Analytical solutions describing quantum swap and Hadamard gate are given with the use of tight-binding approximation. Decoherence effects are described analytically for 2 interacting electrons confined by local potentials with use of tight-binding simplistic model and in Schroedinger formalism with omission of spin degree of freedom. The obtained results can be generalized for the case of N electrostatically interacting quantum bodies confined by local potentials (N-qubit) system representing any electrostatic quantum gate with N1∕N−N1 inputs/outputs. The mathematical structure of system evolution with time is specified.

中文翻译：

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静电量子门中的N体相互作用和紧束缚模型中的退相干效应分析

使用紧束缚近似给出了描述量子交换和 Hadamard 门的解析解。使用紧束缚简单模型和省略自旋自由度的薛定谔形式分析地描述了由局部电位限制的 2 个相互作用电子的退相干效应。得到的结果可以推广到以下情况ñ由局部电位限制的静电相互作用的量子体（ñ-qubit) 系统代表任何静电量子门ñ1∕ñ-ñ1输入/输出。规定了系统随时间演化的数学结构。