Figure 5

(a) Probability distributions \(\pmb{P(n)}\) against the site label n for a DTQW with \(\pmb{N=50}\) and the walker prepared in the initial state \(\pmb{\vert {G} \rangle _{p}\otimes \vert {\phi} \rangle_{c}}\) with \(\pmb{\Sigma=10}\). (b) State fidelity between a Gaussian coherent quantum superposition state of the form in Eq. (16) and the conditional state of the position degree of freedom of a walker initially prepared in Eq. (15) with \(\Sigma=2\) and a growing size N of the lattice. (c) Comparison between the spatial probability distributions for a quantum walk with \(\theta=\pi/20\) in the absence of noise (blue line, top peaks) and one achieved by taking \(\{\beta_{t}\}\in[0.9,1]\) (magenta line, bottom peaks). The fidelity between the corresponding states is as low as 0.22.