Implementation of multidimensional quantum walks using linear optics and classical light

Abstract

Classical optics can be used to efficiently implement certain quantum information processing tasks with a high degree of control, for example, one-dimensional quantum walks through the space of orbital angular momentum of light directed by its polarization. To explore the potential of quantum information processing with classical light, we here suggest a method to realize d-dimensional quantum walks with classical optics-an important step towards robust implementation of certain quantum algorithms. In this scheme, different degrees of freedom of light, such as frequency, orbital angular momentum, and time bins, represent different directions for the walker while the coin to decide which direction the walker takes is realized by employing the polarization combined with different light paths. Introduction. A quantum algorithm is an ordered set of instructions given to a quantum computer to realize a particular processing of quantum information. However, due to the delicate nature of quantum systems, it is not easy to construct a large enough quantum computer that is capable of implementing sufficiently complex quantum algorithms. Interestingly, a number of quantum algorithms, such as the Deutsch algorithm [1], the DeutschJozsa algorithm [2], and Grover's search algorithm [3], can be simulated and implemented with certain classical systems [4] among them with classical states of light [5].

Quantum key distribution with quantum walks

“…Along these lines, our proposals could be seen as alternatives to the already existing QKD protocols, which can be implemented with the current technology. Perhaps, the most relevant setups for QKD purposes would be the optical implementations of QWs [110,111,112,113,114,115,116,117,118]. For a detailed and complete review of QW experimental realisations, we refer to the book [119].…”

Quantum walk as generalized evolution and measurement device

“…Moreover, our method to realize POVM and evolution is not limited to one-dimensional QW. For example, via encoding the measured system into the high dimensional coin state, our algorithm can be directly generalized to high dimensional QW [42], which will highly suppress the required number of QW steps. Furthermore, the architect of recursively implementing unitary operation and state-dependent loss is very similar to optical POVM devices [20].…”

Decomposition of split-step quantum walks for simulating Majorana modes and edge states

“…The schemes presented here are based on the decompositions constructed in the previous section, which make use of the onedimensional OQW. Hence, our implementation scheme for a SSQW uses earlier schemes for OQWs [34][35][36][37][38][39].…”