Period Finding with Adiabatic Quantum Computation

We outline an efficient quantum-adiabatic algorithm that solves Simon's problem, in which one has to determine the `period', or xor-mask, of a given black-box function. We show that the proposed algorithm is exponentially faster than its classical counterpart and has the same complexity as the corresponding circuit-based algorithm. Together with other related studies, this result supports a conjecture that the complexity of adiabatic quantum computation is equivalent to the circuit-based computational model in a stronger sense than the well-known, proven polynomial equivalence between the two paradigms. We also discuss the importance of the algorithm and its theoretical and experimental implications for the existence of an adiabatic version of Shor's integer factorization algorithm that would have the same complexity as the original algorithm.Comment: 6 page

Realizable Quantum Adiabatic Search

Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a mechanism to carry out a quantum adiabatic variant of Grover's search algorithm using a single bosonic particle placed in an optical lattice. By studying the scaling of the gap and relevant matrix element in various spatial dimensions, we show that a quantum speedup can already be gained in three dimensions. We argue that the suggested scheme is realizable with present-day experimental capabilities.Comment: 6 pages, 4 figure

Continuous-Time Quantum Algorithms for Unstructured Problems

We consider a family of unstructured problems, for which we propose a method for constructing analog, continuous-time quantum algorithms that are more efficient than their classical counterparts. In this family of problems, which we refer to as `scrambled output' problems, one has to find a minimum-cost configuration of a given integer-valued n-bit function whose output values have been scrambled in some arbitrary way. Special cases within this set of problems are Grover's search problem of finding a marked item in an unstructured database, certain random energy models, and the functions of the Deutsch-Josza problem. We consider a couple of examples in detail. In the first, we provide a deterministic analog quantum algorithm to solve the seminal problem of Deutsch and Josza, in which one has to determine whether an n-bit boolean function is constant (gives 0 on all inputs or 1 on all inputs) or balanced (returns 0 on half the input states and 1 on the other half). We also study one variant of the random energy model, and show that, as one might expect, its minimum energy configuration can be found quadratically faster with a quantum adiabatic algorithm than with classical algorithms.Comment: 8 pages, 4 figure

Studies of bacteriophages induced from Streptococcus cremoris strain R1 : is R1 a double Lysogen? : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Genetics at Massey University, New Zealand

Early studies on Streptococcus cremoris strain R₁ suggested that it was polylysogenic. Later, it was reported that its induced lysates contained bacteriophages (phages) of two types which were believed to differ in their morphology, buoyant densities, immune specificities and in their responses to heterologous antiphage sera. Further work on the strain did not reproduce the above observations, but did often give results which were consistent with it being a double lysogen. This project was an in-depth investigation of phages induced from R₁, in an attempt to establish the single or double lysogenic nature of the strain. Mid-log phase R₁ cells were harvested, washed with homologous antiphage serum and induced to lyse with ultraviolet light (UVL). The resulting phage lysates were analysed on caesium chloride (CsCl) density gradients. Though the OD₂₅₄ (optical density at 254 nm) scans of the gradients detected the presence of only one phage band, p.f.u. (plaque forming unit) profiles of the gradient fractions on indicator strains R₁C and 368 revealed, in addition to the main phage peak, several minor p.f.u. peaks (termed satellite and shoulder peaks) as possible manifestations of different phage types in the R₁ lysates. Further CsCl density gradient analyses of phage stocks and pooled phage fractions of these minor p.f.u. peaks showed that the latter phages were identical with those of the main phage peaks of mean buoyant density of 1.485 g/ml. Further characterization of the phages recovered from the CsCl gradients by neutralization tests with homologous antiphage serum confirmed the existence of only one serological phage type in the R₁ lysates. Final verification of the unity in phage type in R₁ lysates came from SDS-gel electrophoreses of the phages recovered from the different p.f.u. peaks and from lysates, which showed the largely identical gel patterns of their protein components. Host-specificity tests of the phages provided the last piece of evidence for the conclusion that R₁ is a single lysogen, harbouring only one prophage in its genome. Review of past electron-microscopic studies of R₁ lysates substantially support this conclusion. In fact, reconstruction of R₁ by lysogenization of a cured strain (R₁C) yielded a strain (R₁r) which closely resembled the original in lysogenic properties. From the data collected in the course of this work, it was inferred that 368 lysates possibly contained defective phages. An attempt was made to cure 368 of its supposedly defective prophage in the hope of providing a 'cleaner' strain for studying the host-induced variation observed in the R₁C-368 system. Though possible cured derivatives were obtained, they did not prove to be an improvement over the parental strain 368 with respect to their efficiency of plating for R₁ phages. Finally, phage mutant isolation and recombination experiments were attempted in the hope of gaining an insight into the lysogenic system operating in the R₁ cells. Using UVL and nitrous acid (HNO₂) mutagenesis on the temperate ϕr₁/R₁C induced from R₁, about 75 independently arising clear plaque-forming mutants were isolated for mapping experiments. Pairwise crosses between the UVL and HNO₂- induced mutants were performed by coinfecting R₁C cells. Though far from conclusive, the preliminary results obtained indicated a general low occurrence of turbid-plaqued (wild type) phage recombinants, and hence a low frequency of recombination

Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices

We study the ground-state properties of trapped inhomogeneous systems of hardcore bosons in two- and three-dimensional lattices. We obtain our results both numerically, using quantum Monte Carlo techniques, and via several analytical approximation schemes, such as the Gutzwiller-mean-field approach, a cluster-mean-field method and a spin-wave analysis which takes quantum fluctuations into account. We first study the homogeneous case, for which simple analytical expressions are obtained for all observables of interest, and compare the results with the numerical ones. We obtain the equation of state of the system along with other thermodynamic properties such as the free energy, kinetic energy, superfluid density, condensate fraction and compressibility. In the presence of a trap, superfluid and insulating domains coexist in the system. We show that the spin-wave-based method reproduces the quantum Monte-Carlo results for global as well as for local quantities with a high degree of accuracy. We also discuss the validity of the local density approximation in those systems. Our analysis can be used to describe bosons in optical lattices where the onsite interaction U is much larger than the hopping amplitude t.Comment: 14 pages, 14 figure