Algebraic representation of three qubit quantum circuit problems
The evolution of quantum states serves as good fundamental studies in understanding the quantum information systems which finally lead to the research on quantum computation. To carry out such a study, mathematical tools such as the Lie group and their associated Lie algebra is of great importance....
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my.upm.eprints.1001642024-07-18T07:35:18Z http://psasir.upm.edu.my/id/eprint/100164/ Algebraic representation of three qubit quantum circuit problems Chew, K. Y. Shah, N. M. Chan, K. T. The evolution of quantum states serves as good fundamental studies in understanding the quantum information systems which finally lead to the research on quantum computation. To carry out such a study, mathematical tools such as the Lie group and their associated Lie algebra is of great importance. In this study, the Lie algebra of su(8) is represented in a tensor product operation between three Pauli matrices. This can be realized by constructing the generalized Gell-Mann matrices and comparing them to the Pauli bases. It is shown that there is a one-to-one correlation of the Gell-Mann matrices with the Pauli basis which resembled the change of coordinates. Together with the commutator relations and the frequency analysis of the structure constant via the algebra, the Lie bracket operation will be highlighted providing insight into relating quantum circuit model with Lie Algebra. These are particularly useful when dealing with three-qubit quantum circuit problems which involve quantum gates that is derived from the SU(8) Lie group. UPM Press 2022-09 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/100164/1/Algebraic%20representation%20of%20three%20qubit%20quantum%20circuit%20problems.pdf Chew, K. Y. and Shah, N. M. and Chan, K. T. (2022) Algebraic representation of three qubit quantum circuit problems. Malaysian Journal of Mathematical Sciences, 16 (3). pp. 559-582. ISSN 1823-8343; ESSN: 2289-750X https://mjms.upm.edu.my/lihatmakalah.php?kod=2022/September/16/3/559-582 10.47836/mjms.16.3.10 |
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The evolution of quantum states serves as good fundamental studies in understanding the quantum information systems which finally lead to the research on quantum computation. To carry out such a study, mathematical tools such as the Lie group and their associated Lie algebra is of great importance. In this study, the Lie algebra of su(8) is represented in a tensor product operation between three Pauli matrices. This can be realized by constructing the generalized Gell-Mann matrices and comparing them to the Pauli bases. It is shown that there is a one-to-one correlation of the Gell-Mann matrices with the Pauli basis which resembled the change of coordinates. Together with the commutator relations and the frequency analysis of the structure constant via the algebra, the Lie bracket operation will be highlighted providing insight into relating quantum circuit model with Lie Algebra. These are particularly useful when dealing with three-qubit quantum circuit problems which involve quantum gates that is derived from the SU(8) Lie group. |
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Article |
author |
Chew, K. Y. Shah, N. M. Chan, K. T. |
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Chew, K. Y. Shah, N. M. Chan, K. T. Algebraic representation of three qubit quantum circuit problems |
author_facet |
Chew, K. Y. Shah, N. M. Chan, K. T. |
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Chew, K. Y. |
title |
Algebraic representation of three qubit quantum circuit problems |
title_short |
Algebraic representation of three qubit quantum circuit problems |
title_full |
Algebraic representation of three qubit quantum circuit problems |
title_fullStr |
Algebraic representation of three qubit quantum circuit problems |
title_full_unstemmed |
Algebraic representation of three qubit quantum circuit problems |
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algebraic representation of three qubit quantum circuit problems |
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UPM Press |
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2022 |
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http://psasir.upm.edu.my/id/eprint/100164/1/Algebraic%20representation%20of%20three%20qubit%20quantum%20circuit%20problems.pdf http://psasir.upm.edu.my/id/eprint/100164/ https://mjms.upm.edu.my/lihatmakalah.php?kod=2022/September/16/3/559-582 |
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