Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phases
In this work we study five Grover’s algorithm modifications, where each iteration is constructed by two generalized Householder reflections, against inaccuracies in the phases. By using semi-empirical methods, we investigate various characteristics of the dependence between the probability to find s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-04-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S221137972400278X |
| _version_ | 1797213397025030144 |
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| author | Hristo Tonchev Petar Danev |
| author_facet | Hristo Tonchev Petar Danev |
| author_sort | Hristo Tonchev |
| collection | DOAJ |
| description | In this work we study five Grover’s algorithm modifications, where each iteration is constructed by two generalized Householder reflections, against inaccuracies in the phases. By using semi-empirical methods, we investigate various characteristics of the dependence between the probability to find solution and the phase errors. The first of them is the robustness of the probability to errors in the phase. The second one is how quickly the probability falls beyond the stability interval. And finally, the average success rate of the algorithm when the parameters are in the range of the highly robust interval. Two of the modifications require usage of the same Grover operator each iteration and in the other three it differs. Those semi-empirical methods give us the tool to make prediction of the quantum algorithm modifications’ overall behavior and compare them for even larger register size. |
| first_indexed | 2024-04-24T10:57:37Z |
| format | Article |
| id | doaj.art-a1475b5da7ca420084b4ae92a0607563 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-24T10:57:37Z |
| publishDate | 2024-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-a1475b5da7ca420084b4ae92a06075632024-04-12T04:45:16ZengElsevierResults in Physics2211-37972024-04-0159107595Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phasesHristo Tonchev0Petar Danev1Corresponding authors.; Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,72 Tzarigradsko Chaussée, 1784 Sofia, BulgariaCorresponding authors.; Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,72 Tzarigradsko Chaussée, 1784 Sofia, BulgariaIn this work we study five Grover’s algorithm modifications, where each iteration is constructed by two generalized Householder reflections, against inaccuracies in the phases. By using semi-empirical methods, we investigate various characteristics of the dependence between the probability to find solution and the phase errors. The first of them is the robustness of the probability to errors in the phase. The second one is how quickly the probability falls beyond the stability interval. And finally, the average success rate of the algorithm when the parameters are in the range of the highly robust interval. Two of the modifications require usage of the same Grover operator each iteration and in the other three it differs. Those semi-empirical methods give us the tool to make prediction of the quantum algorithm modifications’ overall behavior and compare them for even larger register size.http://www.sciencedirect.com/science/article/pii/S221137972400278XQuantum InformationQuantum AlgorithmsGrover’s algorithmQuantum SearchGeneralized Householder ReflectionLogistic Regression |
| spellingShingle | Hristo Tonchev Petar Danev Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phases Results in Physics Quantum Information Quantum Algorithms Grover’s algorithm Quantum Search Generalized Householder Reflection Logistic Regression |
| title | Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phases |
| title_full | Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phases |
| title_fullStr | Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phases |
| title_full_unstemmed | Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phases |
| title_short | Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phases |
| title_sort | robustness of different modifications of grover s algorithm based on generalized householder reflections with different phases |
| topic | Quantum Information Quantum Algorithms Grover’s algorithm Quantum Search Generalized Householder Reflection Logistic Regression |
| url | http://www.sciencedirect.com/science/article/pii/S221137972400278X |
| work_keys_str_mv | AT hristotonchev robustnessofdifferentmodificationsofgroversalgorithmbasedongeneralizedhouseholderreflectionswithdifferentphases AT petardanev robustnessofdifferentmodificationsofgroversalgorithmbasedongeneralizedhouseholderreflectionswithdifferentphases |