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Covariantization of quantized calculi over quantum groups [PDF]
Mathematica Bohemica, 2020 We introduce a method for construction of a covariant differential calculus over a Hopf algebra $A$ from a quantized calculus $da=[D,a]$, $a\in A$, where $D$ is a candidate for a Dirac operator for $A$.
Seyed Ebrahim Akrami, Shervin Farzi
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Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model [PDF]
Logical Methods in Computer Science, 2022 In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those.
Alejandro Díaz-Caro, Octavio Malherbe
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Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 Quantum 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.
Anne Hillebrand
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The ZX-calculus is complete for the single-qubit Clifford+T group [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 The ZX-calculus is a graphical calculus for reasoning about pure state qubit quantum mechanics. It is complete for pure qubit stabilizer quantum mechanics, meaning any equality involving only stabilizer operations that can be derived using matrices can ...
Miriam Backens
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Symmetric Quantum Calculus [PDF]
, 2013 We generalize the Hahn variational calculus by studying problems of the calculus of variations with higher-order derivatives. The symmetric quantum calculus is studied, namely the alpha,beta-symmetric, the q-symmetric, and the Hahn symmetric quantum calculus.
Artur M. C. Brito da Cruz
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Making the stabilizer ZX-calculus complete for scalars [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 The ZX-calculus is a graphical language for quantum processes with built-in rewrite rules. The rewrite rules allow equalities to be derived entirely graphically, leading to the question of completeness: can any equality that is derivable using matrices ...
Miriam Backens
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Verification of Linear Optical Quantum Computing using Quantum Process Calculus [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We explain the use of quantum process calculus to describe and analyse linear optical quantum computing (LOQC). The main idea is to define two processes, one modelling a linear optical system and the other expressing a specification, and prove that they ...
Sonja Franke-Arnold +2 more
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A certain ( p , q ) $(p,q)$ -derivative operator and associated divided differences
Journal of Inequalities and Applications, 2016 Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator D q $D_{q}$ and divided difference. As applications of the post-quantum calculus known as the ( p , q ) $(
Serkan Araci +3 more
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Ostrowski Type Inequalities for s-Convex Functions via q-Integrals
Journal of Function Spaces, 2022 The new outcomes of the present paper are q-analogues (q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s-convex mappings.
Khuram Ali Khan +4 more
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A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics [PDF]
, 2018 We introduce the first complete and approximatively universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum mechanics by adding
Jeandel, Emmanuel +2 more
core +5 more sources