Optimizing the Number of Gates Representing an FTA k/n Operator on a Quantum Computer

The classic static fault tree analysis is a deductive method based on Boolean logic widely used for reliability and safety analysis. The method is based on the application of logical operators to show the relationship between component failures that lead to intermediate or top-level adverse events. At the lowest level, it is assumed that the events are basic and that the probability of their occurrence is fixed according to the Bernoulli distribution, for instance, the probability of a failure occurring for a component. Recently, it has been shown that such events can be successfully simulated by means of qubits and that events on middle and highest levels can be written by using quantum gates that simulate logic operators, i.e., can be written utilizing a quantum fault tree. The quantitative and qualitative analysis of the static fault tree can then be simulated on that record aided by a quantum computer. In this article, in addition to the standard set of logical operators (and, or, not), we further explore the static fault tree record that contains the commonly used k/n logical operator. Although the k/n operator can be written employing a combination of a standard set of logical operators, however, such notation is usually not optimal for implementation on a quantum computer, except for the simplest cases. Therefore, in this paper we present a model for optimizing the number of quantum gates in a quantum circuit record for events that are described in a static fault tree by the k/n logic operator. In addition, in the given example of such a static fault tree consisting of six basic events and four derived events we closely present the calculation of the top event probability and the determination of all state vectors in the quantum fault tree that represent minimal cut-sets of the latter. Eventually, we analyse the usage and scaling of resources in a quantum computer and additionally provide a summary of practical limitations in the application of a hybrid static fault tree recording strategy on potential quantum computers in the near future.