QDENSITY/QCWAVE: A Mathematica quantum computer simulation update

Abstract

The Mathematica quantum computer simulation packages QDENSITY and QCWAVE are updated for Mathematica 9-10.3. An overview is given of the new QDensity, QCWave, BTSystem and Circuits packages, which includes: (1) improved treatment of tensor products of states and density matrices, (2) major extension to include qutrit (triplet), as well as qubit (binary) and hybrid qubit/qutrit systems in the associated BTSystem package, (3) updated sample quantum computation algorithms, (4) entanglement studies, including Schmidt decomposition, entropy, mutual information, partial transposition, and calculation of the quantum discord. Examples of Bell’s theorem and concurrence are also included. This update will hopefully aid in studies of QC dynamics. New version program summaryProgram title: QDensity, QCWave, BTSystem, CircuitsCatalogue identifier: ADXH_v4_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v4_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 705731No. of bytes in distributed program, including test data, etc.: 10394409Distribution format: tar.gzProgramming language: Mathematica 9.0-10.3.0.Computer: Any computer which supports Mathematica.Operating system: Any operating system that supports Mathematica.Classification: 4.15.Catalogue identifier of previous version: ADXH_v3_0Journal reference of previous version: Comput. Phys. Comm. 182(2011)1693Does the new version supersede the previous version?: Offers an updated and extended implementation.Nature of problem: Simulation of quantum algorithms, Qubit and Qutrit hybrid systems, entanglement criteria.Solution method: A Mathematica package containing commands to create and analyze quantum circuits is upgraded and extended. Mathematica tutorials and notebooks illustrate the capabilities of the packages and demonstrate quantum computation applications.Reasons for new version: Here the Mathematica (MM) packages QDensity, QCWave [1, 2, 3] are updated for MM 9-10.3. Other quantum computer simulators using a variety of languages, are described in [4]. The new QDENSITY, QCWAVE, BT-System packages include commands for entropy, Schmidt decomposition, partial transposition, quantum discord, mutual information, and circuit diagrams, not only for qubit systems but also for qutrit and hybrid qubit/qutrit systems. The full array of new commands are provided in the Tutorial2014 notebook. Compared to other Mathematica simulators, QDENSITY has a larger user and application base, that is further enhanced by this update to qubit/qutrit systems. In the present upgrade, qubit, qutrit and hybrid (mixed qubit and qutrit) states and mixed qubit and qutrit gates are included (see BTSystems.m). Updated QC algorithms, a sample extension of teleportation to qutrits, examples for random, Bell, GHZ, Werner and X-states are included.Summary of revisions: A new overview manual (OVERVIEW.pdf), installation directions (INSTALL.nb) and tutorials.Running time: Notebooks in the package take only minutes to execute.