QDENSITY—A Mathematica Quantum Computer simulation

Juliá-Dı́az, B.; Burdis, Joseph M.; Tabakin, Frank

doi:10.1016/j.cpc.2005.12.021

Cited by 18 publications

(6 citation statements)

References 10 publications

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“…A brief review was given in our earlier papers in this series [1,5]. Here we proceed directly from one, two and multi-qubit states and their amplitudes to how various operators alter those amplitudes.…”

Section: One-qubit Statesmentioning

confidence: 99%

“…where the operators Ω (1) , Ω (2) · · · Ω (np) act in each of the n p paths with a probability np . Each of these n p terms is evaluated on a separate processor, so that n p equals the total number of processors invoked.…”

Section: Storage Casementioning

confidence: 99%

“…In QDENSITY , the kets | 0 , | 1 are invoked by the commands Ket[0] and Ket [1], and the product state by for example…”

Section: Two-qubit Statesmentioning

confidence: 99%

“…In the notebooks, the operators ss[i] are set equal to the Pauli operators s[i] to generate noise. By replacing ss [1] by s[0] (the 2 × 2 unit operator), all X-noise is turned off "by hand." Then a rerun is generated which has the same structure as with the noise, except the X-noise has been removed.…”

Section: Multiverse Algorithms and Errorsmentioning

confidence: 99%

“…In this paper, QDENSITY [1] (a Mathematica [2] package that provides a flexible simulation of a quantum computer) is extended and upgraded by an add-on called QCWAVE 1 . The earlier flexibility in QDENSITY is enhanced by adopting a simple state vector approach to initializations, operators, gates, and measurements.…”

Section: Introductionmentioning

confidence: 99%

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QCWAVE – A Mathematica quantum computer simulation update

Tabakin¹,

Juliá-Dı́az²

2011

Computer Physics Communications

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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.

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Section: One-qubit Statesmentioning

confidence: 99%

Section: Storage Casementioning

confidence: 99%

“…In QDENSITY , the kets | 0 , | 1 are invoked by the commands Ket[0] and Ket [1], and the product state by for example…”

Section: Two-qubit Statesmentioning

confidence: 99%

Section: Multiverse Algorithms and Errorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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QCWAVE – A Mathematica quantum computer simulation update

Tabakin¹,

Juliá-Dı́az²

2011

Computer Physics Communications

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Quantum computing: A taxonomy, systematic review and future directions

et al. 2021

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Quantum computing (QC) is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum‐mechanical principles such as entanglement and superposition. It is anticipated that this computational advantage of QC will help to solve many complex and computationally intractable problems in several application domains such as drug design, data science, clean energy, finance, industrial chemical development, secure communications, and quantum chemistry. In recent years, tremendous progress in both quantum hardware development and quantum software/algorithm has brought QC much closer to reality. Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era—the next logical step being the quantum advantage whereby quantum computers solve a real‐world problem much more efficiently than classical computing. As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ era. QC is a highly topical and fast‐moving field of research with significant ongoing progress in all facets. A systematic review of the existing literature on QC will be invaluable to understand the state‐of‐the‐art of this emerging field and identify open challenges for the QC community to address in the coming years. This article presents a comprehensive review of QC literature and proposes taxonomy of QC. The proposed taxonomy is used to map various related studies to identify the research gaps. A detailed overview of quantum software tools and technologies, post‐quantum cryptography, and quantum computer hardware development captures the current state‐of‐the‐art in the respective areas. The article identifies and highlights various open challenges and promising future directions for research and innovation in QC.

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Quantum Software Tools Overview

Cruz-Lemus

Serrano

2022

Quantum Software Engineering

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QDENSITY—A Mathematica Quantum Computer simulation

Cited by 18 publications

References 10 publications

QCWAVE – A Mathematica quantum computer simulation update

QCWAVE – A Mathematica quantum computer simulation update

Quantum computing: A taxonomy, systematic review and future directions

Quantum Software Tools Overview

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