Finding Small and Large <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Clique Instances on a Quantum Computer
Algorithms for triangle finding, the smallest nontrivial instance of the k-clique problem, have been proposed for quantum computers. Still, those algorithms assume the use of fixed access time quantum RAM. In this article, we present a practical gate-based approach to both the triangle-finding probl...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2020-01-01
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| Series: | IEEE Transactions on Quantum Engineering |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9298960/ |
| _version_ | 1818620502886842368 |
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| author | Sara Ayman Metwalli Francois Le Gall Rodney Van Meter |
| author_facet | Sara Ayman Metwalli Francois Le Gall Rodney Van Meter |
| author_sort | Sara Ayman Metwalli |
| collection | DOAJ |
| description | Algorithms for triangle finding, the smallest nontrivial instance of the k-clique problem, have been proposed for quantum computers. Still, those algorithms assume the use of fixed access time quantum RAM. In this article, we present a practical gate-based approach to both the triangle-finding problem and its NP-hard k-clique generalization. We examine both constant factors for near-term implementation on a noisy intermediate scale quantum computing (NISQ) device and the scaling of the problem to evaluate long-term use of quantum computers. We compare the time complexity and circuit practicality of the theoretical approach and actual implementation. We propose and apply two different strategies to the k-clique problem, examining the circuit size of Qiskit implementations. We analyze our implementations by simulating triangle finding with various error models, observing the effect on damping the amplitude of the correct answer, and compare to execution on six real IBM quantum machines. Finally, we estimate the approximate quantum volume needed so that the smallest instance of our approach can be executable with minimal error on a real NISQ device. |
| first_indexed | 2024-12-16T17:54:24Z |
| format | Article |
| id | doaj.art-b82dcabe1e844de78641031feb9c7dec |
| institution | Directory Open Access Journal |
| issn | 2689-1808 |
| language | English |
| last_indexed | 2024-12-16T17:54:24Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Transactions on Quantum Engineering |
| spelling | doaj.art-b82dcabe1e844de78641031feb9c7dec2022-12-21T22:22:12ZengIEEEIEEE Transactions on Quantum Engineering2689-18082020-01-01111110.1109/TQE.2020.30456929298960Finding Small and Large <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Clique Instances on a Quantum ComputerSara Ayman Metwalli0https://orcid.org/0000-0002-9874-2306Francois Le Gall1Rodney Van Meter2Keio University Quantum Computing Center, Keio University, Tokyo, JapanGraduate School of Mathematics, Nagoya University, Nagoya, JapanKeio University Quantum Computing Center, Keio University, Tokyo, JapanAlgorithms for triangle finding, the smallest nontrivial instance of the k-clique problem, have been proposed for quantum computers. Still, those algorithms assume the use of fixed access time quantum RAM. In this article, we present a practical gate-based approach to both the triangle-finding problem and its NP-hard k-clique generalization. We examine both constant factors for near-term implementation on a noisy intermediate scale quantum computing (NISQ) device and the scaling of the problem to evaluate long-term use of quantum computers. We compare the time complexity and circuit practicality of the theoretical approach and actual implementation. We propose and apply two different strategies to the k-clique problem, examining the circuit size of Qiskit implementations. We analyze our implementations by simulating triangle finding with various error models, observing the effect on damping the amplitude of the correct answer, and compare to execution on six real IBM quantum machines. Finally, we estimate the approximate quantum volume needed so that the smallest instance of our approach can be executable with minimal error on a real NISQ device.https://ieeexplore.ieee.org/document/9298960/Clique findinggraph algorithmGrover's algorithmnoisy intermediate scale quantum computing (NISQ) |
| spellingShingle | Sara Ayman Metwalli Francois Le Gall Rodney Van Meter Finding Small and Large <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Clique Instances on a Quantum Computer IEEE Transactions on Quantum Engineering Clique finding graph algorithm Grover's algorithm noisy intermediate scale quantum computing (NISQ) |
| title | Finding Small and Large <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Clique Instances on a Quantum Computer |
| title_full | Finding Small and Large <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Clique Instances on a Quantum Computer |
| title_fullStr | Finding Small and Large <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Clique Instances on a Quantum Computer |
| title_full_unstemmed | Finding Small and Large <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Clique Instances on a Quantum Computer |
| title_short | Finding Small and Large <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Clique Instances on a Quantum Computer |
| title_sort | finding small and large inline formula tex math notation latex k tex math inline formula clique instances on a quantum computer |
| topic | Clique finding graph algorithm Grover's algorithm noisy intermediate scale quantum computing (NISQ) |
| url | https://ieeexplore.ieee.org/document/9298960/ |
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