3,873 research outputs found
Applying Grover's algorithm to AES: quantum resource estimates
We present quantum circuits to implement an exhaustive key search for the
Advanced Encryption Standard (AES) and analyze the quantum resources required
to carry out such an attack. We consider the overall circuit size, the number
of qubits, and the circuit depth as measures for the cost of the presented
quantum algorithms. Throughout, we focus on Clifford gates as the
underlying fault-tolerant logical quantum gate set. In particular, for all
three variants of AES (key size 128, 192, and 256 bit) that are standardized in
FIPS-PUB 197, we establish precise bounds for the number of qubits and the
number of elementary logical quantum gates that are needed to implement
Grover's quantum algorithm to extract the key from a small number of AES
plaintext-ciphertext pairs.Comment: 13 pages, 3 figures, 5 tables; to appear in: Proceedings of the 7th
International Conference on Post-Quantum Cryptography (PQCrypto 2016
Addressing Security Properties in Systems of Systems: Challenges and Ideas
Within growing pervasive information systems, Systems of Systems (SoS) emerge as a new research frontier. A SoS is formed by a set of constituent systems that live on their own with well-established functionalities and requirements, and, in certain circumstances, they must collaborate to achieve a common mission. In this scenario, security is one crucial property that needs to be considered since the early stages of SoS lifecycle. Unfortunately, SoS security cannot be guaranteed by addressing the security of each constituent system separately. The aim of this paper is to discuss the challenges faced in addressing the security of SoS and to propose some research ideas centered around the notion of a mission to be carried out by the SoS.Ministerio dell'Universitá e della Ricerca (Italia) GAUSS 2015KWREMXMinisterio de EconomĂa y Competitividad TIN2016-76956-C3-2-R (POLOLAS
Algebraic Approach to Interacting Quantum Systems
We present an algebraic framework for interacting extended quantum systems to
study complex phenomena characterized by the coexistence and competition of
different states of matter. We start by showing how to connect different
(spin-particle-gauge) {\it languages} by means of exact mappings (isomorphisms)
that we name {\it dictionaries} and prove a fundamental theorem establishing
when two arbitrary languages can be connected. These mappings serve to unravel
symmetries which are hidden in one representation but become manifest in
another. In addition, we establish a formal link between seemingly unrelated
physical phenomena by changing the language of our model description. This link
leads to the idea of {\it universality} or equivalence. Moreover, we introduce
the novel concept of {\it emergent symmetry} as another symmetry guiding
principle. By introducing the notion of {\it hierarchical languages}, we
determine the quantum phase diagram of lattice models (previously unsolved) and
unveil hidden order parameters to explore new states of matter. Hierarchical
languages also constitute an essential tool to provide a unified description of
phases which compete and coexist. Overall, our framework provides a simple and
systematic methodology to predict and discover new kinds of orders. Another
aspect exploited by the present formalism is the relation between condensed
matter and lattice gauge theories through quantum link models. We conclude
discussing applications of these dictionaries to the area of quantum
information and computation with emphasis in building new models of computation
and quantum programming languages.Comment: 44 pages, 14 psfigures. Advances in Physics 53, 1 (2004
Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach
Operator entanglement of two-qubit joint unitary operations is revisited.
Schmidt number is an important attribute of a two-qubit unitary operation, and
may have connection with the entanglement measure of the unitary operator. We
found the entanglement measure of two-qubit unitary operators is classified by
the Schmidt number of the unitary operators. The exact relation between the
operator entanglement and the parameters of the unitary operator is clarified
too.Comment: To appear in the Brazilian Journal of Physic
Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments
This work studies the feasibility of optimal control of high-fidelity quantum
gates in a model of interacting two-level particles. One particle (the qubit)
serves as the quantum information processor, whose evolution is controlled by a
time-dependent external field. The other particles are not directly controlled
and serve as an effective environment, coupling to which is the source of
decoherence. The control objective is to generate target one-qubit gates in the
presence of strong environmentally-induced decoherence and under physically
motivated restrictions on the control field. It is found that interactions
among the environmental particles have a negligible effect on the gate fidelity
and require no additional adjustment of the control field. Another interesting
result is that optimally controlled quantum gates are remarkably robust to
random variations in qubit-environment and inter-environment coupling
strengths. These findings demonstrate the utility of optimal control for
management of quantum-information systems in a very precise and specific
manner, especially when the dynamics complexity is exacerbated by inherently
uncertain environmental coupling.Comment: tMOP LaTeX, 9 pages, 3 figures; Special issue of the Journal of
Modern Optics: 37th Winter Colloquium on the Physics of Quantum Electronics,
2-6 January 200
Renormalisation of heavy-light light ray operators
We calculate the renormalisation of different light ray operators with one
light degree of freedom and a static heavy quark. Both - and
-kernels are considered. A comparison with the light-light case suggests
that the mixing with three-particle operators is solely governed by the light
degrees of freedom. Additionally we show that conformal symmetry is already
broken at the level of the one loop counterterms due to the additional
UV-renormalisation of a cusp in the two contributing Wilson-lines. This general
feature can be used to fix the -renormalisation kernels up to a
constant. Some examples for applications of our results are given.Comment: 23 pages, 5 figures; v2: changed some wording, added a few references
and one appendix concerning some subtleties related to gauge fixing and ghost
terms; v3: clarified calculation in section 3.2., added an explicit
calculation in section 5.2, corrected a few typos and one figure, added a few
comments, results unchanged, except for typesetting matches version to appear
in JHE
Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2
We propose a new lattice superfield formalism in momentum representation
which accommodates species doublers of the lattice fermions and their bosonic
counterparts as super multiplets. We explicitly show that one dimensional N=2
model with interactions has exact Lie algebraic supersymmetry on the lattice
for all super charges. In coordinate representation the finite difference
operator is made to satisfy Leibnitz rule by introducing a non local product,
the ``star'' product, and the exact lattice supersymmetry is realized. The
standard momentum conservation is replaced on the lattice by the conservation
of the sine of the momentum, which plays a crucial role in the formulation.
Half lattice spacing structure is essential for the one dimensional model and
the lattice supersymmetry transformation can be identified as a half lattice
spacing translation combined with alternating sign structure. Invariance under
finite translations and locality in the continuum limit are explicitly
investigated and shown to be recovered. Supersymmetric Ward identities are
shown to be satisfied at one loop level. Lie algebraic lattice supersymmetry
algebra of this model suggests a close connection with Hopf algebraic exactness
of the link approach formulation of lattice supersymmetry.Comment: 34 pages, 2 figure
Measuring measurement
Measurement connects the world of quantum phenomena to the world of classical
events. It plays both a passive role, observing quantum systems, and an active
one, preparing quantum states and controlling them. Surprisingly - in the light
of the central status of measurement in quantum mechanics - there is no general
recipe for designing a detector that measures a given observable. Compounding
this, the characterization of existing detectors is typically based on partial
calibrations or elaborate models. Thus, experimental specification (i.e.
tomography) of a detector is of fundamental and practical importance. Here, we
present the realization of quantum detector tomography: we identify the optimal
positive-operator-valued measure describing the detector, with no ancillary
assumptions. This result completes the triad, state, process, and detector
tomography, required to fully specify an experiment. We characterize an
avalanche photodiode and a photon number resolving detector capable of
detecting up to eight photons. This creates a new set of tools for accurately
detecting and preparing non-classical light.Comment: 6 pages, 4 figures,see video abstract at
http://www.quantiki.org/video_abstracts/0807244
SN 2005hj: Evidence for Two Classes of Normal-Bright SNe Ia and Implications for Cosmology
HET Optical spectra covering the evolution from about 6 days before to about
5 weeks after maximum light and the ROTSE-IIIb unfiltered light curve of the
"Branch-normal" Type Ia Supernova SN 2005hj are presented. The host galaxy
shows HII region lines at redshift of z=0.0574, which puts the peak unfiltered
absolute magnitude at a somewhat over-luminous -19.6. The spectra show weak and
narrow SiII lines, and for a period of at least 10 days beginning around
maximum light these profiles do not change in width or depth and they indicate
a constant expansion velocity of ~10,600 km/s. We analyzed the observations
based on detailed radiation dynamical models in the literature. Whereas delayed
detonation and deflagration models have been used to explain the majority of
SNe Ia, they do not predict a long velocity plateau in the SiII minimum with an
unvarying line profile. Pulsating delayed detonations and merger scenarios form
shell-like density structures with properties mostly related to the mass of the
shell, M_shell, and we discuss how these models may explain the observed SiII
line evolution; however, these models are based on spherical calculations and
other possibilities may exist. SN 2005hj is consistent with respect to the
onset, duration, and velocity of the plateau, the peak luminosity and, within
the uncertainties, with the intrinsic colors for models with M_shell=0.2 M_sun.
Our analysis suggests a distinct class of events hidden within the
Branch-normal SNe Ia. If the predicted relations between observables are
confirmed, they may provide a way to separate these two groups. We discuss the
implications of two distinct progenitor classes on cosmological studies
employing SNe Ia, including possible differences in the peak luminosity to
light curve width relation.Comment: ApJ accepted, 31 page
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