Two-walker discrete-time quantum walks on the line with percolation

Abstract

One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles performing a quantum walk on the line when the possibility of lattice imperfections, in the form of missing links, is considered. We investigate two regimes, statical and dynamical percolation, that correspond to different time scales for the imperfections evolution with respect to the quantum-walk one. By studying the qualitative behaviour of three two-particle quantities for different probabilities of having missing bonds, we argue that the chosen symmetry under particle-exchange of the input state strongly affects the output of the walk, even in noisy and highly non-ideal regimes. We provide evidence against the possibility of gathering information about the walkers indistinguishability from the observation of bunching phenomena in the output distribution, in all those situations that require a comparison between averaged quantities. Although the spread of the walk is not substantially changed by the addition of a second particle, we show that the presence of multiple walkers can be beneficial for a procedure to estimate the probability of having a broken link.

Two-particle quantum correlations in stochastically-coupled networks

“…An important aspect to point out regarding the results shown in figure 3 is the computation time required for obtaining them. Remarkably, solving the master equation in equation (13) takes ∼0.521 s; whereas the pure numerical solution of equation (12) takes ∼2.4 h. This implies that our derived master equation improves the computation time by at least four orders of magnitude, while providing the maximum accuracy possible (see appendix B for details).…”

“…which is the master equation that describes the time evolution of two correlated particles in a stochasticallycoupled quantum network. Note that we can write equation (13) in its equivalent Lindblad form by following the procedure described above and noticing that the Hamiltonian for the two-particle system is given by…”

“…The study of quantum random walks in noisy environments have played a fundamental role in understanding non-trivial quantum phenomena observed in an interdisciplinary framework of studies ranging from biology [1,2], chemistry [3], materials science [4] and electronics [5], to photonics [6][7][8][9] and ultracold matter [10,11]. For many years, most of the research efforts had been focused on the propagation of single particles [12]; however, a great interest in describing the dynamics of correlated particles in noisy systems has recently arisen [13][14][15][16], mainly because it has been recognized that many-particle quantum correlations can be preserved in noisy networks by properly controlling the initial state of the particles, their statistics, indistinguishability or their type of interaction [17,18].…”

Bosonic Random Walk Neural Networks for Graph Learning

“…We implement the simulation of quantum walkers as described in Gamble et al (2010); Rigovacca and Di Franco (2016). For simplicity, we shall limit the exposition to involve only 2 particles.…”

Two-particle quantum correlations in stochastically-coupled networks

“…The study of quantum random walks in noisy environments have played a fundamental role in understanding non-trivial quantum phenomena observed in an interdisciplinary framework of studies ranging from biology [1,2], chemistry [3], and electronics [4], to photonics [5,6,7,8] and ultracold matter [9,10]. For many years, most of the research efforts had been focused on the propagation of single particles; however, a great interest in describing the dynamics of correlated particles in noisy systems has recently arisen [11,12,13], mainly because it has been recognized that many-particle quantum correlations can be preserved in noisy networks by properly controlling the initial state of the particles, their statistics, indistinguishability or their type of interaction [14,15].…”