Implementation of Square Root Function Using Quantum Circuits
The design of quantum circuits that implement elementary functions has foundational value for the field of quantum computing and is also important for the development of other quantum algorithms. Here, we present the first design for a quantum circuit that computes the square root of any number v > 1. We include error analysis and asymptotic estimates for complexity and resource requirements. Specifically, if a total error of at most E is desired, then the procedure requires order O(log log 6v^1.5/E) iterations and a maximum of O(log v^1.5/E) qubits at any particular stage. A preliminary design for a circuit extension computing v^z for other fractional powers (besides z = 1/2) is also presented, as well as for the special case where z is a power of 2.