Figure 1
From: Hybrid classical-quantum linear solver using Noisy Intermediate-Scale Quantum machines
(a) Quantum (or classical) random walk on an undirected \(N=4\) graph. The transition probability of going from node \(I\) to node \(J\) or vice versa is equal to \({P}_{I,J}\), these elements forming a \(4\times 4\) matrix. (b) The four nodes on this Hamming cube are labeled by integers \((0,1,2,3)\); they are encoded as four different states \(\mathrm{|00}\rangle \), \(\mathrm{|01}\rangle \), \(\mathrm{|10}\rangle \), \(\mathrm{|11}\rangle \), respectively.
