Simulations of quantum systems evolution with quantum-octave package

Article presents package of functions for GNU Octave computer algebra system. Those functions were designed to perform simple but not necessary efficient simulations of quantum systems, especially quantum computers. The most important feature of this package is the ability to perform calculations with mixed states.We describe application of quantum-octave package for simulation of Grovers algorithm, which is one of the most important quantum algorithms. We also list other possible calculations, which can be performed with this package

Extending scientific computing system with structural quantum programming capabilities

We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave, providing a library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for high-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices