Frequency and temporal effects in linear optical quantum computing

Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be nonidealities associated with the photons and the experimental setup which will introduce a degree of distinguishability between photons. We consider a nondeterministic optical controlled-NOT gate, a fundamental LOQC gate, and examine the effect of temporal and spectral distinguishability on its operation. We also consider the effect of utilizing nonideal photon counters, which have finite bandwidth and time response.

Adaptive phase measurements in linear optical quantum computation

Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.

Optimal unravellings for feedback control in linear quantum systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case: Given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state- based) control problems ( the stationary linear-quadratic-Gaussian class), this question is a semidefinite program. Moreover, the answer also applies to Markovian (current-based) feedback.

Effects of rock properties on specific cutting energy in linear cutting of sandstones by picks

Specific cutting energy (SE) has been widely used to assess the rock cuttability for mechanical excavation purposes. Some prediction models were developed for SE through correlating rock properties with SE values. However, some of the textural and compositional rock parameters i.e. texture coefficient and feldspar, mafic, and felsic mineral contents were not considered. The present study is to investigate the effects of previously ignored rock parameters along with engineering rock properties on SE. Mineralogical and petrographic analyses, rock mechanics, and linear rock cutting tests were performed on sandstone samples taken from sites around Ankara, Turkey. Relationships between SE and rock properties were evaluated using bivariate correlation and linear regression analyses. The tests and subsequent analyses revealed that the texture coefficient and feldspar content of sandstones affected rock cuttability, evidenced by significant correlations between these parameters and SE at a 90% confidence level. Felsic and mafic mineral contents of sandstones did not exhibit any statistically significant correlation against SE. Cementation coefficient, effective porosity, and pore volume had good correlations against SE. Poisson's ratio, Brazilian tensile strength, Shore scleroscope hardness, Schmidt hammer hardness, dry density, and point load strength index showed very strong linear correlations against SE at confidence levels of 95% and above, all of which were also found suitable to be used in predicting SE individually, depending on the results of regression analysis, ANOVA, Student's t-tests, and R2 values. Poisson's ratio exhibited the highest correlation with SE and seemed to be the most reliable SE prediction tool in sandstones.

Effects of rock properties on specific cutting energy in linear cutting of sandstones by picks

Specific cutting energy (SE) has been widely used to assess the rock cuttability for mechanical excavation purposes. Some prediction models were developed for SE through correlating rock properties with SE values. However, some of the textural and compositional rock parameters i.e. texture coefficient and feldspar, mafic, and felsic mineral contents were not considered. The present study is to investigate the effects of previously ignored rock parameters along with engineering rock properties on SE. Mineralogical and petrographic analyses, rock mechanics, and linear rock cutting tests were performed on sandstone samples taken from sites around Ankara, Turkey. Relationships between SE and rock properties were evaluated using bivariate correlation and linear regression analyses. The tests and subsequent analyses revealed that the texture coefficient and feldspar content of sandstones affected rock cuttability, evidenced by significant correlations between these parameters and SE at a 90% confidence level. Felsic and mafic mineral contents of sandstones did not exhibit any statistically significant correlation against SE. Cementation coefficient, effective porosity, and pore volume had good correlations against SE. Poisson's ratio, Brazilian tensile strength, Shore scleroscope hardness, Schmidt hammer hardness, dry density, and point load strength index showed very strong linear correlations against SE at confidence levels of 95% and above, all of which were also found suitable to be used in predicting SE individually, depending on the results of regression analysis, ANOVA, Student's t-tests, and R-2 values. Poisson's ratio exhibited the highest correlation with SE and seemed to be the most reliable SE prediction tool in sandstones.

Error models for mode mismatch in linear optics quantum computing

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode mismatch on its operation, and relate these error models to current fault-tolerant-threshold estimates.

Why people underestimate y when extrapolating in linear functions

E. L. DeLosh, J. R. Busemeyer, and M. A. McDaniel (1997) found that when learning a positive, linear relationship between a continuous predictor (x) and a continuous criterion (y), trainees tend to underestimate y on items that ask the trainee to extrapolate. In 3 experiments, the authors examined the phenomenon and found that the tendency to underestimate y is reliable only in the so-called lower extrapolation region-that is, new values of x that lie between zero and the edge of the training region. Existing models of function learning, such as the extrapolation-association model (DeLosh et al., 1997) and the population of linear experts model (M. L. Kalish, S. Lewandowsky, & J. Kruschke, 2004), cannot account for these results. The authors show that with minor changes, both models can predict the correct pattern of results.

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

A simple proof of the strong subadditivity inequality

Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57-65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

Incorporating level set methods in Geographical Information Systems (GIS) for land-surface process modelling

Land-surface processes include a broad class of models that operate at a landscape scale. Current modelling approaches tend to be specialised towards one type of process, yet it is the interaction of processes that is increasing seen as important to obtain a more integrated approach to land management. This paper presents a technique and a tool that may be applied generically to landscape processes. The technique tracks moving interfaces across landscapes for processes such as water flow, biochemical diffusion, and plant dispersal. Its theoretical development applies a Lagrangian approach to motion over a Eulerian grid space by tracking quantities across a landscape as an evolving front. An algorithm for this technique, called level set method, is implemented in a geographical information system (GIS). It fits with a field data model in GIS and is implemented as operators in map algebra. The paper describes an implementation of the level set methods in a map algebra programming language, called MapScript, and gives example program scripts for applications in ecology and hydrology.

Proteomic analysis of k-casein micro-heterogeneity

The proteome of bovine milk is dominated by just six gene products that constitute approximately 95% of milk protein. Nonetheless, over 150 protein spots can be readily detected following two-dimensional electrophoresis of whole milk. Many of these represent isoforms of the major gene products produced through extensive posttranslational modification. Peptide mass fingerprinting of in-gel tryptic digests (using matrix-assisted laser desorption/ionization-time of flight mass spectrometry (MALDI-TOF MS) in reflectron mode with alpha-cyano-4-hydroxycinnamic acid as the matrix) identified 10 forms of K-casein with isoelectric point (pl) values from 4.47 to 5.81, but could not distinguish between them. MALDI-TOF MS in linear mode, using sinapinic acid as the matrix, revealed a large tryptic peptide (mass > 5990 Da) derived from the C-terminus that contained all the known sites of genetic variance, phosphorylation and glycosylation. Two genetic variants present as singly or doubly phosphorylated forms could be distinguished using mass data alone. Glycoforms containing a single acidic tetrasaccharide were also identified. The differences in electrophoretic mobility of these isoforms were consistent with the addition of the acidic groups. While more extensively glycosylated forms were also observed, substantial loss of N-acetylneuraminic acid from the glycosyl group was evident in the MALDI spectra such that ions corresponding to the intact glycopeptide were not observed and assignment of the glycoforms was not possible. However, by analysing the pl shifts observed on the two-dimensional gels in conjunction with the MS data, the number of N-acetylneuraminic acid residues, and hence the glycoforms present, could be determined.

Optimal photons for quantum-information processing

Photonic quantum-information processing schemes, such as linear optics quantum computing, and other experiments relying on single-photon interference, inherently require complete photon indistinguishability to enable the desired photonic interactions to take place. Mode-mismatch is the dominant cause of photon distinguishability in optical circuits. Here we study the effects of photon wave-packet shape on tolerance against the effects of mode mismatch in linear optical circuits, and show that Gaussian distributed photons with large bandwidth are optimal. The result is general and holds for arbitrary linear optical circuits, including ones which allow for postselection and classical feed forward. Our findings indicate that some single photon sources, frequently cited for their potential application to quantum-information processing, may in fact be suboptimal for such applications.

Divergent selection and the evolution of signal traits and mating preferences

Mating preferences are common in natural populations, and their divergence among populations is considered an important source of reproductive isolation during speciation. Although mechanisms for the divergence of mating preferences have received substantial theoretical treatment, complementary experimental tests are lacking. We conducted a laboratory evolution experiment, using the fruit fly Drosophila serrata, to explore the role of divergent selection between environments in the evolution of female mating preferences. Replicate populations of D. serrata were derived from a common ancestor and propagated in one of three resource environments: two novel environments and the ancestral laboratory environment. Adaptation to both novel environments involved changes in cuticular hydrocarbons, traits that predict mating success in these populations. Furthermore, female mating preferences for these cuticular hydrocarbons also diverged among populations. A component of this divergence occurred among treatment environments, accounting for at least 17.4% of the among- population divergence in linear mating preferences and 17.2% of the among-population divergence in nonlinear mating preferences. The divergence of mating preferences in correlation with environment is consistent with the classic by- product model of speciation in which premating isolation evolves as a side effect of divergent selection adapting populations to their different environments.

Geodesics without differential equations: general relativistic calculations for introductory modern physics classes

Introductory courses covering modem physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.