The SAC simulation of coined quantum walk for step d = T = 100 in phase space for mode ∣ 1 〉 c ∣ x = 0 〉 w (a), ∣ 0 〉 c ∣ x = 0 〉 w (b), ∣ 0 〉 c ∣ x = 40 〉 w (c), and ∣ 1 〉 c ∣ x = 40 〉 w (d). The initial state is the product of a random ∣ ψ ( 0 ) 〉 c and ∣ 0 〉 w . All other modes also show similar trajectories. Insert panel in (a) is a top view showing clearly the “equilibrium point” ( 0 , 0 ) , which is the same for all other modes.