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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/2302.08871 |
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| _version_ | 1866913504043204608 |
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| author | Boito, P. Del Corso, G. M. |
| author_facet | Boito, P. Del Corso, G. M. |
| contents | In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known to be of the order of the square root of classical hitting time: this quadratic speedup is a remarkable example of the computational advantages associated with quantum approaches.
Our purpose here is twofold. On one hand, we provide a detailed proof of quadratic speedup for time-reversible walks within the Szegedy framework, in a language that should be familiar to the linear algebra community. Moreover, we explore the use of a general distribution in place of the stationary distribution in the definition of quantum hitting time, through theoretical considerations and numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08871 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Hitting Time according to a given distribution Boito, P. Del Corso, G. M. Quantum Physics Numerical Analysis 81P45, 65F99 In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known to be of the order of the square root of classical hitting time: this quadratic speedup is a remarkable example of the computational advantages associated with quantum approaches. Our purpose here is twofold. On one hand, we provide a detailed proof of quadratic speedup for time-reversible walks within the Szegedy framework, in a language that should be familiar to the linear algebra community. Moreover, we explore the use of a general distribution in place of the stationary distribution in the definition of quantum hitting time, through theoretical considerations and numerical experiments. |
| title | Quantum Hitting Time according to a given distribution |
| topic | Quantum Physics Numerical Analysis 81P45, 65F99 |
| url | https://arxiv.org/abs/2302.08871 |