A precise error bound for quantum phase estimation.
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be f...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2011-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC3091865?pdf=render |
| _version_ | 1828837791433228288 |
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| author | James M Chappell Max A Lohe Lorenz von Smekal Azhar Iqbal Derek Abbott |
| author_facet | James M Chappell Max A Lohe Lorenz von Smekal Azhar Iqbal Derek Abbott |
| author_sort | James M Chappell |
| collection | DOAJ |
| description | Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers. |
| first_indexed | 2024-12-12T18:48:21Z |
| format | Article |
| id | doaj.art-3e6e748f452246398e39ea39c5b76519 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-12T18:48:21Z |
| publishDate | 2011-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-3e6e748f452246398e39ea39c5b765192022-12-22T00:15:26ZengPublic Library of Science (PLoS)PLoS ONE1932-62032011-01-0165e1966310.1371/journal.pone.0019663A precise error bound for quantum phase estimation.James M ChappellMax A LoheLorenz von SmekalAzhar IqbalDerek AbbottQuantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.http://europepmc.org/articles/PMC3091865?pdf=render |
| spellingShingle | James M Chappell Max A Lohe Lorenz von Smekal Azhar Iqbal Derek Abbott A precise error bound for quantum phase estimation. PLoS ONE |
| title | A precise error bound for quantum phase estimation. |
| title_full | A precise error bound for quantum phase estimation. |
| title_fullStr | A precise error bound for quantum phase estimation. |
| title_full_unstemmed | A precise error bound for quantum phase estimation. |
| title_short | A precise error bound for quantum phase estimation. |
| title_sort | precise error bound for quantum phase estimation |
| url | http://europepmc.org/articles/PMC3091865?pdf=render |
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