Physical Implementation of Quantum Walks

João Fernando Doriguello Diniz

Bereneice Sephton, Angela L. Dudley, Andrew Forbes

In the avid search for means to increase computational power in comparison to that which is currently available, quantum walks (QWs) have become a promising option with derived quantum algorithms providing an associated speed up compared to what is currently used for implementation in classical computers. It has additionally been shown that the physical implementation of QWs will provide a successful computational basis for a quantum computer. It follows that considerable drive for finding such means has been occurring over the 20+ years since its introduction with phenomena such as electrons and photons being employed. Principal problems encountered with such quantum systems involve the vulnerability to environmental influence as well as scalability of the systems. Here we outline how to perform the QW due to interference characteristics inherent in the phenomenon, to mitigate these challenges. We utilize the properties of vector beams to physically implement such a walk in orbital angular momentum space by manipulating polarization and exploiting the non-separability of such beams.

Renato Portugal, M. C. de Oliveira, Jalil Khatibi Moqadam

Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties similar to the ones for quantum computers, though. Therefore, there is a strong motivation to develop new quantum-walk models which might be easier to implement. In this work we present an extension of the staggered quantum walk model that is fitted for physical implementations in terms of time-independent Hamiltonians. We demonstrate that this class of quantum walk includes the entire class of staggered quantum walk model, Szegedy's model, and an important subset of the coined model.

Kendon

Kia Manouchehri

In this thesis we present a theoretical study of quantum walks, with a particular focus on the development of viable schemes concerned with their physical realization. Ever since their introduction over a decade ago, quantum walks have been extensively explored for their non-intuitive dynamics which may hold the key to a new generation of quantum algorithms. This growing interest in the theoretical applications of quantum walks has been paralleled by a flurry of research into a more practical problem: how does one physically implement a quantum walk in the laboratory? We begin this thesis by first presenting an overview of the quantum walk theory, including some of its algorithmic applications. This is then followed by a comprehensive survey of numerous proposals for a physical implementation of quantum walks, underpinned by a wide range of quantum, classical and hybrid technologies. This review consequently highlights what has so far remained a major challenge for the quantum walk enthusiasts; a physical realization that is experimentally viable whilst remaining readily scalable and not limited to problems with specific connectivity criteria. It is precisely this challenge that we seek to examine in the remaining parts of this thesis.

Renato Portugal