179 research outputs found
Characterization of two-qubit perfect entanglers
Here we consider perfect entanglers from another perspective. It is shown
that there are some {\em special} perfect entanglers which can maximally
entangle a {\em full} product basis. We have explicitly constructed a
one-parameter family of such entanglers together with the proper product basis
that they maximally entangle. This special family of perfect entanglers
contains some well-known operators such as {\textsc{cnot}} and
{\textsc{dcnot}}, but {\em not} {\small{\sqrt{\rm{\textsc{swap}}}}}. In
addition, it is shown that all perfect entanglers with entangling power equal
to the maximal value, 2/9, are also special perfect entanglers. It is proved
that the one-parameter family is the only possible set of special perfect
entanglers. Also we provide an analytic way to implement any arbitrary
two-qubit gate, given a proper special perfect entangler supplemented with
single-qubit gates. Such these gates are shown to provide a minimum universal
gate construction in that just two of them are necessary and sufficient in
implementation of a generic two-qubit gate.Comment: 6 pages, 1 eps figur
Minimum orbit dimension for local unitary action on n-qubit pure states
The group of local unitary transformations partitions the space of n-qubit
quantum states into orbits, each of which is a differentiable manifold of some
dimension. We prove that all orbits of the n-qubit quantum state space have
dimension greater than or equal to 3n/2 for n even and greater than or equal to
(3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since
n-qubit states composed of products of singlets achieve these lowest orbit
dimensions.Comment: 19 page
Pocket2Drug: An Encoder-Decoder Deep Neural Network For The Target-Based Drug Design
Computational modeling is an essential component of modern drug discovery. One of its most important applications is to select promising drug candidates for pharmacologically relevant target proteins. Because of continuing advances in structural biology, putative binding sites for small organic molecules are being discovered in numerous proteins linked to various diseases. These valuable data offer new opportunities to build efficient computational models predicting binding molecules for target sites through the application of data mining and machine learning. In particular, deep neural networks are powerful techniques capable of learning from complex data in order to make informed drug binding predictions. In this communication, we describe Pocket2Drug, a deep graph neural network model to predict binding molecules for a given a ligand binding site. This approach first learns the conditional probability distribution of small molecules from a large dataset of pocket structures with supervised training, followed by the sampling of drug candidates from the trained model. Comprehensive benchmarking simulations show that using Pocket2Drug significantly improves the chances of finding molecules binding to target pockets compared to traditional drug selection procedures. Specifically, known binders are generated for as many as 80.5% of targets present in the testing set consisting of dissimilar data from that used to train the deep graph neural network model. Overall, Pocket2Drug is a promising computational approach to inform the discovery of novel biopharmaceuticals
Higher dimensional abelian Chern-Simons theories and their link invariants
The role played by Deligne-Beilinson cohomology in establishing the relation
between Chern-Simons theory and link invariants in dimensions higher than three
is investigated. Deligne-Beilinson cohomology classes provide a natural abelian
Chern-Simons action, non trivial only in dimensions , whose parameter
is quantized. The generalized Wilson -loops are observables of the
theory and their charges are quantized. The Chern-Simons action is then used to
compute invariants for links of -loops, first on closed
-manifolds through a novel geometric computation, then on
through an unconventional field theoretic computation.Comment: 40 page
Quantum circuits with uniformly controlled one-qubit gates
Uniformly controlled one-qubit gates are quantum gates which can be
represented as direct sums of two-dimensional unitary operators acting on a
single qubit. We present a quantum gate array which implements any n-qubit gate
of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit
gates and a single diagonal n-qubit gate. The circuit is based on the so-called
quantum multiplexor, for which we provide a modified construction. We
illustrate the versatility of these gates by applying them to the decomposition
of a general n-qubit gate and a local state preparation procedure. Moreover, we
study their implementation using only nearest-neighbor gates. We give upper
bounds for the one-qubit and controlled-NOT gate counts for all the
aforementioned applications. In all four cases, the proposed circuit topologies
either improve on or achieve the previously reported upper bounds for the gate
counts. Thus, they provide the most efficient method for general gate
decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some
result
Valence bond solid formalism for d-level one-way quantum computation
The d-level or qudit one-way quantum computer (d1WQC) is described using the
valence bond solid formalism and the generalised Pauli group. This formalism
provides a transparent means of deriving measurement patterns for the
implementation of quantum gates in the computational model. We introduce a new
universal set of qudit gates and use it to give a constructive proof of the
universality of d1WQC. We characterise the set of gates that can be performed
in one parallel time step in this model.Comment: 26 pages, 9 figures. Published in Journal of Physics A: Mathematical
and Genera
A practical scheme for quantum computation with any two-qubit entangling gate
Which gates are universal for quantum computation? Although it is well known
that certain gates on two-level quantum systems (qubits), such as the
controlled-not (CNOT), are universal when assisted by arbitrary one-qubit
gates, it has only recently become clear precisely what class of two-qubit
gates is universal in this sense. Here we present an elementary proof that any
entangling two-qubit gate is universal for quantum computation, when assisted
by one-qubit gates. A proof of this important result for systems of arbitrary
finite dimension has been provided by J. L. and R. Brylinski
[arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long
argument using advanced mathematics. In contrast, our proof provides a simple
constructive procedure which is close to optimal and experimentally practical
[C. M. Dawson and A. Gilchrist, online implementation of the procedure
described herein (2002), http://www.physics.uq.edu.au/gqc/].Comment: 3 pages, online implementation of procedure described can be found at
http://www.physics.uq.edu.au/gqc
Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian
We study the null fiber of a moment map related to dual pairs. We construct
an equivariant resolution of singularities of the null fiber, and get conormal
bundles of closed -orbits in the Lagrangian Grassmannian as the
categorical quotient. The conormal bundles thus obtained turn out to be a
resolution of singularities of the closure of nilpotent -orbits, which
is a "quotient" of the resolution of the null fiber.Comment: 17 pages; completely revised and add reference
An Invitation to Higher Gauge Theory
In this easy introduction to higher gauge theory, we describe parallel
transport for particles and strings in terms of 2-connections on 2-bundles.
Just as ordinary gauge theory involves a gauge group, this generalization
involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie
group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes,
which play an important role in string theory and multisymplectic geometry.
Second, every group representation gives a Lie 2-group; the representation of
the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which
leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint
representation of any Lie group on its own Lie algebra gives a 'tangent
2-group', which serves as a gauge 2-group in 4d BF theory, which has
topological gravity as a special case. Fourth, every Lie group has an 'inner
automorphism 2-group', which serves as the gauge group in 4d BF theory with
cosmological constant term. Fifth, every Lie group has an 'automorphism
2-group', which plays an important role in the theory of nonabelian gerbes. And
sixth, every compact simple Lie group gives a 'string 2-group'. We also touch
upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra
that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum
Gravity and Quantum Geometry at the 2009 Corfu Summer Institut
Cavity QED and Quantum Computation in the Weak Coupling Regime
In this paper we consider a model of quantum computation based on n atoms of
laser-cooled and trapped linearly in a cavity and realize it as the n atoms
Tavis-Cummings Hamiltonian interacting with n external (laser) fields.
We solve the Schr{\" o}dinger equation of the model in the case of n=2 and
construct the controlled NOT gate by making use of a resonance condition and
rotating wave approximation associated to it. Our method is not heuristic but
completely mathematical, and the significant feature is a consistent use of
Rabi oscillations.
We also present an idea of the construction of three controlled NOT gates in
the case of n=3 which gives the controlled-controlled NOT gate.Comment: Latex file, 22 pages, revised version. To appear in Journal of Optics
B : Quantum and Semiclassical Optic
- …