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AxiomsIn this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their ...
Jessada Tariboon, Sotiris Ntouyas
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Generalized Ostrowski-Gruss Like Inequality on Time Scales [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we present a generalization of the Montgomery Identity to various time scale versions, including the discrete case, continuous case, and the case of quantum calculus.
Faraz Mehmood +2 more
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Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science.
Simon J. Gay, Ittoop Vergheese Puthoor
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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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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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How to Sum and Exponentiate Hamiltonians in ZXW Calculus
Electronic Proceedings in Theoretical Computer Science, 2023 This paper develops practical summation techniques in ZXW calculus to reason about quantum dynamics, such as unitary time evolution. First we give a direct representation of a wide class of sums of linear operators, including arbitrary qubits ...
Shaikh, Razin A. +2 more
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