Abstract
We present a comprehensive review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains. Moreover, we introduce a novel scheme for DTQWs using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects in photonic systems.
Highlights
Quantum computation is an interdisciplinary field that encompasses several interconnected branches such as quantum algorithms, quantum information, and quantum communication
Among the promising conjectures predicted by quantum information and communication, we find the development of more powerful algorithms that may allow to significantly increase the processing capacity and may enable the quantum simulation of complex physical systems and mathematical problems for which we know no classical digital computer algorithm that could efficiently simulate them at present
We report on the progress in the characterization of geometry and topology of discrete-time quantum walks (DTQW) architectures consisting of a unitary step U given by a sequence of two non-commuting rotations in parameter space, followed by a spindependent translation
Summary
Quantum computation is an interdisciplinary field that encompasses several interconnected branches such as quantum algorithms, quantum information, and quantum communication. Quantum walks involving multiple particles guarantee a relentless tool for encoding quantum information in an exponentially large Hilbert space [42], as well as for simulations in quantum chemical, biological and physical systems [43], in 1D and 2D geometries [44–46]. In this Chapter, we present a comprehensive review of photonic realizations of DTQW in both, the spatial [47] and the temporal [48] realms, based on spatialmultiplexing and time-multiplexing techniques, respectively. Part of this review is based on the work by the Author, selected as the cover story of a Special Issue on Quantum Topology, for the journal Crystals (MDPI) in 2017 [2]
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