Simple exact quantum search
While Grover’s search algorithm is asymptotically optimal, it does not always result in a real solution. If the search fails, the algorithm must be ran again from the beginning, conditionally doubling the effective number of oracle calls. Previous research attempted to fix this issue by modifying th...
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| Published in: | Quantum information processing Vol. 23; no. 10 |
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| Abstract | While Grover’s search algorithm is asymptotically optimal, it does not always result in a real solution. If the search fails, the algorithm must be ran again from the beginning, conditionally doubling the effective number of oracle calls. Previous research attempted to fix this issue by modifying the oracle or alternating between numerically optimized reflectors. In this paper, we present an optimal initial state and reflector that produce an exact search with Grover’s algorithm at the cost of at most one additional oracle call beyond the optimum, a cost which can be nullified if we know a non-solution. We do this without modifying the oracle, without changing the diffuser at each step and even without any numerical optimization procedure required. |
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| AbstractList | While Grover’s search algorithm is asymptotically optimal, it does not always result in a real solution. If the search fails, the algorithm must be ran again from the beginning, conditionally doubling the effective number of oracle calls. Previous research attempted to fix this issue by modifying the oracle or alternating between numerically optimized reflectors. In this paper, we present an optimal initial state and reflector that produce an exact search with Grover’s algorithm at the cost of at most one additional oracle call beyond the optimum, a cost which can be nullified if we know a non-solution. We do this without modifying the oracle, without changing the diffuser at each step and even without any numerical optimization procedure required. |
| ArticleNumber | 356 |
| Author | Tănăsescu, Andrei Popescu, Pantelimon George Guţoiu, Raj Alexandru |
| Author_xml | – sequence: 1 givenname: Raj Alexandru surname: Guţoiu fullname: Guţoiu, Raj Alexandru organization: Computer Science and Engineering Department, National University of Science and Technology POLITEHNICA Bucharest – sequence: 2 givenname: Andrei surname: Tănăsescu fullname: Tănăsescu, Andrei organization: Computer Science and Engineering Department, National University of Science and Technology POLITEHNICA Bucharest – sequence: 3 givenname: Pantelimon George surname: Popescu fullname: Popescu, Pantelimon George email: pgpopescu@upb.ro organization: Computer Science and Engineering Department, National University of Science and Technology POLITEHNICA Bucharest |
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| Cites_doi | 10.1145/502090.502097 10.1103/PhysRevA.77.042324 10.1103/PhysRevA.108.022417 10.1103/PhysRevA.78.052310 10.1103/PhysRevResearch.4.L022013 10.1103/PhysRevLett.79.325 10.1103/PhysRevA.64.022307 10.1016/S0375-9601(99)00631-3 10.1007/s11433-023-2130-9 10.1016/j.ic.2023.105042 10.1016/j.physleta.2007.02.029 10.1103/PhysRevLett.100.160501 10.1016/j.rinp.2024.107595 10.1103/PhysRevResearch.5.023202 10.1090/conm/305/05215 10.1007/s11128-019-2565-2 10.1137/1.9781611976014.5 10.1145/237814.237866 |
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| Keywords | Success rate Grover algorithm Restricted oracle Quantum search |
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| Snippet | While Grover’s search algorithm is asymptotically optimal, it does not always result in a real solution. If the search fails, the algorithm must be ran again... |
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| SubjectTerms | Data Structures and Information Theory Diffusers Mathematical Physics Optimization Physics Physics and Astronomy Quantum Computing Quantum Information Technology Quantum Physics Reflectors Search algorithms Spintronics |
| Title | Simple exact quantum search |
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