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The ZX-calculus is complete for stabilizer quantum mechanics
New Journal of Physics, 2014 The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement ...
Miriam Backens
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, 2009 The lambda calculus, developed in the 1930’s by Church and Curry, is a formalism for expressing higher-order functions. In a nutshell, a higher-order function is a function that inputs or outputs a “black box”, which is itself a (possibly higher-order) function. Higher-order functions are a computationally powerful tool. Indeed, the pure untyped lambda
Peter Selinger, Benoît Valiron
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Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning [PDF]
QuantumZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature.
Quanlong Wang, Richie Yeung, Mark Koch
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A Stochastic Fractional Calculus with Applications to Variational Principles
Fractal and Fractional, 2020 We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes.
Houssine Zine, Delfim F. M. Torres
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Geometry of Quantum Principal Bundles I
, 1995 A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed.
M. Daniel +8 more
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PyZX: Large Scale Automated Diagrammatic Reasoning
, 2020 The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor networks that can represent arbitrary linear maps between qubits.
Kissinger, Aleks, van de Wetering, John
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Quantum Behavior Arises Because Our Universe is a Fractal [PDF]
Reports in Advances of Physical Sciences, 2017 To explain the origin of quantum behavior, we propose a fractal calculus to describe the non-local property of the fractal curve [Y. Tao, J. Appl. Math. 2013 (2013) 308691]. This study demonstrates that if the dimension of time axis is slightly less than
Yong Tao
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Differential calculus on the quantum Heisenberg group
, 1996 The differential calculus on the quantum Heisenberg group is conlinebreak structed. The duality between quantum Heisenberg group and algebra is proved.Comment: AMSTeX, Pages
Bonechi F +7 more
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Bicovariant Differential Calculus on the Quantum D=2 Poincare Group
, 1992 We present a bicovariant differential calculus on the quantum Poincare group in two dimensions.
Bernard +21 more
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Spikes in quantum Regge calculus [PDF]
Classical and Quantum Gravity, 1997 We demonstrate by explicit calculation of the DeWitt-like measure in two-dimensional quantum Regge gravity that it is highly non-local and that the average values of link lengths $l, $, do not exist for sufficient high powers of $n$. Thus the concept of length has no natural definition in this formalism and a generic manifold degenerates into spikes ...
Ambjørn, Jan +3 more
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