Critically damped quantum search

Although measurement and unitary processes can accomplish any quantum evolution in principle, thinking in terms of dissipation and damping can be powerful. We propose a modification of Grover's algorithm in which the idea of damping plays a natural role. Remarkably, we have found that there is a critical damping value that divides between the quantum $O(\sqrt{N})$ and classical O(N) search regimes. In addition, by allowing the damping to vary in a fashion we describe, one obtains a fixed-point quantum search algorithm in which ignorance of the number of targets increases the number of oracle queries only by a factor of 1.5

Vibronic coupling in the superoxide anion: The vibrational dependence of the photoelectron angular distribution

We present a comprehensive photoelectron imaging study of the O₂(X³Σg⁻,v′=0–6)←O₂⁻(X²Πg,v′′=0) and O₂(a¹Δg,v′=0–4)←O₂⁻(X²Πg,v′′=0)photodetachment bands at wavelengths between 900 and 455 nm, examining the effect of vibronic coupling on the photoelectron angular distribution (PAD). This work extends the v′=1–4 data for detachment into the ground electronic state, presented in a recent communication [R. Mabbs, F. Mbaiwa, J. Wei, M. Van Duzor, S. T. Gibson, S. J. Cavanagh, and B. R. Lewis, Phys. Rev. A82, 011401–R (2010)]. Measured vibronic intensities are compared to Franck–Condon predictions and used as supporting evidence of vibronic coupling. The results are analyzed within the context of the one-electron, zero core contribution (ZCC) model [R. M. Stehman and S. B. Woo, Phys. Rev. A23, 2866 (1981)]. For both bands, the photoelectron anisotropy parameter variation with electron kinetic energy,β(E), displays the characteristics of photodetachment from a d-like orbital, consistent with the π∗g 2p highest occupied molecular orbital of O₂⁻. However, differences exist between the β(E) trends for detachment into different vibrational levels of the X³Σg⁻ and a ¹Δg electronic states of O₂. The ZCC model invokes vibrational channel specific “detachment orbitals” and attributes this behavior to coupling of the electronic and nuclear motion in the parent anion. The spatial extent of the model detachment orbital is dependent on the final state of O₂: the higher the neutral vibrational excitation, the larger the electron binding energy. Although vibronic coupling is ignored in most theoretical treatments of PADs in the direct photodetachment of molecular anions, the present findings clearly show that it can be important. These results represent a benchmark data set for a relatively simple system, upon which to base rigorous tests of more sophisticated models.The authors gratefully acknowledge support by the National Science Foundation Grant No. CHE-0748738 and ANU ARC Discovery Projects under Grant Nos. DP0666267 and DP0880850

A quantum genetic algorithm with quantum crossover and mutation operations

In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm which has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.Comment: 21 pages, 1 table, v2: typos corrected, minor modifications in sections 3.5 and 4, v3: minor revision, title changed (original title: Semiclassical genetic algorithm with quantum crossover and mutation operations), v4: minor revision, v5: minor grammatical corrections, to appear in QI

Scale invariance of entanglement dynamics in Grover's quantum search algorithm

We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present. Remarkably, the dynamics of any type of entanglement as well as of genuine multipartite entanglement is independent of the number n of qubits for large n, thus exhibiting a scale invariance property. We compare this result with the entanglement dynamics induced by a fixed-point quantum search algorithm. We also investigate criteria for efficient simulatability in the context of Grover's algorithm.Comment: 5 pages, 4 figures, significantly improved versio

Vibronic coupling in the superoxide anion: the vibrational dependence of the photoelectron angular distribution

We present a comprehensive photoelectron imaging study of the O2(X 3Σg−,v′ = 0–6)←O2−(X 2Πg,v″ = 0) and O2(a 1Δg,v′ = 0–4)←O2−(X 2Πg,v″ = 0) photodetachment bands at wavelengths between 900 and 455 nm, examining the effect of vibronic coupling on the photoelectron angular distribution (PAD). This work extends the v′ = 1–4 data for detachment into the ground electronic state, presented in a recent communication. Measured vibronic intensities are compared to Franck–Condon predictions and used as supporting evidence of vibronic coupling. The results are analyzed within the context of the one-electron, zero core contribution (ZCC) model. For both bands, the photoelectron anisotropy parameter variation with electron kinetic energy, β(E), displays the characteristics of photodetachment from a d-like orbital, consistent with the πg∗ 2p highest occupied molecular orbital of O2−. However, differences exist between the β(E) trends for detachment into different vibrational levels of the X 3Σg− and a 1Δg electronic states of O2. The ZCC model invokes vibrational channel specific “detachment orbitals” and attributes this behavior to coupling of the electronic and nuclear motion in the parent anion. The spatial extent of the model detachment orbital is dependent on the final state of O2: the higher the neutral vibrational excitation, the larger the electron binding energy. Although vibronic coupling is ignored in most theoretical treatments of PADs in the direct photodetachment of molecular anions, the present findings clearly show that it can be important. These results represent a benchmark data set for a relatively simple system, upon which to base rigorous tests of more sophisticated models

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Saltatory remodeling of Hox chromatin in response to rostrocaudal patterning signals

Hox genes controlling motor neuron subtype identity are expressed in rostrocaudal patterns that are spatially and temporally collinear with their chromosomal organization. Here we demonstrate that Hox chromatin is subdivided into discrete domains that are controlled by rostrocaudal patterning signals that trigger rapid, domain-wide clearance of repressive histone H3 Lys27 trimethylation (H3K27me3) polycomb modifications. Treatment of differentiating mouse neural progenitors with retinoic acid leads to activation and binding of retinoic acid receptors (RARs) to the Hox1–Hox5 chromatin domains, which is followed by a rapid domain-wide removal of H3K27me3 and acquisition of cervical spinal identity. Wnt and fibroblast growth factor (FGF) signals induce expression of the Cdx2 transcription factor that binds and clears H3K27me3 from the Hox1–Hox9 chromatin domains, leading to specification of brachial or thoracic spinal identity. We propose that rapid clearance of repressive modifications in response to transient patterning signals encodes global rostrocaudal neural identity and that maintenance of these chromatin domains ensures the transmission of positional identity to postmitotic motor neurons later in development.Leona M. and Harry B. Helmsley Charitable TrustNational Institutes of Health (U.S.) (Grant P01 NS055923)Smith Family Foundatio

Observations of extensive gene expression differences in the cerebellum and potential relevance to Alzheimer's disease

Objectives: In order to determine how gene expression is altered in disease it is of fundamental importance that the global distribution of gene expression levels across the disease-free brain are understood and how differences between tissue types might inform tissue choice for investigation of altered expression in disease state. The aim of this pilot project was to use RNA-sequencing to investigate gene expression differences between five general areas of post-mortem human brain (frontal, temporal, occipital, parietal and cerebellum), and in particular changes in gene expression in the cerebellum compared to cortex regions for genes relevant to Alzheimer’s disease, as the cerebellum is largely preserved from disease pathology and could be an area of interest for neuroprotective pathways. Results: General gene expression profiles were found to be similar between cortical regions of the brain, however the cerebellum presented a distinct expression profile. Focused exploration of gene expression for genes associated with Alzheimer’s disease suggest that those involved in the immunity pathway show little expression in the brain. Furthermore some Alzheimer’s disease associated genes display significantly different expression in the cerebellum compared with other brain regions, which might indicate potential neuroprotective measures