Tuning for Quantum Speedup in Directed Lackadaisical Quantum Walks
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910448612278272 |
|---|---|
| author | Naredi, Pranay Kannan, J. Bharathi Santhanam, M. S. |
| author_facet | Naredi, Pranay Kannan, J. Bharathi Santhanam, M. S. |
| contents | Quantum walks constitute an important tool for designing quantum algorithms and information processing tasks. In a lackadaisical walk, in addition to the possibility of moving out of a node, the walker can remain on the same node with some probability. This is achieved by introducing self-loops, parameterized by self-loop strength $l$, attached to the nodes such that large $l$ implies a higher likelihood for the walker to be trapped at the node. In this work, {\it directed}, lackadaisical quantum walks is studied. Depending on $l$, two regimes are shown to exist -- one in which classical walker dominates and the other dominated by the quantum walker. In the latter case, we also demonstrate the existence of two distinct scaling regimes with $l$ for quantum walker on a line and on a binary tree. Surprisingly, a significant quantum-induced speedup is realized for large $l$. By tuning the initial state, the extent of this speedup can be manipulated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06167 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tuning for Quantum Speedup in Directed Lackadaisical Quantum Walks Naredi, Pranay Kannan, J. Bharathi Santhanam, M. S. Quantum Physics Quantum walks constitute an important tool for designing quantum algorithms and information processing tasks. In a lackadaisical walk, in addition to the possibility of moving out of a node, the walker can remain on the same node with some probability. This is achieved by introducing self-loops, parameterized by self-loop strength $l$, attached to the nodes such that large $l$ implies a higher likelihood for the walker to be trapped at the node. In this work, {\it directed}, lackadaisical quantum walks is studied. Depending on $l$, two regimes are shown to exist -- one in which classical walker dominates and the other dominated by the quantum walker. In the latter case, we also demonstrate the existence of two distinct scaling regimes with $l$ for quantum walker on a line and on a binary tree. Surprisingly, a significant quantum-induced speedup is realized for large $l$. By tuning the initial state, the extent of this speedup can be manipulated. |
| title | Tuning for Quantum Speedup in Directed Lackadaisical Quantum Walks |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2211.06167 |