Quantum algorithms for scientific computing require modules implementing fundamental functions, such as inverses, logarithms, trigonometric functions, and others. We require modules that have a well-controlled numerical error, that are uniformly scalable and reversible (unitary), and that can be implemented efficiently. Such modules are an important first step in the development of quantum libraries and standards for numerical computation.
We present quantum algorithms and circuits for computing the square root, the natural logarithm, and arbitrary fractional powers. We provide performance guarantees in terms of their worst-case accuracy and cost. We further illustrate their performance by comparing to floating point implementations found in widely used numerical software.
Joint work with Mihir K. Bhaskar, Anargyros Papageorgiou, and Iasonas Petras
