Magic State Distillation with Low Space Overhead and Optimal Asymptotic Input Count

We present an infinite family of protocols to distill magic states for $T$-gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the $T$-gate depth of the circuit scale linearly in the logarithm of the target error $\delta$ (up to $\log \log 1/\delta$). Unlike other distillation protocols, this protocol achieves this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. The protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance. The protocol relies on the construction of weakly self-dual CSS codes with many logical qubits and large distance, allowing us to implement control-SWAPs on multiple qubits. We call this code the "inner code". The control-SWAPs are then used to measure properties of the magic state and detect errors, using another code that we call the "outer code". Alternatively, we use weakly-self dual CSS codes which implement controlled Hadamards for the inner code, reducing circuit depth. We present several specific small examples of this protocol.Comment: 39 pages, (v2) renamed "odd" and "even" weakly self-dual CSS codes of (v1) to "normal" and "hyperbolic" codes, respectively. (v3) published in Quantu

Allee Effects May Slow the Spread of Parasites in a Coastal Marine Ecosystem

Allee effects are thought to mediate the dynamics of population colonization, particularly for invasive species. However, Allee effects acting on parasites have rarely been considered in the analogous process of infectious disease establishment and spread. We studied the colonization of uninfected wild juvenile Pacific salmon populations by ectoparasitic salmon lice (Lepeophtheirus salmonis) over a 4-year period. In a data set of 68,376 fish, we observed 85 occurrences of precopular pair formation among 1,259 preadult female and 613 adult male lice. The probability of pair formation was dependent on the local abundance of lice, but this mate limitation is likely offset somewhat by mate-searching dispersal of males among host fish. A mathematical model of macroparasite population dynamics that incorporates the empirical results suggests a high likelihood of a demographic Allee effect, which can cause the colonizing parasite populations to die out. These results may provide the first empirical evidence for Allee effects in a macroparasite. Furthermore, the data give a rare detailed view of Allee effects in colonization dynamics and suggest that Allee effects may dampen the spread of parasites in a coastal marine ecosystem

Alien Registration- Poulin, Marie B. (Waterville, Kennebec County)

https://digitalmaine.com/alien_docs/14771/thumbnail.jp

Alien Registration- Poulin, Marie B. (Waterville, Kennebec County)

https://digitalmaine.com/alien_docs/14771/thumbnail.jp

Studying Musical Savants: A Commentary on Grundy and Ockelford (2014)

On the basis of the ‘zygonic’ theory (Ockelford, 2006), Grundy and Ockelford (2014) investigate musical expectations evoked during the course of hearing a piece for the first time in a prodigious musical savant (Derek Paravicini). Overall, the results provided by Derek support the principles of the zygonic theory, especially that the higher the implication factor of a note, the more likely Derek would predict its occurrence. My commentary first raises the question of the use of such special individuals as musical savants to generalize findings to the general population, and second I will address the issue of the task and the stimuli used

Alien Registration- Poulin, Marie B. (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/29040/thumbnail.jp

The Caenorhabditis elegans CDT-2 ubiquitin ligase is required for attenuation of EGFR signalling in vulva precursor cells.

BACKGROUND: Attenuation of the EGFR (Epidermal Growth Factor Receptor) signalling cascade is crucial to control cell fate during development. A candidate-based RNAi approach in C. elegans identified CDT-2 as an attenuator of LET-23 (EGFR) signalling. Human CDT2 is a component of the conserved CDT2/CUL4/DDB1 ubiquitin ligase complex that plays a critical role in DNA replication and G2/M checkpoint. Within this complex, CDT2 is responsible for substrate recognition. This ubiquitin ligase complex has been shown in various organisms, including C. elegans, to target the replication-licensing factor CDT1, and the CDK inhibitor p21. However, no previous link to EGFR signalling has been identified. RESULTS: We have characterised CDT-2's role during vulva development and found that it is a novel attenuator of LET-23 signalling. CDT-2 acts redundantly with negative modulators of LET-23 signalling and CDT-2 or CUL-4 downregulation causes persistent expression of the egl-17::cfp transgene, a marker of LET-23 signalling during vulva development. In addition, we show that CDT-2 physically interacts with SEM-5 (GRB2), a known negative modulator of LET-23 signalling that directly binds LET-23, and provide genetic evidence consistent with CDT-2 functioning at or downstream of LET-23. Interestingly, both SEM-5 and CDT-2 were identified independently in a screen for genes involved in receptor-mediated endocytosis in oocytes, suggesting that attenuation of LET-23 by CDT-2 might be through regulation of endocytosis. CONCLUSIONS: In this study, we have shown that CDT-2 and CUL-4, members of the CUL-4/DDB-1/CDT-2 E3 ubiquitin ligase complex attenuate LET-23 signalling in vulval precursor cells. In future, it will be interesting to investigate the potential link to endocytosis and to determine whether other signalling pathways dependent on endocytosis, e.g. LIN-12 (Notch) could be regulated by this ubiquitin ligase complex. This work has uncovered a novel function for the CUL-4/DDB-1/CDT-2 E3 ligase that may be relevant for its mammalian oncogenic activity.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Nematic-Wetted Colloids in the Isotropic Phase: Pairwise Interaction, Biaxiality and Defects

We calculate the interaction between two spherical colloidal particles embedded in the isotropic phase of a nematogenic liquid. The surface of the particles induces wetting nematic coronas that mediate an elastic interaction. In the weak wetting regime, we obtain exact results for the interaction energy and the texture, showing that defects and biaxiality arise, although they are not topologically required. We evidence rich behaviors, including the possibility of reversible colloidal aggregation and dispersion. Complex anisotropic self-assembled phases might be formed in dense suspensions.Comment: 4 pages, 6 figure