Quantum Spatial Search with Electric Potential: Long-Time Dynamics and Robustness to Noise

Area of Science:

• Quantum Computing
• Quantum Algorithms
• Condensed Matter Physics

Background:

• Quantum spatial search algorithms offer potential speedups over classical methods.
• Discrete-time quantum walks (DQW) are a key framework for developing quantum search algorithms.

Purpose of the Study:

• To analyze a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb potential for quantum spatial search.
• To investigate the algorithm's performance and robustness under noisy conditions.

Main Methods:

• Simulations of a 2D Dirac DQW with a Coulomb electric field acting as the search oracle.
• Analysis of localization probability and search time scaling with grid size (N).
• Introduction of spatial and spatiotemporal noise to the Coulomb potential to assess robustness.

Main Results:

• Observation of a second localization peak around the target node, reached in O(N) time with O(1/lnN) probability.
• Demonstration of high robustness of the search to spatial noise, particularly for the second localization peak.
• Significant robustness of the first localization peak to spatiotemporal noise.

Conclusions:

• The electric Dirac DQW scheme provides an efficient quantum spatial search mechanism.
• The algorithm exhibits notable resilience to noise, enhancing its practical applicability in quantum systems.