Abstract
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects and the use of non-local coin operations based on two-photon hybrid entanglement.
Highlights
The quantum walk is one of the most striking manifestations of how quantum interference leads to a strong departure between quantum and classical phenomena [1]
We reported on different approaches to photonic discrete-time quantum walk (DTQW) architectures
Implementations based on spatial- or temporal-mode multiplexing techniques, and implementations based on transverse photonic modes controlled by spatial light modulators (SLMs)
Summary
The quantum walk is one of the most striking manifestations of how quantum interference leads to a strong departure between quantum and classical phenomena [1]. DTQWs are robust platforms for modeling a variety of dynamical processes from excitation transfer in spin chains [19,20] to energy transport in biological complexes [21] They enable to study multi-path quantum interference phenomena [22,23,24,25] and can provide for a route to validation of quantum complexity [26,27] and universal quantum computing [28]. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution It works in an automated way by preparing the input state to the n-th step, applying a one-step evolution using the photon polarization as the quantum “coin”, and, measuring the probability distribution at the output spatial modes. Part of this review is based on the work by Puentes, selected as the cover story of a Special Issue on Quantum Topology, for the journal Crystals (MDPI) in 2017 [36]
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