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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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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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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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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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Hahn's Symmetric Quantum Variational Calculus [PDF]
Numerical Algebra, Control & Optimization, 2012 We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational problems within ...
A. B. Malinowska +28 more
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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.
Parthasarathy, K. R.
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The ZX-calculus is incomplete for quantum mechanics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make the ZX-calculus
Christian Schröder de Witt +1 more
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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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Completeness of algebraic CPS simulations [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms.
Ali Assaf, Simon Perdrix
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