1,912 research outputs found
Bounds on the Probability of Success of Postselected Non-linear Sign Shifts Implemented with Linear Optics
The fundamental gates of linear optics quantum computation are realized by
using single photons sources, linear optics and photon counters. Success of
these gates is conditioned on the pattern of photons detected without using
feedback. Here it is shown that the maximum probability of success of these
gates is typically strictly less than 1. For the one-mode non-linear sign
shift, the probability of success is bounded by 1/2. For the conditional sign
shift of two modes, this probability is bounded by 3/4. These bounds are still
substantially larger than the highest probabilities shown to be achievable so
far, which are 1/4 and 2/27, respectively.Comment: 6 page
Noise effect on Grover algorithm
The decoherence effect on Grover algorithm has been studied numerically
through a noise modelled by a depolarizing channel. Two types of error are
introduced characterizing the qubit time evolution and gate application, so the
noise is directly related to the quantum network construction. The numerical
simulation concludes an exponential damping law for the successive probability
of the maxima as time increases. We have obtained an allowed-error law for the
algorithm: the error threshold for the allowed noise behaves as Eth(N) ~ 1/N1.1
(N being the size of the data set). As the power of N is almost one, we
consider the Grover algorithm as robust to a certain extent against
decoherence. This law also provides an absolute threshold: if the free
evolution error is greater than 0.043, Grover algorithm does not work for any
number of qubits affected by the present error model. The improvement in the
probability of success, in the case of two qubits has been illustrated by using
a fault-tolerant encoding of the initial state by means of the [[7,1,3]]
quantum code.Comment: Accepted to be published in Eur. Phys. J. D (2008
A fault-tolerant one-way quantum computer
We describe a fault-tolerant one-way quantum computer on cluster states in
three dimensions. The presented scheme uses methods of topological error
correction resulting from a link between cluster states and surface codes. The
error threshold is 1.4% for local depolarizing error and 0.11% for each source
in an error model with preparation-, gate-, storage- and measurement errors.Comment: 26 page
Optical Quantum Computing
In 2001 all-optical quantum computing became feasible with the discovery that
scalable quantum computing is possible using only single photon sources, linear
optical elements, and single photon detectors. Although it was in principle
scalable, the massive resource overhead made the scheme practically daunting.
However, several simplifications were followed by proof-of-principle
demonstrations, and recent approaches based on cluster states or error encoding
have dramatically reduced this worrying resource overhead, making an
all-optical architecture a serious contender for the ultimate goal of a
large-scale quantum computer. Key challenges will be the realization of
high-efficiency sources of indistinguishable single photons, low-loss, scalable
optical circuits, high efficiency single photon detectors, and low-loss
interfacing of these components.Comment: 5 pages, 4 figure
Experimental magic state distillation for fault-tolerant quantum computing
Any physical quantum device for quantum information processing is subject to
errors in implementation. In order to be reliable and efficient, quantum
computers will need error correcting or error avoiding methods. Fault-tolerance
achieved through quantum error correction will be an integral part of quantum
computers. Of the many methods that have been discovered to implement it, a
highly successful approach has been to use transversal gates and specific
initial states. A critical element for its implementation is the availability
of high-fidelity initial states such as |0> and the Magic State. Here we report
an experiment, performed in a nuclear magnetic resonance (NMR) quantum
processor, showing sufficient quantum control to improve the fidelity of
imperfect initial magic states by distilling five of them into one with higher
fidelity
Quantum Computing with Very Noisy Devices
In theory, quantum computers can efficiently simulate quantum physics, factor
large numbers and estimate integrals, thus solving otherwise intractable
computational problems. In practice, quantum computers must operate with noisy
devices called ``gates'' that tend to destroy the fragile quantum states needed
for computation. The goal of fault-tolerant quantum computing is to compute
accurately even when gates have a high probability of error each time they are
used. Here we give evidence that accurate quantum computing is possible with
error probabilities above 3% per gate, which is significantly higher than what
was previously thought possible. However, the resources required for computing
at such high error probabilities are excessive. Fortunately, they decrease
rapidly with decreasing error probabilities. If we had quantum resources
comparable to the considerable resources available in today's digital
computers, we could implement non-trivial quantum computations at error
probabilities as high as 1% per gate.Comment: 47 page
Symmetrised Characterisation of Noisy Quantum Processes
A major goal of developing high-precision control of many-body quantum
systems is to realise their potential as quantum computers. Probably the most
significant obstacle in this direction is the problem of "decoherence": the
extreme fragility of quantum systems to environmental noise and other control
limitations. The theory of fault-tolerant quantum error correction has shown
that quantum computation is possible even in the presence of decoherence
provided that the noise affecting the quantum system satisfies certain
well-defined theoretical conditions. However, existing methods for noise
characterisation have become intractable already for the systems that are
controlled in today's labs. In this paper we introduce a technique based on
symmetrisation that enables direct experimental characterisation of key
properties of the decoherence affecting a multi-body quantum system. Our method
reduces the number of experiments required by existing methods from exponential
to polynomial in the number of subsystems. We demonstrate the application of
this technique to the optimisation of control over nuclear spins in the solid
state.Comment: About 12 pages, 5 figure
Valence Bond Solids for Quantum Computation
Cluster states are entangled multipartite states which enable to do universal
quantum computation with local measurements only. We show that these states
have a very simple interpretation in terms of valence bond solids, which allows
to understand their entanglement properties in a transparent way. This allows
to bridge the gap between the differences of the measurement-based proposals
for quantum computing, and we will discuss several features and possible
extensions
Upper bounds on success probabilities in linear optics
We develop an abstract way of defining linear-optics networks designed to
perform quantum information tasks such as quantum gates. We will be mainly
concerned with the nonlinear sign shift gate, but it will become obvious that
all other gates can be treated in a similar manner. The abstract scheme is
extremely well suited for analytical as well as numerical investigations since
it reduces the number of parameters for a general setting. With that we show
numerically and partially analytically for a wide class of states that the
success probability of generating a nonlinear sign shift gate does not exceed
1/4 which to our knowledge is the strongest bound to date.Comment: 8 pages, typeset using RevTex4, 5 EPS figure
Quantum Estimation of Parameters of Classical Spacetimes
We describe a quantum limit to measurement of classical spacetimes.
Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the
single parameter in any one-parameter family of spacetime metrics. We employ
the locally covariant formulation of quantum field theory in curved spacetime,
which allows for a manifestly background-independent derivation. The result is
an uncertainty relation that applies to all globally hyperbolic spacetimes.
Among other examples, we apply our method to detection of gravitational waves
using the electromagnetic field as a probe, as in laser-interferometric
gravitational-wave detectors. Other applications are discussed, from
terrestrial gravimetry to cosmology.Comment: 23 pages. This article supersedes arXiv:1108.522
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