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Coherence as resource in scattering quantum walk search on complete graph.
Yun-Long Su1,2,3, Si-Yuan Liu4,5,6, Xiao-Hui Wang2,3
1Institute of Modern Physics, Northwest University, Xi'an, 710069, China.
Scientific Reports
|July 25, 2018
Summary
Coherence drives quantum walk search speed-up by increasing success probability. Without coherence, the quantum algorithm performs like a classical search, highlighting coherence
Area of Science:
- Quantum Information Science
- Quantum Computing Algorithms
- Graph Theory
Background:
- Quantum walks offer advantages over classical search algorithms.
- Coherence is a key resource in quantum computation.
- Scattering quantum walks are a specific type of quantum walk with potential applications.
Purpose of the Study:
- To investigate the role of coherence in scattering quantum walk search.
- To analyze the algorithm's performance on large complete graphs (N >> v).
- To understand the impact of noise on coherence and search success probability.
Main Methods:
- Theoretical analysis of coherence consumption in quantum walk search.
- Modeling the effects of photon loss and random phase shifts.
- Comparison of quantum search with classical blind search.
Main Results:
- Coherence consumption correlates with increased success probability and query efficiency.
- Incoherent states result in classical blind search performance.
- Photon loss and phase shifts degrade performance by reducing coherence and hindering interference.
Conclusions:
- Coherence is essential for achieving quantum speed-up in scattering quantum walk search.
- Noise significantly impacts the algorithm's effectiveness.
- Understanding coherence dynamics is crucial for practical quantum search implementations.
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