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The Hahn Quantum Variational Calculus [PDF]
Journal of Optimization Theory and Applications, 2010 We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied.
A. B. Malinowska +48 more
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A symmetric quantum calculus [PDF]
, 2011 We introduce the $\alpha,\beta$-symmetric difference derivative and the $\alpha,\beta$-symmetric N\"orlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generalization of the forward and backward $h$-calculus.Comment:
da Cruz, Artur M. C. Brito +2 more
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Depicting qudit quantum mechanics and mutually unbiased qudit theories [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these ...
André Ranchin
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Qutrit Dichromatic Calculus and Its Universality [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We introduce a dichromatic calculus (RG) for qutrit systems. We show that the decomposition of the qutrit Hadamard gate is non-unique and not derivable from the dichromatic calculus.
Quanlong Wang, Xiaoning Bian
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Novel Error Bounds of Milne Formula Type Inequalities via Quantum Calculus with Computational Analysis and Applications [PDF]
MathematicsQuantum calculus is a powerful extension of classical calculus, providing novel tools for deriving sharper and more efficient analytical results without relying on limits.
Amjad E. Hazma +3 more
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Equivariant Quantum Schubert Calculus [PDF]
Advances in Mathematics, 2004 We study the T-equivariant quantum cohomology of the Grassmannian. We prove the vanishing of a certain class of equivariant quantum Littlewood-Richardson coefficients, which implies an equivariant quantum Pieri rule. As in the equivariant case, this implies an algorithm to compute the equivariant quantum Littlewood-Richardson coefficients.
Leonardo C. Mihalcea
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The Falling Body Problem in Quantum Calculus [PDF]
Frontiers in Physics, 2020 The quantum calculus, q-calculus, is a relatively new branch in which the derivative of a real function can be calculated without limits. In this paper, the falling body problem in a resisting medium is revisited in view of the q-calculus to the first ...
Abdulaziz M. Alanazi +3 more
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A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 We 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
Renaud Vilmart
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Quantum Stochastic Calculus and Quantum Gaussian Processes [PDF]
Indian Journal of Pure and Applied Mathematics, 2014 In this lecture we present a brief outline of boson Fock space stochastic calculus based on the creation, conservation and annihilation operators of free field theory, as given in the 1984 paper of Hudson and Parthasarathy. We show how a part of this architecture yields Gaussian fields stationary under a group action.
K. R. Parthasarathy
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Quantum Integrability and Generalised Quantum Schubert Calculus [PDF]
Advances in Mathematics, 2017 We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six-vertex ...
Gorbounov, Vassily, Korff, Christian
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