Parallelism for Quantum Computation with Qudits

Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a protocol for implementing parallelized non-local two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates.Comment: 9 pages, 3 figure

Synthesis and Characterization of Mixed Methyl/Allyl Monolayers on Si(111)

The formation of mixed methyl/allyl monolayers has been accomplished through a two-step halogenation/alkylation reaction on Si(111) surfaces. The total coverage of alkylated Si, the surface recombination velocities, and the degree of surface oxidation as a function of time have been investigated using X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy, and microwave conductivity measurements. The total coverage of alkyl groups, the rate of oxidation, and the surface recombination velocities of Si(111) terminated by mixed monolayers were found to be close to those observed for CH_3−Si(111) surfaces. Hence, the mixed-monolayer surfaces retained the beneficial properties of CH_3−Si(111) surfaces while allowing for convenient secondary surface functionalization

In Situ Nanomechanical Measurements of Interfacial Strength in Membrane-Embedded Chemically Functionalized Si Microwires for Flexible Solar Cells

Arrays of vertically aligned Si microwires embedded in polydimethylsiloxane (PDMS) have emerged as a promising candidate for use in solar energy conversion devices. Such structures are lightweight and concurrently demonstrate competitive efficiency and mechanical flexibility. To ensure reliable functioning under bending and flexing, strong interfacial adhesion between the nanowire and the matrix is needed. In situ uniaxial tensile tests of individual, chemically functionalized, Si microwires embedded in a compliant PDMS matrix reveal that chemical functionality on Si microwire surfaces is directly correlated with interfacial adhesion strength. Chemical functionalization can therefore serve as an effective methodology for accessing a wide range of interfacial adhesion between the rigid constituents and the soft polymer matrix; the adhesion can be quantified by measuring the mechanical strength of such systems

Asymptotically Optimal Quantum Circuits for d-level Systems

As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum computation has stimulated much recent interest in algorithms factoring unitary evolutions of an n-qubit state space into component two-particle unitary evolutions. In the absence of symmetry, Shende, Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa (VMS) use the QR matrix factorization and Gray codes in an optimal order construction involving two-particle evolutions. In this work, we note that Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a generic (symmetry-less) n-qudit evolution. However, the VMS result applied to virtual-qubits only recovers optimal order in the case that d is a power of two. We further construct a QR decomposition for d-multi-level quantum logics, proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing the complexity question for all d-level systems (d finite.) Gray codes are not required, and the optimal Theta(d^{2n}) asymptotic also applies to gate libraries where two-qudit interactions are restricted by a choice of certain architectures.Comment: 18 pages, 5 figures (very detailed.) MatLab files for factoring qudit unitary into gates in MATLAB directory of source arxiv format. v2: minor change

Dynamical Interactions and the Black Hole Merger Rate of the Universe

Binary black holes can form efficiently in dense young stellar clusters, such as the progenitors of globular clusters, via a combination of gravitational segregation and cluster evaporation. We use simple analytic arguments supported by detailed N-body simulations to determine how frequently black holes born in a single stellar cluster should form binaries, be ejected from the cluster, and merge through the emission of gravitational radiation. We then convolve this ``transfer function'' relating cluster formation to black hole mergers with (i) the distribution of observed cluster masses and (ii) the star formation history of the universe, assuming that a significant fraction gcl of star formation occurs in clusters and that a significant fraction gcand of clusters undergo this segregation and evaporation process. We predict future ground--based gravitational wave (GW) detectors could observe ~500 (gcl/0.5) (gcand/0.1) double black hole mergers per year, and the presently operating LIGO interferometer would have a chance (50%) at detecting a merger during its first full year of science data. More realistically, advanced LIGO and similar next-generation gravitational wave observatories provide unique opportunities to constrain otherwise inaccessible properties of clusters formed in the early universe.Comment: 4 pages, 2 figures. To appear in PRD Rapid Communication

Time Reversal and n-qubit Canonical Decompositions

For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits. The generalization may also be studied using the CCD, leading again to maximal concurrence capacity for most unitaries. The key technique is to consider the spin-flip as a time reversal symmetry operator in Wigner's axiomatization; the original CCD derivation may be restated entirely in terms of this time reversal. En route, we observe a Kramers' nondegeneracy: the existence of a nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide examples of how to apply this work to study the kinematics and dynamics of entanglement in spin chain Hamiltonians.Comment: 20 pages, 3 figures; v2 (17pp.): major revision, new abstract, introduction, expanded bibliograph

Civic Engagement Assessment: Linking Activities to Attitudes

In the March-April 2005 issue of Assessment Update, Trudy Banta issued a call to readers to provide information on individual campuses’ efforts to assess civic engagement. This call has prompted us to share the multifaceted approach that Tuffs University has taken to describe and assess this area of student endeavor. Specifically, we will describe an in-depth study designed to investigate undergraduates’ participation in and attitudes toward civic engagement

Isobaric multiplet yrast energies and isospin non-conserving forces

The isovector and isotensor energy differences between yrast states of isobaric multiplets in the lower half of the $pf$ region are quantitatively reproduced in a shell model context. The isospin non-conserving nuclear interactions are found to be at least as important as the Coulomb potential. Their isovector and isotensor channels are dominated by J=2 and J=0 pairing terms, respectively. The results are sensitive to the radii of the states, whose evolution along the yrast band can be accurately followed.Comment: 4 pages, 4 figures. Superseeds second part of nucl-th/010404