1,924 research outputs found
A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space
Geometric algebra is a mathematical structure that is inherent in any metric
vector space, and defined by the requirement that the metric tensor is given by
the scalar part of the product of vectors. It provides a natural framework in
which to represent the classical groups as subgroups of rotation groups, and
similarly their Lie algebras. In this article we show how the geometric algebra
of a six-dimensional real Euclidean vector space naturally allows one to
construct the special unitary group on a two-qubit (quantum bit) Hilbert space,
in a fashion similar to that used in the well-established Bloch sphere model
for a single qubit. This is then used to illustrate the Cartan decompositions
and subalgebras of the four-dimensional special unitary group, which have
recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev.
A 67, 042313, 2003] to study the entangling capabilities of two-qubit
unitaries.Comment: 14 pages, 2 figures, in press (Proceedings of SPIE Conference on
Defense & Security
On the swap-distances of different realizations of a graphical degree sequence
One of the first graph theoretical problems which got serious attention
(already in the fifties of the last century) was to decide whether a given
integer sequence is equal to the degree sequence of a simple graph (or it is
{\em graphical} for short). One method to solve this problem is the greedy
algorithm of Havel and Hakimi, which is based on the {\em swap} operation.
Another, closely related question is to find a sequence of swap operations to
transform one graphical realization into another one of the same degree
sequence. This latter problem got particular emphases in connection of fast
mixing Markov chain approaches to sample uniformly all possible realizations of
a given degree sequence. (This becomes a matter of interest in connection of --
among others -- the study of large social networks.) Earlier there were only
crude upper bounds on the shortest possible length of such swap sequences
between two realizations. In this paper we develop formulae (Gallai-type
identities) for these {\em swap-distance}s of any two realizations of simple
undirected or directed degree sequences. These identities improves considerably
the known upper bounds on the swap-distances.Comment: to be publishe
Subsystem Pseudo-pure States
A critical step in experimental quantum information processing (QIP) is to
implement control of quantum systems protected against decoherence via
informational encodings, such as quantum error correcting codes, noiseless
subsystems and decoherence free subspaces. These encodings lead to the promise
of fault tolerant QIP, but they come at the expense of resource overheads.
Part of the challenge in studying control over multiple logical qubits, is
that QIP test-beds have not had sufficient resources to analyze encodings
beyond the simplest ones. The most relevant resources are the number of
available qubits and the cost to initialize and control them. Here we
demonstrate an encoding of logical information that permits the control over
multiple logical qubits without full initialization, an issue that is
particularly challenging in liquid state NMR. The method of subsystem
pseudo-pure state will allow the study of decoherence control schemes on up to
6 logical qubits using liquid state NMR implementations.Comment: 9 pages, 1 Figur
Reflection Symmetries for Multiqubit Density Operators
For multiqubit density operators in a suitable tensorial basis, we show that
a number of nonunitary operations used in the detection and synthesis of
entanglement are classifiable as reflection symmetries, i.e., orientation
changing rotations. While one-qubit reflections correspond to antiunitary
symmetries, as is known for example from the partial transposition criterion,
reflections on the joint density of two or more qubits are not accounted for by
the Wigner Theorem and are well-posed only for sufficiently mixed states. One
example of such nonlocal reflections is the unconditional NOT operation on a
multiparty density, i.e., an operation yelding another density and such that
the sum of the two is the identity operator. This nonphysical operation is
admissible only for sufficiently mixed states.Comment: 9 page
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Role of angiopoietin-like protein 3 in sugar-induced dyslipidemia in rhesus macaques: suppression by fish oil or RNAi.
Angiopoietin-like protein 3 (ANGPTL3) inhibits lipid clearance and is a promising target for managing cardiovascular disease. Here we investigated the effects of a high-sugar (high-fructose) diet on circulating ANGPTL3 concentrations in rhesus macaques. Plasma ANGPTL3 concentrations increased âŒ30% to 40% after 1 and 3 months of a high-fructose diet (both P < 0.001 vs. baseline). During fructose-induced metabolic dysregulation, plasma ANGPTL3 concentrations were positively correlated with circulating indices of insulin resistance [assessed with fasting insulin and the homeostatic model assessment of insulin resistance (HOMA-IR)], hypertriglyceridemia, adiposity (assessed as leptin), and systemic inflammation [C-reactive peptide (CRP)] and negatively correlated with plasma levels of the insulin-sensitizing hormone adropin. Multiple regression analyses identified a strong association between circulating APOC3 and ANGPTL3 concentrations. Higher baseline plasma levels of both ANGPTL3 and APOC3 were associated with an increased risk for fructose-induced insulin resistance. Fish oil previously shown to prevent insulin resistance and hypertriglyceridemia in this model prevented increases of ANGPTL3 without affecting systemic inflammation (increased plasma CRP and interleukin-6 concentrations). ANGPTL3 RNAi lowered plasma concentrations of ANGPTL3, triglycerides (TGs), VLDL-C, APOC3, and APOE. These decreases were consistent with a reduced risk of atherosclerosis. In summary, dietary sugar-induced increases of circulating ANGPTL3 concentrations after metabolic dysregulation correlated positively with leptin levels, HOMA-IR, and dyslipidemia. Targeting ANGPTL3 expression with RNAi inhibited dyslipidemia by lowering plasma TGs, VLDL-C, APOC3, and APOE levels in rhesus macaques
Design of Strongly Modulating Pulses to Implement Precise Effective Hamiltonians for Quantum Information Processing
We describe a method for improving coherent control through the use of
detailed knowledge of the system's Hamiltonian. Precise unitary transformations
were obtained by strongly modulating the system's dynamics to average out
unwanted evolution. With the aid of numerical search methods, pulsed
irradiation schemes are obtained that perform accurate, arbitrary, selective
gates on multi-qubit systems. Compared to low power selective pulses, which
cannot average out all unwanted evolution, these pulses are substantially
shorter in time, thereby reducing the effects of relaxation. Liquid-state NMR
techniques on homonuclear spin systems are used to demonstrate the accuracy of
these gates both in simulation and experiment. Simulations of the coherent
evolution of a 3-qubit system show that the control sequences faithfully
implement the unitary operations, typically yielding gate fidelities on the
order of 0.999 and, for some sequences, up to 0.9997. The experimentally
determined density matrices resulting from the application of different control
sequences on a 3-spin system have overlaps of up to 0.99 with the expected
states, confirming the quality of the experimental implementation.Comment: RevTeX3, 11 pages including 2 tables and 5 figures; Journal of
Chemical Physics, in pres
Selective coherence transfers in homonuclear dipolar coupled spin systems
Mapping the physical dipolar Hamiltonian of a solid-state network of nuclear
spins onto a system of nearest-neighbor couplings would be extremely useful for
a variety of quantum information processing applications, as well as NMR
structural studies. We demonstrate such a mapping for a system consisting of an
ensemble of spin pairs, where the coupling between spins in the same pair is
significantly stronger than the coupling between spins on different pairs. An
amplitude modulated RF field is applied on resonance with the Larmor frequency
of the spins, with the frequency of the modulation matched to the frequency of
the dipolar coupling of interest. The spin pairs appear isolated from each
other in the regime where the RF power (omega_1) is such that omega_weak <<
omega_1 << omega_strong. Coherence lifetimes within the two-spin system are
increased from 19 us to 11.1 ms, a factor of 572.Comment: 4 pages. Paper re-submitted with minor changes to clarify that the
scheme demonstrated is not an exact mapping onto a nearest neighbor system.
However, this is the first demonstration of a controlled evolution in a
subspace of an extended spin system, on a timescale that is much larger than
the dipolar dephasing tim
Multivariate calibration approach for quantitative determination of cell-line cross contamination by intact cell mass spectrometry and artificial neural networks
Cross-contamination of eukaryotic cell lines used in biomedical research represents a highly relevant problem. Analysis of repetitive DNA sequences, such as Short Tandem Repeats (STR), or Simple Sequence Repeats (SSR), is a widely accepted, simple, and commercially available technique to authenticate cell lines. However, it provides only qualitative information that depends on the extent of reference databases for interpretation. In this work, we developed and validated a rapid and routinely applicable method for evaluation of cell culture cross-contamination levels based on mass spectrometric fingerprints of intact mammalian cells coupled with artificial neural networks (ANNs). We used human embryonic stem cells (hESCs) contaminated by either mouse embryonic stem cells (mESCs) or mouse embryonic fibroblasts (MEFs) as a model. We determined the contamination level using a mass spectra database of known calibration mixtures that served as training input for an ANN. The ANN was then capable of correct quantification of the level of contamination of hESCs by mESCs or MEFs. We demonstrate that MS analysis, when linked to proper mathematical instruments, is a tangible tool for unraveling and quantifying heterogeneity in cell cultures. The analysis is applicable in routine scenarios for cell authentication and/or cell phenotyping in general
Quantum Codes for Controlling Coherent Evolution
Control over spin dynamics has been obtained in NMR via coherent averaging,
which is implemented through a sequence of RF pulses, and via quantum codes
which can protect against incoherent evolution. Here, we discuss the design and
implementation of quantum codes to protect against coherent evolution. A
detailed example is given of a quantum code for protecting two data qubits from
evolution under a weak coupling (Ising) term in the Hamiltonian, using an
``isolated'' ancilla which does not evolve on the experimental time scale. The
code is realized in a three-spin system by liquid-state NMR spectroscopy on
13C-labelled alanine, and tested for two initial states. It is also shown that
for coherent evolution and isolated ancillae, codes exist that do not require
the ancillae to initially be in a (pseudo-)pure state. Finally, it is shown
that even with non-isolated ancillae quantum codes exist which can protect
against evolution under weak coupling. An example is presented for a six qubit
code that protects two data spins to first order.Comment: Reformatted single spaced with figures incorporated into text (18
pages, 6 figures, PDF only, submitted to J. Chem. Phys.
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