Calculating the upper limit of calculation speed and complexity growth rate using the mathematical method of disturbance theory

The speed of calculation and the level of ability to perform calculations for a computing system are two fundamental questions in computer science. Also, the concept of complexity of performing calculations in machine language and the measure provided for complexity are important quantities. In this article, we calculate the growth rate of the complexity of performing calculations for an asynchronous oscillator by using mathematical methods and specifically using the disturbance theory. The reason for choosing an oscillator is that most physical systems can be simulated with an oscillator. Also, we calculate the maximum dynamic evolution of the quantum states that changes the computation rate, and as an important achievement of this work, we show that for even-order perturbation, the rate of complexity increases, while for odd-order perturbation, the rate We will have a decreasing behavior. This method can be considered as a theoretical model for the upper limit of calculations.