Quantum Boomerang in Discrete Walks: A New Mechanism for Wave Packet Return ✦
The emergence of the quantum boomerang effect in discrete quantum walks with phase disorder is investigated. It is shown that the effect is caused solely by the intrinsic momentum dynamics and does not require external asymmetry. The evolution of the mean position depends significantly on the initial walker state and the quantum coin operator, enabling selective triggering of the boomerang effect in both or just one component of the wave packet associated with specific internal states. When varying the coin parameter θ near the Pauli-Z coin, a power-law decay of the maximum mean position, proportional to the square of the inverse parameter θ, is found. A dependence X_Max proportional to W^(-2) is also revealed, consistent with the localization length in disordered quantum systems. This dependence on internal states provides a tool for controlling quantum transport and may find applications in quantum state manipulation, spatial separation of information carriers, and targeted data retrieval.
Context
Understanding how information spreads in disordered quantum systems is crucial for describing decoherence and localization. The boomerang effect sits at the boundary between ballistic spreading and full Anderson localization, showcasing the return of a wave packet's average position after an initial displacement. Previously observed in ultracold atoms, it remained unexplored in quantum computing platforms like discrete quantum walks. This work fills that gap, revealing how internal degrees of freedom and superposition of states, as described by Erwin Schrödinger, can generate the boomerang effect without external momentum, drawing on concepts by David Deutsch in quantum computing.
Methods
The authors numerically simulated one-dimensional discrete quantum walks of a qubit with initial states on the Bloch sphere. The evolution operator included phase disorder characterized by width W, and a quantum coin parameterized by angle θ. Calculations were performed for a chain of N+1 sites, averaging over 50,000 disorder realizations. The dynamics of the centroid X(t) and its components in the coin basis were tracked to reveal each contribution to the boomerang effect. This allowed studying the influence of entanglement between internal and spatial degrees of freedom.
Results
It was found that with disorder (W=0.2) and asymmetric initial states, the centroid first shifts and then returns, exhibiting the quantum boomerang effect. Unlike predictions from the standard model, after return the wave packet localizes on the opposite side of the starting point, not at zero. The maximum displacement Xmax shows power-law dependence: Xmax ~ θ^{-2} near the Pauli-Z coin, and Xmax ~ W^{-2} on disorder strength. For symmetric initial states, the effect is absent. The return time strongly depends on the coin choice: for θ near π/2 (Pauli-X coin), Anderson localization suppresses the boomerang, while for small θ it persists even under strong disorder. With weak disorder (W=0.1) and θ=π/9, the maximum displacement reached ~90 lattice steps.
Implications
These results deepen our understanding of the boundary between ballistic transport and localization in quantum systems with internal degrees of freedom. Selectively controlling the boomerang effect via initial state and coin parameters paves the way for controlled spatial separation of quantum information carriers. This could be harnessed for targeted information extraction and noise suppression in quantum algorithms implemented on quantum walk platforms.
Future development
Future research could involve multidimensional lattices, correlated or time-dependent disorder, and the role of measurements in the spirit of John von Neumann and decoherence. This will test the robustness of the boomerang effect in open quantum systems and extend its application to quantum simulations and secure data transmission protocols.
Impact
The results will impact the development of quantum computers and simulators based on quantum walks, as well as quantum transport control in photonic lattices and superconducting circuits.
Next steps
Next steps: experimental realization of the effect in integrated photonic circuits or ion traps to verify the predicted power laws.
Key open problems
The boomerang effect connects unsolved problems in physics: the transition from quantum chaos to localization, and the role of entanglement in suppressing transport, which could shed light on thermalization mechanisms in isolated quantum systems.
🎯 The effect is called 'boomerang' because the wave packet, like the Australian hunting tool, comes back—but, as it turns out, not always to the launch point!
Key numbers
- максимальное смещение центроида: ~90 steps at W=0.1, θ=π/9
- показатель степенного спада: -2
- число реализаций беспорядка: 50,000