607 research outputs found
Completeness of the ZW and ZX calculi
No full textThis thesis looks at two quantum motivated graphical calculi, the ZW calculus and ZX calculus. These two calculi are intended to perform qubit calculations using string diagrams. Both calculi are universal in the sense that they are able to represent all qubit maps, but they lack the completeness which means that they don't allow all qubit computation. The main goal of the thesis is to address the completeness issue.
The ZW calculus was completed by Hadzihasanovic in his DPhil thesis. We build on his work to do a completion for a fragment of the ZW calculus which describes operations in the fermionic quantum circuits. In the process, we discovered an important family of maps, the even and odd projectors. The even projectors is particularly important for the completion process. Next, we further restrict the calculus to only "even" maps and complete this fragment too. The odd projectors are important for this completion process. We give an interesting story for the even fragment ZW calculus: it describes a world without "real" particles, and the fermionic particles are manifestation of the curvature of spacetime and self 'fermionic' intersection and interaction of spacetime.
The ZX calculus was not complete and we solve this issue in this thesis. The technique used is a refinement of the one used in the paper on 'A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics' by Jeandel, Perdrix, and Vilmart. The basic idea of the technique is to translate the ZX calculus to the ZW calculus to analyse the problem, then translate it back. We also obtained many interesting generalising results which includes the completeness for the Clifford+T fragment and any fragments containing the Clifford+T fragment.
Finally, we end off with some interesting possible continuation of the thesis. Many of them are low hanging fruits. One of them is the extension of the calculi to represent qudits maps. The other is to generalise the ZW calculus to take semi-ring parameters which may be suited for other areas of computer science.</p
Towards a Minimal Stabilizer ZX-calculus
No full text13+15 pagesInternational audienceThe stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics. The language is sound and complete: one can transform a stabilizer ZX-diagram into another one using the graphical rewrite rules if and only if these two diagrams represent the same quantum evolution or quantum state. We previously showed that the stabilizer ZX-calculus can be simplified by reducing the number of rewrite rules, without losing the property of completeness [Backens, Perdrix & Wang, EPTCS 236:1--20, 2017]. Here, we show that most of the remaining rules of the language are indeed necessary. We do however leave as an open question the necessity of two rules. These include, surprisingly, the bialgebra rule, which is an axiomatisation of complementarity, the cornerstone of the ZX-calculus. Furthermore, we show that a weaker ambient category -- a braided autonomous category instead of the usual compact closed category -- is sufficient to recover the meta rule 'only connectivity matters', even without assuming any symmetries of the generators
Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus
No full textQuantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac notation difficult to verify. This is why Coecke and Duncan have introduced a diagrammatic language for quantum protocols, called the ZX-calculus. This diagrammatic notation is both intuitive and formally rigorous. It is a simple, graphical, high level language that emphasises the composition of systems and naturally captures the essentials of quantum mechanics. In the author's MSc thesis it has been shown for over 25 quantum protocols that the ZX-calculus provides a relatively easy and more intuitive presentation. Moreover, the author embarked on the task to apply categorical quantum mechanics on quantum security; earlier works did not touch anything but Bennett and Brassard's quantum key distribution protocol, BB84. Superdense coding with the Greenberger-Horne-Zeilinger state and quantum key distribution with the W-state are presented in the ZX-calculus in this paper
Ru-doped phosphorene for electrochemical ammonia synthesis
No full textThe electrochemical ammonia synthesis has attracted increasing attention due to its energy saving characteristics. However, developing novel electrocatalysts and their mechanism remain great challenges. Here, several transition metal (TM) atoms doped on phosphorene were studied as N2 fixation electrocatalysts by using density functional theory (DFT) calculations. The results demonstrate that single Ru atom doped phosphorene shows an excellent catalytic activity for ammonia synthesis via the enzymatic pattern. A small overpotential of 0.696 V is achieved for this process. The effect of oxidation in the catalyst was also discussed in our work. Oxidation deactivates the catalyst, which should be avoided in the experiment. Our outcomes offer a novel perspective for single-atom catalytic ammonia synthesis with phosphorene as a substrate.No Full Tex
On-top pair-correlation function in the homogeneous electron liquid
No full textThe ladder theory, in which the Bethe-Goldstone equation for the effective potential between two scattering particles plays a central role, is well known for its satisfactory description of the short-range correlations in the homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in the limit of large transfer momentum between two scattering particles, we obtain accurate results for the on-top pair-correlation function g(0), in both three dimensions and two dimensions. Furthermore, we prove, in general, that the ladder theory satisfies the cusp condition for the pair-correlation function g(r) at zero distance r=0.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000235009500047&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Physics, Condensed MatterSCI(E)8ARTICLE3null7
Impacts of subsidy policies on vaccination decisions in contact networks
No full textAuthor name used in this publication: Hai-Feng ZhangVersion of RecordPublishedVoR allowe
Improved fifth-order geometric aberration coeincients of electron lenses
No full textIn this paper, fifth-order geometric aberrations of round electron lenses have been restudied. Improved analytical formulae of the aberration coefficients were derived by the computer algebra software-Mathematica-and their correctness verified by cross-checking with numerical integration and differential algebraic techniques for a given electromagnetic lens.Physics, AppliedSCI(E)EI3ARTICLE5653-6593
Long-wavelength behavior of the dynamical spin-resolved local-field factor in a two-dimensional electron liquid
No full textThe high-frequency limits of the singular component A(omega) of the small wave-vector expansion of the longitudinal (L) and transverse (T) components of the spin-resolved exchange-correlation kernel tensor f(xc,sigmasigma)('L,T)(q,omega)=-v(q)G(sigmasigma)('L,T)(q,omega) in a two-dimensional isotropic electron liquid with arbitrary spin polarization are studied. Here G(sigmasigma)('L,T)(q,omega) is the spin-resolved local-field factor, v(q) is the Coulomb interaction in momentum space, and sigma denotes spin. Particularly, the real part of A(omega) is found to be logarithmically divergent at large omega. The large wave-vector structure of the corresponding spin-resolved static structure factor is also established.Physics, Condensed MatterSCI(E)1ARTICLE23null7
APFIM AND FEM STUDY OF MO-LA ALLOY WIRE
No full textPhysics, MultidisciplinarySCI(E)0ARTICLEC-6283-2864
A STUDY OF MINIATURIZED ELECTROSTATIC OCTUPOLE DEFLECTORS
No full textIn this paper the computer simulation and the computational results of miniaturized electrostatic octupole deflectors have been presented. It has been shown that both axial and azimuthal fringing effects must be taken into account for such deflectors with small length-to-radius ratio. The axial fringing effects make deflection sensitivity higher, have no effects on deflection coma and chromatism coefficients, and change the behaviors of deflection field curvature, astigmatism, and distortion coefficients for the round-lens-type aberrations. The azimuthal fringing effects decrease deflection sensitivity but hardly affect any round-lens-type deflection aberration coefficients. For miniaturized electrostatic octupole deflectors the computational results also show that four-fold deflection coma, astigmatism, and distortion are all extremly small and can be completely neglected.Instruments & InstrumentationNuclear Science & TechnologyPhysics, Particles & FieldsSpectroscopySCI(E)
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