Kleshchev's decomposition numbers and branching coefficients in the Fock space

10.1090/S0002-9947-07-04202-XTransactions of the American Mathematical Society36031179-119

High Dynamic Range RF Front End with Noise Cancellation and Linearization for WiMAX Receivers

This research deals with verification of the high dynamic range for a heterodyne radio frequency (RF) front end. A 2.6 GHz RF front end is designed and implemented in a hybrid microwave integrated circuit (HMIC) for worldwide interoperability for microwave access (WiMAX) receivers. The heterodyne RF front end consists of a low-noise amplifier (LNA) with noise cancellation, an RF bandpass filter (BPF), a downconverter with linearization, and an intermediate frequency (IF) BPF. A noise canceling technique used in the low-noise amplifier eliminates a thermal noise and then reduces the noise figure (NF) of the RF front end by 0.9 dB. Use of a downconverter with diode linearizer also compensates for gain compression, which increases the input-referred third-order intercept point (IIP3) of the RF front end by 4.3 dB. The proposed method substantially increases the spurious-free dynamic range (DRf) of the RF front end by 3.5 dB

Property testing of unitary operators

In this paper, we systematically study property testing of unitary operators. We first introduce a distance measure that reflects the average difference between unitary operators. Then we show that, with respect to this distance measure, the orthogonal group, quantum juntas (i.e. unitary operators that only nontrivially act on a few qubits of the system) and Clifford group can be all efficiently tested. In fact, their testing algorithms have query complexities independent of the system's size and have only one-sided error. Then we give an algorithm that tests any finite subset of the unitary group, and demonstrate an application of this algorithm to the permutation group. This algorithm also has one-sided error and polynomial query complexity, but it is unknown whether it can be efficiently implemented in general

Parallelotope tilings and q-decomposition numbers

We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of Uq(slₑ). These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the Ext¹ -quivers of v-Schur algebras at complex e-th roots of unity generated by simple modules corresponding to these canonical basis vectors are given by the 1-skeletons of the polytopal complexes

A v-analogue of Peel's theorem

We compute the v-decomposition numbers dλμ(v) for λ being a hook partition, and μ e-regular

Implementation of a three-quantum-bit search algorithm

We report the experimental implementation of Grover's quantum search algorithm on a quantum computer with three quantum bits. The computer consists of molecules of $^{13}$C-labeled CHFBr$_2$, in which the three weakly coupled spin-1/2 nuclei behave as the bits and are initialized, manipulated, and read out using magnetic resonance techniques. This quantum computation is made possible by the introduction of two techniques which significantly reduce the complexity of the experiment and by the surprising degree of cancellation of systematic errors which have previously limited the total possible number of quantum gates.Comment: Published in Applied Physics Letters, vol. 76, no. 5, 31 January 2000, p.646-648, after minor revisions. (revtex, mypsfig2.sty, 3 figures

Prescription for experimental determination of the dynamics of a quantum black box

We give an explicit prescription for experimentally determining the evolution operators which completely describe the dynamics of a quantum mechanical black box -- an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible, and illustrate the general theory by considering specifically one and two quantum bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication, and computation systems.Comment: 6 pages, Revtex. Submitted to J. Mod. Op

Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems

We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random finite-connectivity spin glass system at certain critical value of the constraint density. At the transition point, exponentially many configuration communities emerge from the ground-state configuration space, making the entropy density s(q) of configuration-pairs a non-concave function of configuration-pair overlap q. Each configuration community is a collection of relatively similar configurations and it forms a stable thermodynamic phase in the presence of a suitable external field. We calculate s(q) by the replica-symmetric and the first-step replica-symmetry-broken cavity methods, and show by simulations that the configuration space heterogeneity leads to dynamical heterogeneity of particle diffusion processes because of the entropic trapping effect of configuration communities. This work clarifies the fine structure of the ground-state configuration space of random spin glass models, it also sheds light on the glassy behavior of hard-sphere colloidal systems at relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic