Categorical Quantum Dynamics

Gogioso, Stefano

doi:10.48550/arxiv.1709.09772

Cited by 1 publication

(1 citation statement)

References 86 publications

(152 reference statements)

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“…Specifically, these techniques allow us to reason about quantum dynamics and quantum chemistry in the ZXW calculus. Previous diagrammatic approaches [10,11,12] to quantum dynamics have tackled the problem from an abstract categorical perspective. In this paper, we develop diagrammatic techniques to tackle problems of quantum chemistry and condensed matter physics in a concrete and practical way.…”

Section: Introductionmentioning

confidence: 99%

How to Sum and Exponentiate Hamiltonians in ZXW Calculus

Shaikh,

Wang,

Yeung

2023

Electron. Proc. Theor. Comput. Sci.

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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 Hamiltonians, in ZXW calculus. As an application, we demonstrate the linearity of the Schrödinger equation and give a diagrammatic representation of the Hamiltonian in Greene-Diniz et al [13], which is the first paper that models carbon capture using quantum computing. We then use the Cayley-Hamilton theorem to show in principle how to exponentiate arbitrary qubits Hamiltonians in ZXW calculus. Finally, we develop practical techniques and show how to do Taylor expansion and Trotterization diagrammatically for Hamiltonian simulation. This sets up the framework for using ZXW calculus to the problems in quantum chemistry and condensed matter physics.

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Section: Introductionmentioning

confidence: 99%