Tuning for Quantum Speedup in Directed Lackadaisical Quantum Walks

• URL: http://arxiv.org/abs/2211.06167v3
• Date: Thu, 16 May 2024 12:55:56 GMT
• Title: Tuning for Quantum Speedup in Directed Lackadaisical Quantum Walks
• Authors: Pranay Naredi, J. Bharathi Kannan, M. S. Santhanam,
• Abstract summary: Quantum walks constitute an important tool for designing quantum algorithms and information processing tasks. In a lackadaisical walk, the walker can remain on the same node with some probability. Surprisingly, a significant quantum-induced speedup is realized for large $l$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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