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Quantum Optimization Quantum Machine Learning Quantum Simulation

Faster Search by Lackadaisical Quantum Walk

arXiv

Authors: Thomas G. Wong

Year

2017

Paper ID

45075

Status

Preprint

Abstract Read

~2 min

Abstract Words

131

Citations

N/A

Abstract

In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of O\(1/log N\) in O\(sqrt{N log N}\) steps, which with amplitude amplification yields an overall runtime of O\(sqrt{N} log N\). We show that making the quantum walk lackadaisical or lazy by adding a self-loop of weight 4/N to each vertex speeds up the search, causing the success probability to reach a constant near 1 in O\(sqrt{N log N}\) steps, thus yielding an O\(sqrt{log N}\) improvement over the typical, loopless algorithm. This improved runtime matches the best known quantum algorithms for this search problem. Our results are based on numerical simulations since the algorithm is not an instance of the abstract search algorithm.

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This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
It adds a 2017 reference point for readers tracking recent quantum research.
In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of O(1/log N) in O(sqrtN log N) steps, which...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1706.06939 [2] arXiv https://arxiv.org/abs/1706.06939 [3] Publisher https://arxiv.org/abs/1706.06939

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