Bosonic and Fermionic Models of Two-Dimensional Quantum Walks

Linda Sansoni

Linda Sansoni, Fabio Sciarrino, Giuseppe Vallone +4 more

Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Here we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such an experiment has been realized by exploiting polarization entanglement to simulate the bunching-antibunching feature of noninteracting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behavior, maintaining remarkable control on both phase and balancement.

Xizhou Qin, Yongguan Ke, Xi‐Wen Guan +3 more

We investigate continuous-time quantum walks of two indistinguishable particles [two bosons, or two fermions, or two hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are consistent with the recent experimental observation of two-magnon dynamics [Fukuhara et al., Nature (London) 502, 76 (2013)]. The two interacting particles can undergo independent walking and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with a statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk speed of bosons is found to be exactly three times that of fermions and HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.

Dan Li, Michael Mc Gettrick, Weiwei Zhang +1 more

Salvador Godoy, Francisco Espinosa‐Magaña

With the help of quantum-scattering-theory methods and the approximation of the stationary phase, we propose a one-dimensional quantum-random-walk (QRW) model, which describes for both tunneling and scattering above the potential, the coherent diffusion of independent particles described by wave packets in a periodic one-dimensional lattice. The QRW model describes for each lattice cell the time evolution of modulating amplitudes of two opposite-moving wave packets as they are scattered by periodic potential barriers. Since the QRW model is a coherent process, interference contributions in the probabilities bring about strong departures from classical results. For many identical free particles we obtain the theoretical and graphical Bose and Fermi two-body QRW probability distribution. The result is generalized to N identical free particles and we obtain the N-body Bose and Fermi QRW probability distribution.

Dan Li, Michael Mc Gettrick, Weiwei Zhang +1 more