Photonic Discrete-time Quantum Walks and Applications

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.

Negative correlations can play a positive role in disordered quantum walks

“…Their setup allows the reconstruction of the local spinor state for each site which in turn provides an indirect way to quantify the entanglement entropy and related measures. In a broader view, our work brings about further prospect in the definition of correlated disorder in experimental setups for realizing quantum walk 6 – 8 .…”

“…Inasmuch as the random walk has been at the cradle of the development of processes and techniques through out one hundred-off years, the introduction of its quantum counterpart, the quantum walk 1 (QW), urged a range of prospective applications, namely those related to the Feynman’s quantum computer proposal made some 10 years earlier 2 . Formally defined by a succession of local and unitary operations on qubits, QWs have definitely established as the direct path to understand complex quantum phenomena by means of relatively simple protocols 3 – 5 that can be reproduced in a laboratory 6 – 8 or the development of quantum algorithms 5 . Explicitly, the quantum walk evolves on a Hilbert space, , by means of the combined application of two unitary operators , the operator acts on subspace and plays the role of quantum coin related to internal (spin) states, s , whereas the external states related to the subspace change due to the shift operator , .…”

Universal and optimal coin sequences for high entanglement generation in 1D discrete time quantum walks

“…The evolution itself consists of the recurrent application of a coin and shift operator which in general leads to entanglement between the walker and coin. Quantum walks have already been realized in a variety of physical systems such as cold atoms [10,11], trapped ions [12,13], superconducting qubits [14,15], neutral atoms [16,17], nuclear magnetic resonance systems [18,19] and photonic architectures [20][21][22]. Hybrid entanglement generation has been observed as well [23,24].…”

Generating highly entangled states via discrete-time quantum walks with Parrondo sequences

“…DTQW's are characterized by an evolution which consists of repeated application of two operators, the coin operator, and the shift operator. Parrondo's paradox has been explored several times using one-dimensional DTQW's [5,6,20,21]. It was shown that instead of a single coin if a twocoin initial state is considered, Parrondo's paradox can be observed in quantum walks even in the asymptotic limits [22], and further replacing a two-state coin(qubit) with a three state coin(qutrit) also leads to Parrondo's paradox in asymptotic limits [23].…”