**6. Conclusions**

In this article we introduce the discrete quantum computing as an alternative road to real quantum computing. The discrete quantum computing model is of great interest in itself both because, while maintaining all the important properties of quantum computing, it is an especially simplicity model and because error control is theoretically easier in this model. The introduced discrete quantum computing model satisfies some surprising properties that the authors believed would not hold and has deep connections to Number Theory.

The reason we set out on this alternative road to quantum computing is because error control in quantum computing is an extremely difficult challenge. The fact that the quantum computing model is continuous means that the golden rule of error control cannot be used: small errors are exactly corrected. A quantum computer is a very complex system from the point of view of error control. It allows reaching any quantum state (solution to the instance of a problem) by any path (algorithm). Doing this while keeping the error (entropy?) controlled is certainly an impressive challenge. As a consequence of the difficulty of controlling errors in continuous systems, there is no analog (continuous) device remotely comparable in operational complexity to a computer.

However, Quantum Physics does not allow the implementation of a discrete quantum computing model that allows self-correction of errors. To overcome this difficulty we ask Quantum Physics to go one step further in describing physical systems, beyond the prediction of measurement results. For this we propose a hypothesis about the nature of elementary particles that tries to overcome the never-understandable principle of wave-particle duality.

Summarizing, we propose an alternative road to quantum computing that passes through the discretization of this computing model and overcoming the interpretation gaps of Quantum Physics relative to the physical systems.

*Topics on Quantum Information Science*
