Steered discrete-time quantum walks for engineering of quantum states
Gururaj Kadiri · Physical Review A · 2023
We analyze the strengths and limitations of steered discrete-time quantum walks with position-independent coins in generating quantum states of bipartite quantum systems comprising of a qubit coupled to a qudit system. We demonstrate that not all quantum states in the composite space are accessible through such quantum walks, even under the most generalized definition of a quantum step, leading to a bifurcation of the composite Hilbert space into ``walk-accessible states'' and the ``walk-inaccessible states.'' We give an algorithm for generating any walk-accessible state from a simple-to-realize product state in a minimal number of walk steps, all of unit step size. We further give a prescription towards constructing minimal quantum walks between any pair of such walk-accessible states. Linear optics has been a popular physical system for implementing coin-based quantum walks, where the composite space is built up of spin and orbital angular momenta of light beams. We establish that in such an implementation, any generalized quantum step can be implemented up to a global phase using a single $q$-plate and a pair of homogeneous wave plates. We then give a quantum walk based scheme for realizing arbitrary vector beams consisting of a finite number of OAM components, using only $q$ plates and wave plates.