QCWAVE – A Mathematica quantum computer simulation update

Abstract

This Mathematica 7.0/8.0 package upgrades and extends the quantum computer simulation code called QDENSITY. Use of the density matrix was emphasized in QDENSITY, although that code was also applicable to a quantum state description. In the present version, the quantum state version is stressed and made amenable to future extensions to parallel computer simulations. The add-on QCWAVE extends QDENSITY in several ways. The first way is to describe the action of one, two and three-qubit quantum gates as a set of small (2 × 2, 4 × 4 or 8 × 8) matrices acting on the 2 nq amplitudes for a system of n q qubits. This procedure was described in our parallel computer simulation QCMPI and is reviewed here. The advantage is that smaller storage demands are made, without loss of speed, and that the procedure can take advantage of message passing interface (MPI) techniques, which will hopefully be generally available in future Mathematica versions.Another extension of QDENSITY provided here is a multiverse approach, as described in our QCMPI paper. This multiverse approach involves using the present slave-master parallel processing capabilities of Mathematica 7.0/8.0 to simulate errors and error correction. The basic idea is that parallel versions of QCWAVE run simultaneously with random errors introduced on some of the processors, with an ensemble average used to represent the real world situation. Within this approach, error correction steps can be simulated and their efficacy tested. This capability allows one to examine the detrimental effects of errors and the benefits of error correction on particular quantum algorithms.Other upgrades provided in this version includes circuit-diagram drawing commands, better Dirac form and amplitude display features. These are included in the add-ons QCWave.m and Circuits.m, and are illustrated in tutorial notebooks.In separate notebooks, QCWAVE is applied to sample algorithms in which the parallel multiverse setup is illustrated and error correction is simulated. These extensions and upgrades will hopefully help in both instruction and in application to QC dynamics and error correction studies.

qTorch: The quantum tensor contraction handler

“…However, until a large-scale and viable quantum computer has been realized, numerically simulating quantum circuits on a classical computer will be necessary for predicting the behavior of quantum computers. Such simulations can play an important role in the development of quantum computing by (1) numerically verifying the correctness and characterizing the performance of quantum algorithms [1][2][3][4][5], (2) simulating error and decoherence due to the interaction between the quantum computer and its environment [6][7][8][9], and (3) improving our understanding of the boundary between classical and quantum computing in terms of computational power, for which recent efforts for characterizing the advantage of quantum computers over classical computers [10][11][12][13][14][15][16][17] serve as an example of this direction.…”

An efficient quantum circuit analyser on qubits and qudits

“…The QDENSITY package [1] provides many functions for the simulation of quantum circuits, two of which simulate the CNOT gate and the Toffoli gate. A more recent paper [7] introduces QCWAVE as an extension of the QDENSITY package. QCWAVE has the functions Op2 and Op3 that can be used to reproduce the action of CNOT n and Toffoli n gates on state vectors, but does not give the matrix of the gates itself.…”

States and Channels in Quantum Mechanics Without Complex Numbers

“…During the last few years Mathematica computing system has become very popular in the area of quantum information theory and the foundations of quantum mechanics. The main reason for this is its ability to merge the symbolic and numerical capabilities [4], both of which are often necessary to understand the theoretical and practical aspects of quantum systems [5,6,7,8].…”