encoded
states may be generated in an ion trap.Comment: 5 pages, 4 figures, RevTe
Unitarity, quasi-normal modes and the AdS_3/CFT_2 correspondence
In general, black-hole perturbations are governed by a discrete spectrum of
complex eigen-frequencies (quasi-normal modes). This signals the breakdown of
unitarity. In asymptotically AdS spaces, this is puzzling because the
corresponding CFT is unitary. To address this issue in three dimensions, we
replace the BTZ black hole by a wormhole, following a suggestion by Solodukhin
[hep-th/0406130]. We solve the wave equation for a massive scalar field and
find an equation for the poles of the propagator. This equation yields a rich
spectrum of {\em real} eigen-frequencies. We show that the throat of the
wormhole is , where is Newton's constant. Thus, the quantum
effects which might produce the wormhole are non-perturbative.Comment: 9 page
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