A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins
In this work, the quantum random walk search algorithm with a walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with an arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are u...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/16/3/150 |
| _version_ | 1797613938905448448 |
|---|---|
| author | Hristo Tonchev Petar Danev |
| author_facet | Hristo Tonchev Petar Danev |
| author_sort | Hristo Tonchev |
| collection | DOAJ |
| description | In this work, the quantum random walk search algorithm with a walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with an arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are used to find walk coins that make the quantum algorithm more robust to deviations in the coin’s parameters. This is achieved by introducing functional dependence between these parameters. The functions that give the best performance of the algorithm are studied in detail by numerical statistical methods. A thorough comparison between our modification and an algorithm, with coins made using only Householder reflection, shows significant advantages of the former. By applying a deep neural network, we make a prediction for the parameters of an optimal coin with an arbitrary size and estimate the algorithm’s stability for such a coin. |
| first_indexed | 2024-03-11T07:02:43Z |
| format | Article |
| id | doaj.art-9739f16a6301438c83efc9b0c29785be |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-11T07:02:43Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-9739f16a6301438c83efc9b0c29785be2023-11-17T09:09:15ZengMDPI AGAlgorithms1999-48932023-03-0116315010.3390/a16030150A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder CoinsHristo Tonchev0Petar Danev1Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussée, 1784 Sofia, BulgariaInstitute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussée, 1784 Sofia, BulgariaIn this work, the quantum random walk search algorithm with a walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with an arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are used to find walk coins that make the quantum algorithm more robust to deviations in the coin’s parameters. This is achieved by introducing functional dependence between these parameters. The functions that give the best performance of the algorithm are studied in detail by numerical statistical methods. A thorough comparison between our modification and an algorithm, with coins made using only Householder reflection, shows significant advantages of the former. By applying a deep neural network, we make a prediction for the parameters of an optimal coin with an arbitrary size and estimate the algorithm’s stability for such a coin.https://www.mdpi.com/1999-4893/16/3/150quantum algorithmsquantum random walkquantum searchquditsgeneralized householder reflectionsupervised machine learning |
| spellingShingle | Hristo Tonchev Petar Danev A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins Algorithms quantum algorithms quantum random walk quantum search qudits generalized householder reflection supervised machine learning |
| title | A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins |
| title_full | A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins |
| title_fullStr | A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins |
| title_full_unstemmed | A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins |
| title_short | A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins |
| title_sort | machine learning study of high robustness quantum walk search algorithm with qudit householder coins |
| topic | quantum algorithms quantum random walk quantum search qudits generalized householder reflection supervised machine learning |
| url | https://www.mdpi.com/1999-4893/16/3/150 |
| work_keys_str_mv | AT hristotonchev amachinelearningstudyofhighrobustnessquantumwalksearchalgorithmwithqudithouseholdercoins AT petardanev amachinelearningstudyofhighrobustnessquantumwalksearchalgorithmwithqudithouseholdercoins AT hristotonchev machinelearningstudyofhighrobustnessquantumwalksearchalgorithmwithqudithouseholdercoins AT petardanev machinelearningstudyofhighrobustnessquantumwalksearchalgorithmwithqudithouseholdercoins |