A Rudimentary Quantum Compiler(2cnd Ed.)

TL;DR

This paper introduces a recursive algorithm for decomposing any unitary matrix into elementary quantum operations, utilizing the CS Decomposition, with an implementation called Qubiter that is publicly available.

Contribution

It presents a novel recursive algorithm for quantum circuit synthesis based on the CS Decomposition, unifying it with the FFT as a special case.

Findings

Algorithm effectively reduces unitary matrices to elementary operations.

Qubiter software implements the algorithm and is publicly accessible.

The method generalizes existing quantum compilation techniques.

Abstract

We 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.