234 research outputs found
Quantum Algorithms
This article surveys the state of the art in quantum computer algorithms,
including both black-box and non-black-box results. It is infeasible to detail
all the known quantum algorithms, so a representative sample is given. This
includes a summary of the early quantum algorithms, a description of the
Abelian Hidden Subgroup algorithms (including Shor's factoring and discrete
logarithm algorithms), quantum searching and amplitude amplification, quantum
algorithms for simulating quantum mechanical systems, several non-trivial
generalizations of the Abelian Hidden Subgroup Problem (and related
techniques), the quantum walk paradigm for quantum algorithms, the paradigm of
adiabatic algorithms, a family of ``topological'' algorithms, and algorithms
for quantum tasks which cannot be done by a classical computer, followed by a
discussion.Comment: 71 pages, 1 figure, to appear in the Springer Encyclopedia of
Complexity and Systems Scienc
Secure Biometrics: Concepts, Authentication Architectures and Challenges
BIOMETRICS are an important and widely used class of methods for identity
verification and access control. Biometrics are attractive because they are
inherent properties of an individual. They need not be remembered like
passwords, and are not easily lost or forged like identifying documents. At the
same time, bio- metrics are fundamentally noisy and irreplaceable. There are
always slight variations among the measurements of a given biometric, and,
unlike passwords or identification numbers, biometrics are derived from
physical characteristics that cannot easily be changed. The proliferation of
biometric usage raises critical privacy and security concerns that, due to the
noisy nature of biometrics, cannot be addressed using standard cryptographic
methods. In this article we present an overview of "secure biometrics", also
referred to as "biometric template protection", an emerging class of methods
that address these concerns.Comment: 16 pages, 11 figures, 1 tabl
Abelian Hypergroups and Quantum Computation
Motivated by a connection, described here for the first time, between the
hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic
objects that model collisions of physical particles), we develop a stabilizer
formalism using abelian hypergroups and an associated classical simulation
theorem (a la Gottesman-Knill). Using these tools, we develop the first
provably efficient quantum algorithm for finding hidden subhypergroups of
nilpotent abelian hypergroups and, via the aforementioned connection, a new,
hypergroup-based algorithm for the HNSP on nilpotent groups. We also give
efficient methods for manipulating non-unitary, non-monomial stabilizers and an
adaptive Fourier sampling technique of general interest.Comment: 41 pages + 6 pages appendices. Added references and corrected typos
in this version (sections 1-2
Analog to Digital Cognitive Radio: Sampling, Detection and Hardware
The proliferation of wireless communications has recently created a
bottleneck in terms of spectrum availability. Motivated by the observation that
the root of the spectrum scarcity is not a lack of resources but an inefficient
managing that can be solved, dynamic opportunistic exploitation of spectral
bands has been considered, under the name of Cognitive Radio (CR). This
technology allows secondary users to access currently idle spectral bands by
detecting and tracking the spectrum occupancy. The CR application revisits this
traditional task with specific and severe requirements in terms of spectrum
sensing and detection performance, real-time processing, robustness to noise
and more. Unfortunately, conventional methods do not satisfy these demands for
typical signals, that often have very high Nyquist rates.
Recently, several sampling methods have been proposed that exploit signals' a
priori known structure to sample them below the Nyquist rate. Here, we review
some of these techniques and tie them to the task of spectrum sensing in the
context of CR. We then show how issues related to spectrum sensing can be
tackled in the sub-Nyquist regime. First, to cope with low signal to noise
ratios, we propose to recover second-order statistics from the low rate
samples, rather than the signal itself. In particular, we consider
cyclostationary based detection, and investigate CR networks that perform
collaborative spectrum sensing to overcome channel effects. To enhance the
efficiency of the available spectral bands detection, we present joint spectrum
sensing and direction of arrival estimation methods. Throughout this work, we
highlight the relation between theoretical algorithms and their practical
implementation. We show hardware simulations performed on a prototype we built,
demonstrating the feasibility of sub-Nyquist spectrum sensing in the context of
CR.Comment: Submitted to IEEE Signal Processing Magazin
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals
Conventional sub-Nyquist sampling methods for analog signals exploit prior
information about the spectral support. In this paper, we consider the
challenging problem of blind sub-Nyquist sampling of multiband signals, whose
unknown frequency support occupies only a small portion of a wide spectrum. Our
primary design goals are efficient hardware implementation and low
computational load on the supporting digital processing. We propose a system,
named the modulated wideband converter, which first multiplies the analog
signal by a bank of periodic waveforms. The product is then lowpass filtered
and sampled uniformly at a low rate, which is orders of magnitude smaller than
Nyquist. Perfect recovery from the proposed samples is achieved under certain
necessary and sufficient conditions. We also develop a digital architecture,
which allows either reconstruction of the analog input, or processing of any
band of interest at a low rate, that is, without interpolating to the high
Nyquist rate. Numerical simulations demonstrate many engineering aspects:
robustness to noise and mismodeling, potential hardware simplifications,
realtime performance for signals with time-varying support and stability to
quantization effects. We compare our system with two previous approaches:
periodic nonuniform sampling, which is bandwidth limited by existing hardware
devices, and the random demodulator, which is restricted to discrete multitone
signals and has a high computational load. In the broader context of Nyquist
sampling, our scheme has the potential to break through the bandwidth barrier
of state-of-the-art analog conversion technologies such as interleaved
converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in
Signal Processing, the special issue on Compressed Sensin
Quantum computing from a mathematical perspective: a description of the quantum circuit model
This paper is an essentially self-contained and rigorous description of the
fundamental principles of quantum computing from a mathematical perspective. It
is intended to help mathematicians who want to get a grasp of this quickly
growing discipline and find themselves taken aback by the language gap between
mathematics and the pioneering fields on the matter: computer science and
quantum physics
Automatically generating Feynman rules for improved lattice field theories
Deriving the Feynman rules for lattice perturbation theory from actions and
operators is complicated, especially when improvement terms are present. This
physically important task is, however, suitable for automation. We describe a
flexible algorithm for generating Feynman rules for a wide range of lattice
field theories including gluons, relativistic fermions and heavy quarks. We
also present an efficient implementation of this in a freely available,
multi-platform programming language (\python), optimised to deal with a wide
class of lattice field theories
Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups
Knot and link invariants naturally arise from any braided Hopf algebra. We
consider the computational complexity of the invariants arising from an
elementary family of finite-dimensional Hopf algebras: quantum doubles of
finite groups (denoted D(G), for a group G). Regarding algorithms for these
invariants, we develop quantum circuits for the quantum Fourier transform over
D(G); in general, we show that when one can uniformly and efficiently carry out
the quantum Fourier transform over the centralizers Z(g) of the elements of G,
one can efficiently carry out the quantum Fourier transform over D(G). We apply
these results to the symmetric groups to yield efficient circuits for the
quantum Fourier transform over D(S_n). With such a Fourier transform, it is
straightforward to obtain additive approximation algorithms for the related
link invariant. Additionally, we show that certain D(G) invariants (such as
D(A_n) invariants) are BPP-hard to additively approximate, SBP-hard to
multiplicatively approximate, and #P-hard to exactly evaluate. Finally, we make
partial progress on the question of simulating anyonic computation in groups
uniformly as a function of the group size. In this direction, we provide
efficient quantum circuits for the Clebsch-Gordan transform over D(G) for
"fluxon" irreps, i.e., irreps of D(G) characterized by a conjugacy class of G.
For general irreps, i.e., those which are associated with a conjugacy class of
G and an irrep of a centralizer, we present an efficient implementation under
certain conditions such as when there is an efficient Clebsch-Gordan transform
over the centralizers. We remark that this also provides a simulation of
certain anyonic models of quantum computation, even in circumstances where the
group may have size exponential in the size of the circuit.Comment: 30 page
Quantum Complexity: restrictions on algorithms and architectures
A dissertation submitted to the University of Bristol in accordance with the
requirements of the degree of Doctor of Philosophy (PhD) in the Faculty of
Engineering, Department of Computer Science, July 2009.Comment: 137 pages, 10 figs
Sub-Nyquist Wideband Spectrum Sensing and Sharing
PhDThe rising popularity of wireless services resulting in spectrum shortage has motivated
dynamic spectrum sharing to facilitate e cient usage of the underutilized spectrum.
Wideband spectrum sensing is a critical functionality to enable dynamic spectrum access
by enhancing the opportunities of exploring spectral holes, but entails a major implemen-
tation challenge in compact commodity radios that have limited energy and computation
capabilities. The sampling rates speci ed by the Shannon-Nyquist theorem impose great
challenges both on the acquisition hardware and the subsequent storage and digital sig-
nal processors. Sub-Nyquist sampling was thus motivated to sample wideband signals
at rates far lower than the Nyquist rate, while still retaining the essential information in
the underlying signals.
This thesis proposes several algorithms for invoking sub-Nyquist sampling in wideband
spectrum sensing. Speci cally, a sub-Nyquist wideband spectrum sensing algorithm is
proposed that achieves wideband sensing independent of signal sparsity without sampling
at full bandwidth by using the low-speed analog-to-digital converters based on sparse
Fast Fourier Transform. To lower signal spectrum sparsity while maintaining the channel
state information, the received signal is pre-processed through a proposed permutation
and ltering algorithm. Additionally, a low-complexity sub-Nyquist wideband spectrum
sensing scheme is proposed that locates occupied channels blindly by recovering the sig-
nal support, based on the jointly sparse nature of multiband signals. Exploiting the
common signal support shared among multiple secondary users, an e cient coopera-
tive spectrum sensing scheme is developed, in which the energy consumption on signal
acquisition, processing, and transmission is reduced with the detection performance guar-
antee. To further reduce the computation complexity of wideband spectrum sensing, a
hybrid framework of sub-Nyquist wideband spectrum sensing with geolocation database
is explored. Prior channel information from geolocation database is utilized in the sens-
ing process to reduce the processing requirements on the sensor nodes. The models of
the proposed algorithms are derived and veri ed by numerical analyses and tested on
both real-world and simulated TV white space signals
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