Detailed Account of Complexity for Implementation of Circuit-Based Quantum Algorithms

Abstract

In this review article, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware. In particular, some steps of the implementation, as the preparation of an arbitrary superposition state and readout of the final state, in most of the cases can surpass the complexity aspects of the algorithm itself. We present the complexity involved in the full implementation of circuit-based quantum algorithms, from state preparation to the number of measurements needed to obtain good statistics from the final states of the quantum system, in order to assess the overall space and time costs of the processes.