1,387 research outputs found
Finite Controllability of Infinite-Dimensional Quantum Systems
Quantum phenomena of interest in connection with applications to computation
and communication almost always involve generating specific transfers between
eigenstates, and their linear superpositions. For some quantum systems, such as
spin systems, the quantum evolution equation (the Schr\"{o}dinger equation) is
finite-dimensional and old results on controllability of systems defined on on
Lie groups and quotient spaces provide most of what is needed insofar as
controllability of non-dissipative systems is concerned. However, in an
infinite-dimensional setting, controlling the evolution of quantum systems
often presents difficulties, both conceptual and technical. In this paper we
present a systematic approach to a class of such problems for which it is
possible to avoid some of the technical issues. In particular, we analyze
controllability for infinite-dimensional bilinear systems under assumptions
that make controllability possible using trajectories lying in a nested family
of pre-defined subspaces. This result, which we call the Finite Controllability
Theorem, provides a set of sufficient conditions for controllability in an
infinite-dimensional setting. We consider specific physical systems that are of
interest for quantum computing, and provide insights into the types of quantum
operations (gates) that may be developed.Comment: This is a much improved version of the paper first submitted to the
arxiv in 2006 that has been under review since 2005. A shortened version of
this paper has been conditionally accepted for publication in IEEE
Transactions in Automatic Control (2009
Sufficient condition for the coherent control of n -qubit systems
We study quantum systems with even numbers N of levels that are completely state controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1) 2 as discussed by Albertini and D\u27Allesandro [IEEE Trans. Autom. Control 48, 1399 (2003)]. These Lie algebras are smaller than the corresponding su(N) with dimension N2 -1. We show that this reduction constrains the field-free Hamiltonian to have symmetric energy levels. An example of such a system is an n -qubit system with state-independent interaction terms. Using Clifford\u27s geometric algebra to represent the quantum wave function of a finite system, we present an explicit example of a two-qubit system that can be controlled by the elements of the Lie algebra sp(4) [isomorphic to spin(5) and so(5)] with dimension 10 rather than su(4) with dimension 15, but only if its field-free energy levels are symmetrically distributed about an average. These results enable one to envision more efficient algorithms for the design of fields for quantum-state engineering in certain quantum-computing applications, and provide more insight into the fundamental structure of quantum control
Reply to “Comment on ‘Photodetachment in combined static and dynamic electric fields’”
While distortion of the initial negative-ion state by a strong static electric field can have observable effects, the effect attributed by the authors of the preceding Comment [Phys. Rev. A 64, 037401 (2001)] to a cross term between the detaching laser field and the static field is spurious, an artifact of their procedures. Other points of dispute are also clarified
Overcoming the su(2^n) sufficient condition for the coherent control of n-qubit systems
We study quantum systems with even numbers N of levels that are completely
state-controlled by unitary transformations generated by Lie algebras
isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than
the respective su(N) with dimension N^2-1. We show that this reduction
constrains the Hamiltonian to have symmetric energy levels. An example of such
a system is an n-qubit system. Using a geometric representation for the quantum
wave function of a finite system, we present an explicit example that shows a
two-qubit system can be controlled by the elements of the Lie algebra sp(4)
(isomorphic to spin(5) and so(5)) with dimension ten rather than su(4) with
dimension fifteen. These results enable one to envision more efficient
algorithms for the design of fields for quantum-state engineering, and they
provide more insight into the fundamental structure of quantum control.Comment: 13 pp., 2 figure
Statistical physics-based reconstruction in compressed sensing
Compressed sensing is triggering a major evolution in signal acquisition. It
consists in sampling a sparse signal at low rate and later using computational
power for its exact reconstruction, so that only the necessary information is
measured. Currently used reconstruction techniques are, however, limited to
acquisition rates larger than the true density of the signal. We design a new
procedure which is able to reconstruct exactly the signal with a number of
measurements that approaches the theoretical limit in the limit of large
systems. It is based on the joint use of three essential ingredients: a
probabilistic approach to signal reconstruction, a message-passing algorithm
adapted from belief propagation, and a careful design of the measurement matrix
inspired from the theory of crystal nucleation. The performance of this new
algorithm is analyzed by statistical physics methods. The obtained improvement
is confirmed by numerical studies of several cases.Comment: 20 pages, 8 figures, 3 tables. Related codes and data are available
at http://aspics.krzakala.or
Gravid uterus in a neglected incisional hernia: a rare case report
Incidence of incisional hernia in pregnancy is rare and is mainly managed conservatively. An ideal technique for repairing incisional hernia in pregnant patients has yet to be established, but it is clear that each case must be dealt with on an individual basis. It is essential for surgeons to consider the length of the surgery, the presence of contamination, the age of the fetus, the size of the defect, and the chances of recurrence before selecting which technique to employ when repairing abdominal wall hernia in pregnancy. We report a case of term pregnancy in a third gravida, aged 30 years with previous two vaginal deliveries with incisional hernia with overlying hyperpigmented lax skin patch. Incisional hernia developed as a complication because of the previous surgical history of open appendectomy 10 years back which was complicated in the post-operative period, 22 days later leading to an emergency laparotomy in view of intestinal obstruction. Caesarean section was done with simultaneous repair of the incisional hernia with nonabsorbable sutures. The post-operative recovery was uneventful
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