Mapping quantitative trait loci for seizure response to a GABAA receptor inverse agonist in mice

To define the genetic contributions affecting individual differences in seizure threshold, a beta carboline [methyl-beta-carboline-3-carboxylate (beta-CCM)]-induced model of generalized seizures was genetically dissected in mice. beta-CCM is a GABAA receptor inverse agonist and convulsant. By measuring the latency to generalized seizures after beta-CCM administration to A/J and C57BL6/J mice and their progeny, we estimated a heritability of 0.28 +/- 0.10. A genome wide screen in an F2 population of these parental strains (n = 273) mapped quantitative trait loci (QTLs) on proximal chromosome 7 [logarithm of the likelihood for linkage (LOD) = 3.71] and distal chromosome 10 (LOD = 4.29) for seizure susceptibility, explaining approximately 22 and 25%, respectively, of the genetic variance for this seizure trait. The best fitting logistic regression model suggests that the A/J allele at each locus increases the likelihood of seizures approximately threefold. In a subsequent backcross population (n = 223), we mapped QTLs on distal chromosome 4 (LOD = 2.88) and confirmed the distal chromosome 10 QTLs (LOD = 4.36). In the backcross, the C57BL/6J allele of the chromosome 10 QTL decreases the risk of seizures approximately twofold. These QTLs may ultimately lead to the identification of genes influencing individual differences in seizure threshold in mice and the discovery of novel anticonvulsant agents. The colocalization on distal chromosome 10 of a beta-CCM susceptibility QTL and a QTL for open field ambulation and vertical movement suggests the existence of a single, pleiotropic locus, which we have named Exq1

Hamiltonian Determination with Restricted Access in Transverse Field Ising Chain

We propose a method to evaluate parameters in the Hamiltonian of the Ising chain under site-dependent transverse fields, with a proviso that we can control and measure one of the edge spins only. We evaluate the eigenvalues of the Hamiltonian and the time-evoultion operator exactly for a 3-spin chain, from which we obtain the expectation values of $\sigma_x$ of the first spin. The parameters are found from the peak positions of the Fourier transform of the expectation value. There are four assumptions in our method, which are mild enough to be satisfied in many physical systems.Comment: 15pages, 4 figure

Statistical Constraints on State Preparation for a Quantum Computer

Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. Owing to considerations of quantum statistics, this requires that the entropy of the system go down. This, in turn, has two practical implications: (i) the initial state cannot be controlled; (ii) the temperature of the system must be reduced. These factors, in addition to decoherence and sensitivity to errors, must be considered in the implementation of quantum computers.Comment: 7 pages; the final published versio

Statistical analysis of coherent structures in transitional pipe flow

Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about Re=2200, and it decreases to about 20% for Re=2500. The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.Comment: 11 pages, 26 (sub)figure

Realization of quantum process tomography in NMR

Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits.Comment: 8 pages, 7 EPS figures, REVTe

NMR Simulation of an Eight-State Quantum System

The propagation of excitation along a one-dimensional chain of atoms is simulated by means of NMR. The physical system used as an analog quantum computer is a nucleus of 133-Cs (spin 7/2) in a liquid crystalline matrix. The Hamiltonian of migration is simulated by using a special 7-frequency pulse, and the dynamics is monitored by following the transfer of population from one of the 8 spin energy levels to the other.Comment: 10 pages, 3 figure

Fetching marked items from an unsorted database in NMR ensemble computing

Searching a marked item or several marked items from an unsorted database is a very difficult mathematical problem. Using classical computer, it requires $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an algorithm that fetches marked items in an unsorted database directly. It requires only a single query. It can find a single marked item or multiple number of items.Comment: 4 pages and 1 figur

Temporal Interferometry: A Mechanism for Controlling Qubit Transitions During Twisted Rapid Passage with Possible Application to Quantum Computing

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\phi (t)$ at the same time that it is inverted. For polynomial twist: $\phi (t) \sim Bt^{n}$. We show that for $n \geq 3$, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength $B$, which can be used to control the time-separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wavefunction. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum CNOT and NOT gates is discussed.Comment: 29 pages, 16 figures, submitted to Phys. Rev.

Approximate quantum counting on an NMR ensemble quantum computer

We demonstrate the implementation of a quantum algorithm for estimating the number of matching items in a search operation using a two qubit nuclear magnetic resonance (NMR) quantum computer.Comment: 4 pages LaTeX/RevTex including 4 figures (3 LaTeX, 1 PostScript). Submitted to Physical Review Letter

NMR Techniques for Quantum Control and Computation

Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to a new level, motivated by the interest in quantum information processing. NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. Here, we survey and summarize a broad variety of pulse control and tomographic techniques which have been developed for and used in NMR quantum computation. Many of these will be useful in other quantum systems now being considered for implementation of quantum information processing tasks.Comment: 33 pages, accepted for publication in Rev. Mod. Phys., added subsection on T_{1,\rho} (V.A.6) and on time-optimal pulse sequences (III.A.6), redid some figures, made many small changes, expanded reference