Specifying the unitary evolution of a qudit for a general nonstationary Hamiltonian via the generalized Gell-Mann representation

• URL: http://arxiv.org/abs/2004.09896v1
• Date: Tue, 21 Apr 2020 10:49:19 GMT
• Title: Specifying the unitary evolution of a qudit for a general nonstationary Hamiltonian via the generalized Gell-Mann representation
• Authors: Elena R. Loubenets and Christian K\"ading
• Abstract summary: We introduce a new general formalism describing the unitary evolution of a qudit $(dgeq2)$ in terms of the Bloch-like vector space. We derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit $(d\geq2)$ in terms of the Bloch-like vector space and specify how in a general case this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case $(d=2)$, we specify the unitary evolution of a qubit via the evolution of a unit vector in $\mathbb{R}^{4}$ and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians. This new analytical expression includes the qubit solutions known in the literature only as particular cases.

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