Logic circuits from zero forcing.
Logic circuits from zero forcing.
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DOI：
10.1007/s11047-014-9438-5
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发表时间：
2015
影响因子：
2.1
通讯作者：
Young M
中科院分区：
文献类型：
--
作者：
Burgarth D;Giovannetti V;Hogben L;Severini S;Young M
我们设计逻辑电路的基础上的概念，迫零图，电路的每个门是一个小工具，迫零执行。我们表明，这样的电路可以评估每一个单调的布尔函数。通过使用两个顶点对每个逻辑位进行编码，我们获得了通用计算。我们还强调了一个现象的“回迫”作为每个功能的属性。当在给定时间步已经使用的门的输入被在后面阶段实际执行的计算进一步修改时，在电路中发生这种现象。最后，我们证明了迫零也可以用来实现可逆计算。这里介绍的模型提供了一个潜在的新工具，在布尔函数的分析，特别注意单调性。此外，鉴于迫零在量子力学中的应用，与布尔函数的联系可能会在量子控制理论和工程量子自旋系统的研究中提出一个新的方向。这是一个开放的技术问题，以验证是否有一个零强制和接触电路的计算之间的联系。
We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of “back forcing” as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we show that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.