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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.14314 |
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| _version_ | 1866913342091689984 |
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| author | Ortega, Sergio A. Martin-Delgado, Miguel A. |
| author_facet | Ortega, Sergio A. Martin-Delgado, Miguel A. |
| contents | Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a classical simulator. However, the current simulation algorithms require a great deal of memory due to the particular formulation of this quantum walk. In this paper we propose a memory-saving algorithm that scales as $\mathcal{O}(N^2)$ with the size $N$ of the graph. We provide additional procedures for simulating Szegedy's quantum walk over mixed states and also the Semiclassical Szegedy walk. With these techniques we have built a classical simulator in Python called SQUWALS. We show that our simulator scales as $\mathcal{O}(N^2)$ in both time and memory resources. This package provides some high-level applications for algorithms based on Szegedy's quantum walk, as for example the quantum PageRank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14314 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | SQUWALS: A Szegedy QUantum WALks Simulator Ortega, Sergio A. Martin-Delgado, Miguel A. Quantum Physics Software Engineering Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a classical simulator. However, the current simulation algorithms require a great deal of memory due to the particular formulation of this quantum walk. In this paper we propose a memory-saving algorithm that scales as $\mathcal{O}(N^2)$ with the size $N$ of the graph. We provide additional procedures for simulating Szegedy's quantum walk over mixed states and also the Semiclassical Szegedy walk. With these techniques we have built a classical simulator in Python called SQUWALS. We show that our simulator scales as $\mathcal{O}(N^2)$ in both time and memory resources. This package provides some high-level applications for algorithms based on Szegedy's quantum walk, as for example the quantum PageRank. |
| title | SQUWALS: A Szegedy QUantum WALks Simulator |
| topic | Quantum Physics Software Engineering |
| url | https://arxiv.org/abs/2307.14314 |