Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm-a global-optimization method inspired by nature's evolutionary process-for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses.

Quantitative interactions between the A-type K+ current and inositol trisphosphate receptors regulate intraneuronal Ca2+ waves and synaptic plasticity

Key points center dot Active calcium signal propagation occurs when an initial calcium trigger elicits calcium release through endoplasmic reticulum (ER) receptors. A high concentration of the calcium trigger in thin-calibre dendrites would suppress release of calcium through hippocampal inositol trisphosphate receptors (InsP3Rs). center dot Could the high-density expression of A-type K+ channels in thin-calibre dendrites be a mechanism for inhibiting this suppression, thereby restoring the utility of the ER as a substrate for active calcium propagation? center dot Quantitative analyses involving experimentally constrained models reveal a bell-shaped dependence of calcium released through InsP3Rs on the A-type K+ channel density, during the propagation of a calcium wave. center dot A-type K+ channels regulated the relative contribution of ER calcium to the induction of synaptic plasticity in the presence of model metabotropic glutamate receptors. center dot These results identify a novel form of interaction between active dendrites and the ER membrane and suggest that A-type K+ channels are ideally placed for inhibiting the suppression of InsP3Rs in thin-calibre dendrites. Abstract The A-type potassium current has been implicated in the regulation of several physiological processes. Here, we explore a role for the A-type potassium current in regulating the release of calcium through inositol trisphosphate receptors (InsP3R) that reside on the endoplasmic reticulum (ER) of hippocampal pyramidal neurons. To do this, we constructed morphologically realistic, conductance-based models equipped with kinetic schemes that govern several calcium signalling modules and pathways, and constrained the distributions and properties of constitutive components by experimental measurements from these neurons. Employing these models, we establish a bell-shaped dependence of calcium release through InsP3Rs on the density ofA-type potassium channels, during the propagation of an intraneuronal calcium wave initiated through established protocols. Exploring the sensitivities of calcium wave initiation and propagation to several underlying parameters, we found that ER calcium release critically depends on dendritic diameter and that wave initiation occurred at branch points as a consequence of a high surface area to volume ratio of oblique dendrites. Furthermore, analogous to the role ofA-type potassium channels in regulating spike latency, we found that an increase in the density ofA-type potassium channels led to increases in the latency and the temporal spread of a propagating calcium wave. Next, we incorporated kinetic models for the metabotropic glutamate receptor (mGluR) signalling components and a calcium-controlled plasticity rule into our model and demonstrate thatthe presence of mGluRs induced a leftward shift in a BienenstockCooperMunro-like synaptic plasticity profile. Finally, we show that the A-type potassium current could regulate the relative contribution of ER calcium to synaptic plasticity induced either through 900 pulses of various stimulus frequencies or through theta burst stimulation. Our results establish a novel form of interaction between active dendrites and the ER membrane, uncovering a powerful mechanism that could regulate biophysical/biochemical signal integration and steer the spatiotemporal spread of signalling microdomains through changes in dendritic excitability.

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments obtained from statistical trials encodes a classical probability distribution. However, it is well known that an incompatible set of moments arises in the quantum scenario, when correlation outcomes associated with measurements on spatially separated entangled states are considered. This feature, viz., the incompatibility of moments with a joint probability distribution, is reflected in the violation of Bell inequalities. Here, we focus on sequential measurements on a single quantum system and investigate if moments and joint probabilities are compatible with each other. By considering sequential measurement of a dichotomic dynamical observable at three different time intervals, we explicitly demonstrate that the moments and the probabilities are inconsistent with each other. Experimental results using a nuclear magnetic resonance system are reported here to corroborate these theoretical observations, viz., the incompatibility of the three-time joint probabilities with those extracted from the moment sequence when sequential measurements on a single-qubit system are considered.

Quantum simulation using fidelity-profile optimization

Experimental quantum simulation of a Hamiltonian H requires unitary operator decomposition (UOD) of its evolution unitary U = exp(-iHt) in terms of native unitary operators of the experimental system. Here, using a genetic algorithm, we numerically evaluate the most generic UOD (valid over a continuous range of Hamiltonian parameters) of the unitary operator U, termed fidelity-profile optimization. The optimization is obtained by systematically evaluating the functional dependence of experimental unitary operators (such as single-qubit rotations and time-evolution unitaries of the system interactions) to the Hamiltonian (H) parameters. Using this technique, we have solved the experimental unitary decomposition of a controlled-phase gate (for any phase value), the evolution unitary of the Heisenberg XY interaction, and simulation of the Dzyaloshinskii-Moriya (DM) interaction in the presence of the Heisenberg XY interaction. Using these decompositions, we studied the entanglement dynamics of a Bell state in the DM interaction and experimentally verified the entanglement preservation procedure of Hou et al. Ann. Phys. (N.Y.) 327, 292 (2012)] in a nuclear magnetic resonance quantum information processor.

Quadrature Domains in C-n

We prove two density theorems for quadrature domains in , . It is shown that quadrature domains are dense in the class of all product domains of the form , where is a smoothly bounded domain satisfying Bell's Condition R and is a smoothly bounded domain and also in the class of all smoothly bounded complete Hartogs domains in C-2.

Integration of holographic sensors into microfluidics for the real-time pH sensing of L. casei metabolism

We describe developments in the integration of analyte specific holographic sensors into PDMS-based microfluidic devices for the purpose of continuous, low-impact monitoring of extra-cellular change in micro-bioreactors. Holographic sensors respond to analyte concentration via volume change, which makes their reduction in size and integration into spatially confined fluidics difficult. Through design and process modification many of these constraints have been addressed, and a microfluidics-based device capable of real-time monitoring of the pH change caused by Lactobacillus casei fermentation is presented as a general proof-of-concept for a wide array of possible devices.