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Itô Calculus and Quantum White Noise Calculus [PDF]
, 2007 Ito calculus has been generalized in white noise analysis and in quantum stochastic calculus. Quantum white noise calculus is a third generalization, unifying the two above mentioned ones and bringing some unexpected insight into some old problems studied in different fields, such as the renormalization problem in physics and the representation theory ...
ACCARDI, LUIGI, Boukas, A.
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Sequent Calculus Representations for Quantum Circuits [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional quantum logics
Cameron Beebe
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General Non-Markovian Quantum Dynamics
Entropy, 2021 A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus.
Vasily E. Tarasov
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ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 We present a new graphical calculus that is sound and complete for a universal family of quantum circuits, which can be seen as the natural string-diagrammatic extension of the approximately (real-valued) universal family of Hadamard+CCZ circuits.
Miriam Backens, Aleks Kissinger
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The Journal of King Mongkut's University of Technology North Bangkok, 2020 The radioactive decay law was first formulated by Ernest Rutherford and Frederick Soddy in 1902. As a well-known law, one of its primary applications is to determine the date of ancient specimens. The pro- cess is known as radiocarbon dating and is subjected to the known properties of radioactive nuclei.
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New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions [PDF]
Sahand Communications in Mathematical AnalysisThe main objective of this paper is to establish some new inequalities related to the open Newton-Cotes formulas in the setting of q-calculus. We establish a quantum integral identity first and then prove the desired inequalities for $q$-differentiable ...
Jarunee Soontharanon +4 more
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AKLT-States as ZX-Diagrams: Diagrammatic Reasoning for Quantum States
PRX Quantum, 2022 From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalyzed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation, but cannot ...
Richard D.P. East +3 more
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The Quantum Probability Calculus
Synthese, 1974 Quantum mechanics has opened a vast sector of physics to probability calculus. In fact most of the physical interpretation of the formalism of quantum mechanics is expressed in terms of probability statements ...
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Quantum and braided ZX calculus*
Journal of Physics A: Mathematical and Theoretical, 2022 Abstract We apply quantum group methods to quantum computing, starting with the notion of interacting Frobenius Hopf algebras for ZX calculus with noncommutative algebra and noncocommutative coalgebra. We introduce the notion of *-structures in ZX calculus at this algebraic level and construct examples based on the quantum group u
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Quantum integrability and generalised quantum Schubert calculus [PDF]
Advances in Mathematics, 2017 57 pages, 10 figures; v2: some references added and some minor changes; v3: abstract shortened, some typos corrected and a discussion of the Bethe roots for the non-equivariant case added; v4: accepted ...
Gorbounov, Vassily, Korff, Christian
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