Qdensity - a Mathematica Quantum Computer Simulation

This Mathematica 5.2 package~\footnote{QDENSITY is available at http://www.pitt.edu/~tabakin/QDENSITY} is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in {\it Qdensity.m} which contains the tools needed in quantum circuits, e.g. multiqubit kets, projectors, gates, etc. Selected examples of the basic commands are presented here and a tutorial notebook, {\it Tutorial.nb} is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: {\it QFT.nb}, {\it Teleportation.nb}, {\it Grover.nb} and {\it Shor.nb} where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of ``one way computing" ideas, are included as an additional tool in the notebook {\it Cluster.nb}. A Mathematica palette containing most commands in QDENSITY is also included: {\it QDENSpalette.nb} .Comment: The Mathematica 5+ package is available at: http://www.pitt.edu/~tabakin/QDENSITY/QDENSITY.htm Minor corrections, accepted in Computer Physics Communication

An efficient quantum circuit analyser on qubits and qudits

This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme reduces the evaluation of multiple unitary gate operations with many conditionals to just two matrix additions, regardless of the number of conditionals or gate dimensions. This improves significantly the capability of a quantum circuit analyser implemented in a classical computer. This is also the first efficient quantum circuit analyser to include qudit quantum logic gates

Generating and using truly random quantum states in Mathematica

The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing.Comment: 12 pages, 3 figures, see http://www.iitis.pl/~miszczak/trqs.html for related softwar

Qcmpi: A Parallel Environment for Quantum Computing

QCMPI is a quantum computer (QC) simulation package written in Fortran 90 with parallel processing capabilities. It is an accessible research tool that permits rapid evaluation of quantum algorithms for a large number of qubits and for various "noise" scenarios. The prime motivation for developing QCMPI is to facilitate numerical examination of not only how QC algorithms work, but also to include noise, decoherence, and attenuation effects and to evaluate the efficacy of error correction schemes. The present work builds on an earlier Mathematica code QDENSITY, which is mainly a pedagogic tool. In QCMPI, the stress is on state vectors, in order to employ a large number of qubits. The parallel processing feature is implemented by using the Message-Passing Interface (MPI) protocol. Codes for Grover's search and Shor's factoring algorithms are provided as examples. A major feature of this work is that concurrent versions of the algorithms can be evaluated with each version subject to alternate noise effects, which corresponds to the idea of solving a stochastic Schr\"{o}dinger equation.Comment: Package webpage http://www.pitt.edu/~tabakin/QCMP

Quintuple: A Tool for Introducing Quantum Computing Into the Classroom

In May 2016 IBM released access to its 5-qubit quantum computer to the scientific community, its “IBM Quantum Experience” since acquiring over 60,000 users from students, educators and researchers around the globe. In the time since the “IBM Quantum Experience” became available, a flurry of research results on 5-qubit systems has been published derived from the platform hardware. Quintuple is an open-source object-oriented Python module implementing the ideal simulation of “IBM's Quantum Experience” hardware. Quintuple quantum algorithms can be programmed and run via a custom language fully compatible with the “IBM's Quantum Experience” or in pure Python. Over 40 example programs are provided with expected results, including Grover's Algorithm and the Deutsch-Jozsa algorithm. Quintuple's implementation is aimed at students and educators wishing to incorporate quantum computing into the classroom and enables students to follow a quantum computing calculation step-by-step and to verify hand calculations. For these students and educators, Quintuple contributes to the study of 5-qubit systems and the development and debugging of quantum algorithms for deployment on the “IBM Quantum Experience” hardware