Controllable simulation of topological phases and edge states with quantum walk

Panahiyan, S.; Fritzsche, S.

doi:10.1016/j.physleta.2020.126828

Cited by 6 publications

(1 citation statement)

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“…Owing to quantum superposition effects, these walks display distinct statistical properties compared to their classical counterparts. Quantum walks have proved to be of immense utility in varied domains, like in quantum computation [6][7][8], quantum search [9], quantum algorithms [10,11], generating random numbers [12], modeling topological phenomena [13][14][15][16][17] etc. In the DTQWs, the walker is modeled as a qudit, belonging to a potentially infinite-dimensional space called the "walk space", while the coin is modeled as a qubit, belonging to two-dimensional space called the "coin-space".…”

Section: Introduction To Quantum Walksmentioning

confidence: 99%

Steered discrete-time quantum walks for engineering of quantum states

Kadiri¹

2022

Preprint

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We analyze the strengths and limitations of steered discrete time quantum walks 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 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, all normalized quantum states are "walk-accessible". Furthermore, any generalized quantum step can be implemented upto a global phase using a single q-plate and a pair of homogeneous waveplates. We then give a quantum walk based scheme for realizing arbitrary vector beams, using only q-plates and waveplates.

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