The quantum-dot cellular automata (QCA) present great promising advantages for emerging nano logic circuits. However, feedback design in QCA sequential circuit is often a big problem. Especially in line feedback shift registers (LFSR), each feedback loop consists of at least a modulo-2 adder and a trigger unit, which is hard to implement using the conventional methods. Given the importance of LFSR in communication systems, a design methodology with QCA is proposed in this work. At first, a new structure is presented to be used in every single feedback LFSR since it can make the feedback loop consume only one clock cycle of delay. Subsequently, quantitative criteria are presented to judge whether any multi-feedback LFSR can be directly designed using the proposed structure. LFSR that cannot satisfy the criteria are supposed to be transformed to their equivalent forms. We verify any LFSR can be transformed to the type of single feedback, according to the theorem of searching the monic and irreducible polynomials over Galois field GF (2). The step-by-step method of transforming multi-feedback into single feedback is given on the consideration of all kinds of cases. Further, two other simple transforming methods are presented to cope with the exponential growth of clock delay in the multi-to-single transforming method. The most remarkable advantage of this series of methods is to keep from introducing undesired bits into the payload data flowing in the sequential circuits.

中文翻译：

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量子元胞自动机线反馈移位寄存器的设计方法


量子点元胞自动机（QCA）为新兴的纳米逻辑电路带来了巨大的有前途的优势。然而，QCA时序电路中的反馈设计往往是一个大问题。尤其是在线反馈移位寄存器(LFSR)中，每个反馈环路至少由一个模2加法器和一个触发单元组成，这很难用传统方法实现。鉴于 LFSR 在通信系统中的重要性，本文提出了一种 QCA 设计方法。首先，提出了一种新的结构，用于每个单独的反馈LFSR，因为它可以使反馈环路仅消耗一个时钟周期的延迟。随后，提出了定量标准来判断是否可以使用所提出的结构直接设计任何多反馈 LFSR。不能满足标准的 LFSR 应转换为其等效形式。根据伽罗瓦域 GF (2) 上搜索单次多项式和不可约多项式的定理，我们验证了任何 LFSR 都可以转化为单反馈类型。考虑到各种情况，给出了将多反馈转化为单反馈的逐步方法。此外，还提出了另外两种简单的转换方法来应对多单转换方法中时钟延迟的指数增长。这一系列方法最显着的优点是避免将不需要的位引入到时序电路中流动的有效负载数据中。