Miscellaneous Quantum Algorithms

Abstract

So far, we have discussed classical and particularly quantum algorithms for integer factoring, discrete logarithms and elliptic curve discrete logarithms. This does not mean quantum algorithms can only be used to solve integer factorization problem, discrete logarithm problem and elliptic curve discrete logarithm problem. In fact, quantum algorithms and quantum computers in general can solve other problems with either superpolynomially (exponentially) speedup or polynomially speedup. In this last and short chapter, we shall discuss some various other quantum algorithms and methods for more number-theoretic problems. Unlike the previous chapters, we will not emphasize on the introduction of the details quantum algorithms for number-theoretic problems, rather we shall concentrated on new ideas and new developments in quantum algorithms for number-theoretic problems.