Universal dynamical scaling laws in three-state quantum walks.

Area of Science:

• Quantum mechanics
• Quantum computation
• Condensed matter physics

Background:

• Quantum walks are fundamental tools for quantum computation and simulation.
• Understanding wave packet dynamics, especially trapping and spreading, is crucial for controlling quantum systems.

Purpose of the Study:

• To investigate the finite-time scaling behavior of a three-state quantum walk near its detrapping point.
• To analyze the influence of the coin operator's parameter (ρ) and mixing angle (θ) on wave packet dynamics.
• To elucidate the scaling of the participation ratio and survival probability.

Main Methods:

• Finite-time scaling analysis applied to a three-state quantum walk on a line.
• Parametrization of the coin operator by ρ to control spreading velocity.
• Preparation of a symmetric input state with a specific mixing angle θ.
• Analysis of the detrapping angle θc(ρ) where wave packet trapping ceases.

Main Results:

• Relevant quantities, including survival probability and participation ratio, exhibit single-parameter scaling near the detrapping angle θc.
• The participation ratio demonstrates linear growth in time with a logarithmic correction.
• This finding provides insight into previously reported sublinear behavior of the participation ratio.

Conclusions:

• The study reveals universal scaling behaviors for quantum walks near critical points.
• The identified linear scaling with a logarithmic correction for the participation ratio offers a more precise description of wave packet spreading.
• These results contribute to a deeper understanding of quantum transport phenomena and the design of quantum algorithms.