Abstract
We propose quantum Boolean networks, which can be classified as deterministic reversible asynchronous Boolean networks. This model is based on the previously developed concept of quantum Boolean functions. A quantum Boolean network is a Boolean network where the functions associated with the nodes are quantum Boolean functions. We study some properties of this novel model and, using a quantum simulator, we study how the dynamics change in function of connectivity of the network and the set of operators we allow. For some configurations, this model resembles the behavior of reversible Boolean networks, while for other configurations a more complex dynamic can emerge. For example, cycles larger than 2N were observed. Additionally, using a scheme akin to one used previously with random Boolean networks, we computed the average entropy and complexity of the networks. As opposed to classic random Boolean networks, where “complex” dynamics are restricted mainly to a connectivity close to a phase transition, quantum Boolean networks can exhibit stable, complex, and unstable dynamics independently of their connectivity.
Highlights
Boolean networks were originally proposed in the late 1960s to model the behavior of regulatory networks by Kauffman [1]
Quantum computation may prove beneficial to enrich the model of Boolean networks, considering that the dynamics described by quantum mechanics is fundamentally different from that of classical dynamics
We proposed a new Boolean network model using the paradigm of quantum computation: quantum Boolean networks, which exhibit a deterministic, asynchronous, and reversible dynamic
Summary
Boolean networks were originally proposed in the late 1960s to model the behavior of regulatory networks by Kauffman [1]. Landauer linked the irreversibility of conventional computational operations and the thermodynamic behavior of the computational device He stated that whenever a bit is overwritten with a new value, the previous information is not physically destroyed. Reversible computing has received limited attention, since it is quite complicated to implement and in many cases it is possible to get along without it It has been slowly gaining followers [5], mainly due to the recently grim predictions casted upon conventional computing: in the near future, making a transistor smaller will no longer yield any practical improvement [6]. This paper is structured as follows: Section 2 serves to recall some useful concepts related to Boolean networks and provides a brief introduction to quantum computing.
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