100,721 research outputs found
When-and how- can a cellular automaton be rewritten as a lattice gas?
No full textAbstractBoth cellular automata (CA) and lattice-gas automata (LG) provide finite algorithmic presentations for certain classes of infinite dynamical systems studied by symbolic dynamics; it is customary to use the terms ‘cellular automaton’ and ‘lattice gas’ for a dynamic system itself as well as for its presentation. The two kinds of presentation share many traits but also display profound differences on issues ranging from decidability to modeling convenience and physical implementability.Following a conjecture by Toffoli and Margolus, it had been proved by Kari that any invertible CA, at least up to two dimensions, can be rewritten as an isomorphic LG. But until now it was not known whether this is possible in general for noninvertible CA—which comprise “almost all” CA and represent the bulk of examples in theory and applications. Even circumstantial evidence–whether in favor or against–was lacking.Here, for noninvertible CA, (a) we prove that an LG presentation is out of the question for the vanishingly small class of surjective ones. We then turn our attention to all the rest–noninvertible and nonsurjective–which comprise all the typical ones, including Conway’s ‘Game of Life’. For these (b) we prove by explicit construction that all the one-dimensional ones are representable as LG, and (c) we present and motivate the conjecture that this result extends to any number of dimensions.The tradeoff between dissipation rate and structural complexity implied by the above results have compelling implications for the thermodynamics of computation at a microscopic scale
Codes and Protocols for Distilling , controlled-, and Toffoli Gates
No full textWe present several different codes and protocols to distill , controlled-, and Toffoli (or ) gates. One construction is based on codes that generalize the triorthogonal codes, allowing any of these gates to be induced at the logical level by transversal . We present a randomized construction of generalized triorthogonal codes obtaining an asymptotic distillation efficiency . We also present a Reed-Muller based construction of these codes which obtains a worse but performs well at small sizes. Additionally, we present protocols based on checking the stabilizers of magic states at the logical level by transversal gates applied to codes; these protocols generalize the protocols of
. Several examples, including a Reed-Muller code for -to-Toffoli distillation, punctured Reed-Muller codes for -gate distillation, and some of the check based protocols, require a lower ratio of input gates to output gates than other known protocols at the given order of error correction for the given code size. In particular, we find a T-gate to Toffoli gate code with distance as well as triorthogonal codes with parameters with very low prefactors in front of the leading order error terms in those codes
How to turn a second-order cellular automaton into a lattice gas: a new inversion scheme
No full text"Theoretical Aspects of Cellular Automata
Combined effect of point defects and layer number on the adsorption of benzene and toluene on graphene
No full textUnderstanding the adsorption properties of organic molecules on graphene-based substrates is important for such applications as air and water filters. Pristine graphene is often the model substrate used in the theoretical investigations of this problem. While useful, pristine single-layer graphene is however an idealized model. In this work, we assess the effect of the presence of point defects (single vacancy, divacancy, and the Stone-Wales defect) in single-layer and bilayer graphene on the energetics of adsorption of benzene and toluene. Our calculations benchmark three different dispersion-corrected DFT schemes, namely PBE-D2, vdW-DF1, and vdW-DF2-C09. Whereas the presence of the single vacancy and the double vacancy does not appear to alter the adsorption energies of the aromatic molecules by an appreciable amount, the Stone-Wales defect and the addition of a second graphene layer stabilizes their interaction with the substrate by several tens of meV
A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond
No full textInternational audienceWe consider a ZX-calculus augmented with triangle nodes which is well-suited to reason on the so-called Toffoli-Hadamard fragment of quantum mechanics. We precisely show the form of the matrices it represents, and we provide an axiomatisation which makes the language complete for the Toffoli-Hadamard quantum mechanics. We extend the language with arbitrary angles and show that any true equation involving linear diagrams which constant angles are multiple of π are derivable. We show that a single axiom is then necessary and sufficient to make the language equivalent to the ZX-calculus which is known to be complete for Clifford+T quantum mechanics. As a by-product, it leads to a new and simple complete axiomatisation for Clifford+T quantum mechanics
Quantum Fourier Addition, Simplified to Toffoli Addition
No full textQuantum addition circuits are considered being of two types: 1)
Toffolli-adder circuits which use only classical reversible gates (CNOT and
Toffoli), and 2) QFT-adder circuits based on the quantum Fourier
transformation. We present the first systematic translation of the QFT-addition
circuit into a Toffoli-based adder. This result shows that QFT-addition has
fundamentally the same fault-tolerance cost (e.g. T-count) as the most
cost-efficient Toffoli-adder: instead of using approximate decompositions of
the gates from the QFT circuit, it is more efficient to merge gates. In order
to achieve this, we formulated novel circuit identities for multi-controlled
gates and apply the identities algorithmically. The employed techniques can be
used to automate quantum circuit optimisation heuristics.Comment: accepted in PR
Efficient Toffoli gates using qudits
No full textThe simplest decomposition of a Toffoli gate acting on 3 qubits requires five 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to 6. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just 3 if one of the three quantum systems has a third state that is accessible during the computation-i.e., is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (e.g., atoms, photonic polarization plus spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success
Fredkin and Toffoli quantum gates: fuzzy representations and comparison
No full textIn the framework of quantum computation with mixed states, fuzzy representations based on continuous t-norms for Toffoli and Fredkin quantum gates are introduced. A comparison between both gates is also studied
Fredkin and Toffoli Quantum Gates: Fuzzy Representations and Comparison
No full textIn the framework of quantum computation with mixed states, fuzzy representations based on continuous t-norms for Toffoli and Fredkin quantum gates are introduced. A comparison between both gates is also studied
Osteoprotegerin: a pancreatic islets dysfunction and vascular injury modulator
No full textBackground. Osteoprotegerin (OPG) is a soluble glycoprotein of the tumor necrosis factor (TNF) receptor superfamily, which was initially identified as a key regulator in bone turnover. It acts as a decoy receptor for the receptor activator of nuclear factor kB ligand (RANKL) and for the TNF-related apoptosis-inducing ligand (TRAIL), counterbalancing their biological effects. OPG is produced by a wide range of tissues, including the cardiovascular system, and its levels are particularly high in aortic and renal arteries. Several studies have clearly demonstrated that the serum levels of OPG are elevated in diabetic and nondiabetic patients affected by cardiovascular diseases, and increased levels of OPG represent a risk factor for cardiovascular mortality, especially in diabetic patients. However, in spite of the reported findings, the physiopathological role of elevated serum levels of OPG in vascular biology and in pancreatic islet function are not well understood.
Aim of the study. The aims of our studies were:
Study 1. Evaluate the potential role of OPG in the pathogenesis of diabetes associated atherosclerosis.
Study 2. Investigate OPG effects on pancreatic islet function and its interaction with local pancreatic renin-angiotensin system (RAS).
Materials and Methods. Study 1.A. In vivo study: 80 apoE knockout male mice were further randomized into 4 groups (n=20) and followed for 3 months. One group of non diabetic animals received an intraperitoneal (i.p.) injection of vehicle and served as a control; another group of non-diabetic animals received every 3 weeks an i.p. injection of human recombinant OPG (OPG). The other two groups, rendered diabetic by 5 daily i.p. injections of streptozotocin (55mg/Kg/die), received injections of OPG or an equivalent volume of vehicle. At the end of the study, animals were culled, the blood was collected for biochemical analysis, and the entire aorta was excised out to study the total plaques extent and to evaluate the lesion composition and complexity of the aortic plaques. B. In vitro study: Murine vascular smooth muscle cells (VMSC) were treated with different concentrations of OPG, TGFβ and SB431542 (TGFβ- type 1 receptor inhibitor). Subsequently, cellular proliferation and pro-fibrotic markers gene expression were evaluated at different time points. OPG protein release was measured in growth media (ELISA technique).
Study 2. 40 male mice C57Bl/6J, aged 10 weeks, were randomized into 4 groups (n=10) and studied for 3 months. Group 1 received every 3 weeks an i.p. injection of vehicle and served
as a control. Group 2 received every 3 weeks an i.p. injection of OPG. Group 3 received the ACE inhibitor ramipril at the dose of 10mg/Kg/die in drinking water in co-treatment with i.p. injections of vehicle. Group 4 received ramipril in co-treatment with i.p. injections of OPG. At the end of the study, animals were culled, the blood was collected for biochemical analysis, and the pancreas was dissected out for subsequent quantitative RT-PCR measurements and immunohistochemical analysis.
Results. Study 1.A. At the end of the study, diabetic animals injected with OPG presented a significant increase in total plaques extent, with an increase of smooth muscle cells content in aortic plaques. Moreover OPG treated animals showed an increase in the collagen content in aortic media in respect to control mice. B. OPG promoted VSMC proliferation and pro-fibrotic markers gene expression. TGFβ treatment of VSMC induced a dose-dependent increase of OPG gene and protein expression, that was completed prevented by pre-treatment with the SB431542 inhibitor.
Study 2. OPG-treated animals showed increased islet monocyte-macrophage infiltration, fibrosis and apoptosis with reduction of islet function. The remodeling of islet architecture was associated with increased pancreatic expression of components of the RAS, growth factor genes (TGFβ and CTGF) and inflammatory molecules (MCP-1 and VCAM-1). Prevention of these changes with improvement of insulin secretion was observed in ramipril treated animals.
Conclusion. Study 1.A-B OPG seems to play an important pathogenetic role in the development and progression of diabetic atherosclerosis.
Study 2. Our data suggest that OPG might play an important role in promoting beta cell dysfunction and the upregulation of the local RAS represents one possible mechanism responsible for the OPG-induced beta cell dysfunction
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