Quantum walks on Cayley graphs

We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert space and consider various classes of graphs on which the structure of quantum walks may differ. We completely characterise quantum walks on free groups and present partial results on more general cases. Some examples are given, including a family of quantum walks on the hypercube involving a Clifford Algebra.Comment: J. Phys. A (accepted for publication

Hardness of approximation for quantum problems

The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the second level of this quantum hierarchy, but that these problems are in fact hard to approximate. Using these techniques, we also obtain hardness of approximation for the class QCMA. Our approach is based on the use of dispersers, and is inspired by the classical results of Umans regarding hardness of approximation for the second level of the classical polynomial hierarchy [Umans, FOCS 1999]. The problems for which we prove hardness of approximation for include, among others, a quantum version of the Succinct Set Cover problem, and a variant of the local Hamiltonian problem with hybrid classical-quantum ground states.Comment: 21 pages, 1 figure, extended abstract appeared in Proceedings of the 39th International Colloquium on Automata, Languages and Programming (ICALP), pages 387-398, Springer, 201

No evidence for reduced Simon cost in elderly bilinguals and bidialectals

We explored whether a bilingual advantage in executive control is associated with differences in cultural and ethnic background associated with the bilinguals’ immigrant status, and whether dialect use in monolinguals can also incur such an advantage. Performance on the Simon task in older non-immigrant (Gaelic-English) and immigrant (Bengali, Gujarati, Hindi, Malay, Punjabi, Urdu-English) bilinguals was compared with three groups of older monolingual English speakers, who were either monodialectal users of the same English variety as the bilinguals or were bidialectal users of a local variety of Scots. Results showed no group differences in overall reaction times as well as in the Simon effect thus providing no evidence that an executive control advantage is related to differences in cultural and ethnic background as was found for immigrant compared to non-immigrant bilinguals, nor that executive control may be improved by use of dialect. We suggest the role of interactional contexts and bilingual literacy as potential explanations for inconsistent findings of a bilingual advantage in executive control

Cognitive cost of switching between standard and dialect varieties

Switching between languages in picture naming incurs a cost associated with inhibition of the non-target language (Meuter & Allport, 1999).This cost is symmetrical in balanced bilinguals and asymmetrical in unbalanced bilinguals with higher cost associated with switching back into L1 (Costa & Santesteban,2004).We investigated whether cost is incurred in similar ways by bidialectals switching between two dialects.To increase generalisablity, we conducted this experiment in 2 locations: in Scotland using Standard Scottish English and Dundonian-Scots bidialectals) and in Germany using German and Öcher bidialectals).We also investigated differences between active vs. passive, and older vs. younger bidialectals

Individual differences in the discrimination of novel speech sounds: effects of sex, temporal processing, musical and cognitive abilities

This study examined whether rapid temporal auditory processing, verbal working memory capacity, non-verbal intelligence, executive functioning, musical ability and prior foreign language experience predicted how well native English speakers (N = 120) discriminated Norwegian tonal and vowel contrasts as well as a non-speech analogue of the tonal contrast and a native vowel contrast presented over noise. Results confirmed a male advantage for temporal and tonal processing, and also revealed that temporal processing was associated with both non-verbal intelligence and speech processing. In contrast, effects of musical ability on non-native speech-sound processing and of inhibitory control on vowel discrimination were not mediated by temporal processing. These results suggest that individual differences in non-native speech-sound processing are to some extent determined by temporal auditory processing ability, in which males perform better, but are also determined by a host of other abilities that are deployed flexibly depending on the characteristics of the target sounds

Can monolinguals be like bilinguals? Evidence from dialect switching

Bilinguals rely on cognitive control mechanisms like selective activation and inhibition of lexical entries to prevent intrusions from the non-target language. We present cross-linguistic evidence that these mechanisms also operate in bidialectals. Thirty-two native German speakers who sometimes use the Öcher Platt dialect, and thirty-two native English speakers who sometimes use the Dundonian Scots dialect completed a dialect-switching task. Naming latencies were higher for switch than for non-switch trials, and lower for cognate compared to non-cognate nouns. Switch costs were symmetrical, regardless of whether participants actively used the dialect or not. In contrast, sixteen monodialectal English speakers, who performed the dialectswitching task after being trained on the Dundonian words, showed asymmetrical switch costs with longer latencies when switching back into Standard English. These results are reminiscent of findings for balanced vs. unbalanced bilinguals, and suggest that monolingual dialect speakers can recruit control mechanisms in similar ways as bilinguals

Decoherence and Quantum Walks: anomalous diffusion and ballistic tails

The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a particle makes quantum transitions between the sites of a d-dimensional hypercubic lattice whilst strongly coupled to a bath of two-level systems which 'record' the transitions. The long-time evolution of an initial wave packet is found to be most unusual: the mean square displacement of the particle density matrix shows long-range ballitic behaviour, but simultaneously a kind of weakly-localised behaviour near the origin. This result may have important implications for the design of quantum computing algorithms, since it describes a class of quantum walks.Comment: 4 pages, 1 figur