Simon’s Algorithm and Autocorrelation Spectrum

Abstract

Simon’s algorithm is another important evidence that more efficient evaluations of certain properties are possible in quantum domain over the classical paradigm. Given a vectorial Boolean function on n variables that has certain periodicity, this algorithm is capable of obtaining the period in time complexity polynomial in n. In this chapter, we explain this algorithm in detail. Then we concentrate on the autocorrelation spectrum of a single output Boolean function and study how the quantum strategies fare in this domain. We present quantum algorithms to study the Walsh spectrum of higher order derivatives of a Boolean function. Examples and Qiskit codes are presented to explain the methods.