Algorithms on ensemble quantum computers
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As...
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Springer Netherlands
2009
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3063506/ |
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pubmed-30635062011-04-05 Algorithms on ensemble quantum computers Boykin, P. Oscar Mor, Tal Roychowdhury, Vwani Vatan, Farrokh Article In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor’s factorization algorithm, Grover’s search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma_{z}^{1/4},$$\end{document} as these operations cannot be implemented “bitwise”, and their standard fault-tolerant implementations require measurement. Springer Netherlands 2009-05-30 2010-06 /pmc/articles/PMC3063506/ /pubmed/21475662 http://dx.doi.org/10.1007/s11047-009-9133-0 Text en © Springer Science+Business Media B.V. 2009 |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Boykin, P. Oscar Mor, Tal Roychowdhury, Vwani Vatan, Farrokh |
| spellingShingle |
Boykin, P. Oscar Mor, Tal Roychowdhury, Vwani Vatan, Farrokh Algorithms on ensemble quantum computers |
| author_facet |
Boykin, P. Oscar Mor, Tal Roychowdhury, Vwani Vatan, Farrokh |
| author_sort |
Boykin, P. Oscar |
| title |
Algorithms on ensemble quantum computers |
| title_short |
Algorithms on ensemble quantum computers |
| title_full |
Algorithms on ensemble quantum computers |
| title_fullStr |
Algorithms on ensemble quantum computers |
| title_full_unstemmed |
Algorithms on ensemble quantum computers |
| title_sort |
algorithms on ensemble quantum computers |
| description |
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor’s factorization algorithm, Grover’s search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\sigma_{z}^{1/4},$$\end{document} as these operations cannot be implemented “bitwise”, and their standard fault-tolerant implementations require measurement. |
| publisher |
Springer Netherlands |
| publishDate |
2009 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3063506/ |
| _version_ |
1611446814577262592 |