Abstract
We realize the quasi-periodic dynamics of a quantum walker over 2.5 quasi-periods by realizing the walker as a single photon passing through a quantum-walk optical-interferometer network. We introduce fully controllable polarization-independent phase shifters in each optical path to realize arbitrary site-dependent phase shifts, and employ large clear-aperture beam displacers, while maintaining high-visibility interference, to enable 10 quantum-walk steps to be reached. By varying the half-wave-plate setting, we control the quantum-coin bias thereby observing a transition from quasi-periodic dynamics to ballistic diffusion.
Highlights
The quantum walk (QW) [1, 2] is a quantized version of the ubiquitous random walk (RW) used for describing diffusion [3], for probabilistic algorithms [4] to solve constraint satisfaction problems in computer science [5], for quantum transport in complex systems [6] and for demonstrating intriguing nonlinear dynamical quantum phenomena [7]
We realize quasi-periodic dynamics of a quantum walker over 2.5 quasi-periods by realizing the walker as a single photon passing through a quantum-walk optical-interferometer network
The randomness o√f the coin flip leads to a diffusion rate that increases as t with t the time of evolution; this square-root dependence is characteristic of diffusive spreading, with “spread” signifying the width of the position distribution Pt(x) at time t
Summary
The quantum walk (QW) [1, 2] is a quantized version of the ubiquitous random walk (RW) used for describing diffusion [3], for probabilistic algorithms [4] to solve constraint satisfaction problems in computer science [5], for quantum transport in complex systems [6] and for demonstrating intriguing nonlinear dynamical quantum phenomena [7]. By varying the half-wave-plate setting, we control the quantum-coin bias thereby observing a transition from quasi-periodic dynamics to ballistic diffusion.
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