2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/93989We present a new algorithm for reducing an arbitrary unitary matrix U into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). Our algorithm applies recursively a mathematical technique called the CS Decomposition to build a binary tree of matrices whose product, in some order, equals the original matrix U. We show that the Fast Fourier Transform (FFT) algorithm is a special case of our algorithm. We report on a C++ program called "Qubiter" that implements the ideas of this paper. Qubiter(PATENT PENDING) source code is publicly available.1 LaTeX file(49 pages), 11 eps files. This paper comprises two of my previous papers entitled "A Rudimentary Quantum Compiler" and "An Optimization for Qubiter", plus a substantial amount of new materialQuantum Physicstext