Quantum gate synthesis by small perturbation of a particle in a box with electric field

IF 2.5 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

Journal of Computational Electronics Pub Date : 2025-09-25 DOI:10.1007/s10825-025-02425-z

Kumar Gautam

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Abstract

A quantum unitary gate is studied theoretically by perturbing a free charged particle in a one-dimensional box with a time- and position-varying electric field. The perturbed Hamiltonian is composed of a free particle Hamiltonian plus a perturbing electric potential such that the Schrödinger evolution in time T, the unitary evolution operator of the unperturbed system after truncation to a finite number of energy levels, approximates a given unitary gate such as the quantum Fourier transform gate. The idea is to truncate the half-wave Fourier sine series to M terms in the spatial variable \(\textbf{x}\) before extending the potential as a Dyson series in the interaction picture to compute the evolution operator matrix elements up to the linear and quadratic integral functionals of \( \textbf{V}_n(t)^{\prime}\)s. As a result, we used the Dyson series with the Frobenius norm to reduce the difference between the derived gate energy and the given gate energy, and we determined the temporal performance criterion by plotting the noise-to-signal energy ratio. A mathematical explanation for a quantum gate’s magnetic control has also been provided. In addition, we provide a mathematical explanation for a quantum gate that uses magnetic control.

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有电场的盒子中粒子的微扰合成量子门

用时变和位变电场扰动一维盒子中的自由带电粒子，从理论上研究了量子酉门。摄动哈密顿量由自由粒子哈密顿量加上摄动电势组成，使得时间T中的Schrödinger演化，即未摄动系统截断到有限个能级后的幺正演化算符，近似于给定的幺正门，如量子傅立叶变换门。我们的想法是将半波傅立叶正弦级数截断为空间变量\(\textbf{x}\)中的M项，然后将势扩展为相互作用图中的Dyson级数，以计算演化算子矩阵元素，直至\( \textbf{V}_n(t)^{\prime}\) s的线性和二次积分函数。因此，我们使用带有Frobenius范数的Dyson级数来减少导出的门能量与给定的门能量之间的差异。并通过绘制噪声与信号能量比来确定时域性能标准。对量子门的磁控制也给出了数学解释。此外，我们还提供了使用磁控制的量子门的数学解释。

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来源期刊

Journal of Computational Electronics ENGINEERING, ELECTRICAL & ELECTRONIC-PHYSICS, APPLIED

CiteScore

4.50

自引率

4.80%

发文量

142

审稿时长

>12 weeks

期刊介绍： he Journal of Computational Electronics brings together research on all aspects of modeling and simulation of modern electronics. This includes optical, electronic, mechanical, and quantum mechanical aspects, as well as research on the underlying mathematical algorithms and computational details. The related areas of energy conversion/storage and of molecular and biological systems, in which the thrust is on the charge transport, electronic, mechanical, and optical properties, are also covered. In particular, we encourage manuscripts dealing with device simulation; with optical and optoelectronic systems and photonics; with energy storage (e.g. batteries, fuel cells) and harvesting (e.g. photovoltaic), with simulation of circuits, VLSI layout, logic and architecture (based on, for example, CMOS devices, quantum-cellular automata, QBITs, or single-electron transistors); with electromagnetic simulations (such as microwave electronics and components); or with molecular and biological systems. However, in all these cases, the submitted manuscripts should explicitly address the electronic properties of the relevant systems, materials, or devices and/or present novel contributions to the physical models, computational strategies, or numerical algorithms.