A loop in time

Synge Todo

Huiquan Wang, Jie Zhou, Junjie Wu +1 more

How self-loops on vertices affect quantum walks is an interesting issue, and self-loops play important roles in quantum walk based algorithms. However, the original model that adjusting the effect of self-loops by changing their number has limitations. For example, the effect of self-loops cannot be adjusted continuously, for their number must be an integer. In this paper, we proposed a model of adjustable self-loop on discrete-time quantum walk, whose weight is controlled by a real parameter in the coin operator. The proposed method not only generalises the situations where the number of self-loops is an integer, but also provides a way to adjust the weight of the self-loop continuously. It enhances the potential of self-loops in applications. For instance, we improve the success rate of the quantum walk based search on a $20\times20$ two-dimension lattice from $23.6\%$ to $97.2\%$ by the proposed method. And the success rate of the improved search, which only scales as $O(1/\log{N})$ before being improved, even increases slightly with the size of the lattice. To the best of our knowledge, this is the first time that such an improvement is achieved on the quantum walk based spatial search.

David Thomas Pegg

The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one particular case at least, the condition of self consistency is ensured by the interference of quantum mechanical amplitudes associated with the loop. If this can be applied to all loops then we have a mechanism by which inconsistent loops eliminate themselves.

Kimberly R. Chapin, Marlan O. Scully, Muhammad Suhail Zubairy

Shuofeng Liang, Leicheng Yin, Zhenzhen Zhang +5 more

Abstract The stability of the scattering loop is fundamental for coherent random lasing in a dynamic scattering system. In this work, fluorescence of DPP (N, N-di [3-(isobutyl polyhedral oligomeric silsesquioxanes) propyl] perylene diimide) is scattered to produce RL and we realize the transition from incoherent RL to coherent RL by controlling the Brownian motion of the scatterers (dimer aggregates of DPP) and the stability of scattering loop. To produce coherent random lasers, the loop needs to maintain a stable state within the loop-stable time, which can be determined through controlled Brownian motion of scatterers in the scattering system. The result shows that the loop-stable time is within 5.83 × 10 −5 s to 1.61 × 10 −4 s based on the transition from coherent to incoherent random lasing. The time range could be tuned by finely controlling the viscosity of the solution. This work not only develops a method to predict the loop-stable time, but also develops the study between Brownian motion and random lasers, which opens the road to a variety of novel interdisciplinary investigations involving modern statistical mechanics and disordered photonics.

Dieter Meschede