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arXiv:1203.0785 · Quantum Information Processing

Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle

C. M. Chandrashekar, Thomas Busch

Published Mar 22, 2012• 15 citations
arXivHTMLPDF
DOI
10.1007/s11128-012-0387-6

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Quantum walks on a line with a single particle possess a classical analogue. Involving more walkers opens up the possibility of studying collective quantum effects, such as many-particle correlations. In this context, entangled initial states and the indistinguishability of the particles play a role. We consider the directional correlations between two particles performing a quantum walk on a line. For non-interacting particles, we find analytic asymptotic expressions and give the limits of directional correlations. We show that by introducing δ-interaction between the particles, one can exceed the limits for non-interacting particles.
We investigate the implementation of controlled-phase (CP) gates with quantum walks in a dual-rail encoding through the use of interacting particles. While previous proposals have focused on indistinguishable particles (bosons or fermions) to achieve unitary fidelity for plane-wave scattering, practical implementations require finite-size wavepackets and routing through single-particle gates, both factors that introduce unavoidable fidelity losses. We show that extending the interaction range beyond on-site or first-neighbor terms provides sufficient control over the scattering potential to engineer CP gates with distinguishable particles that match the ideal bosonic/fermionic performance. For finite Gaussian wavepackets, we derive analytical approximations for the gate fidelity in terms of the transmission coefficient's magnitude and phase derivatives. We find that while distinguishable-particle scattering alone exhibits slightly lower fidelity than the indistinguishable case, the overall architecture that we propose avoids the additional single-particle gates required for routing indistinguishable particles. The roundabout gates needed for the latter indeed introduce fidelity losses approximately one order of magnitude larger than the interaction-induced losses, making the distinguishable-particle approach competitive for practical implementations. Our results establish multi-neighbor interactions as a tool for quantum information processing with continuous-time quantum walks and provide quantitative guidelines for optimizing gate fidelities in finite-size systems.
We investigate the dynamics of continuous-time two-particle quantum walks on a one-dimensional noisy lattice. Depending on the initial condition, we show how the interplay between particle indistinguishability and interaction determines distinct propagation regimes. A realistic model for the environment is considered by introducing non-Gaussian noise as time-dependent fluctuations of the tunneling amplitudes between adjacent sites. We observe that the combined effect of particle interaction and fast noise (weak coupling with the environment) provides a faster propagation compared to the noiseless case. This effect can be understood in terms of the band structure of the Hubbard model, and a detailed analysis as a function of both noise and system parameters is presented.