From 098e3564028cdd111f8c8522ae09cd698b0e2a91 Mon Sep 17 00:00:00 2001
From: Yuning Zhang <neuromancer43@gmail.com>
Date: Wed, 20 Nov 2024 14:00:18 +0100
Subject: [PATCH] Update README.md

---
 README.md | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)

diff --git a/README.md b/README.md
index ad88a85..6572724 100644
--- a/README.md
+++ b/README.md
@@ -13,6 +13,33 @@ pkg> add SpinShuttling
 
 ## Example: 
 
+Consider the sequential shuttling of a pair of entangled spins preparing in Bell state. If the distance between the two spins is small enough, then the noise experienced by them will have a non-zero covariance. The spatially correlated noise can be modeled by a 2D Gaussian random field, $W(t, x)$. Since the wavefunction of the spin is highly constrained by the moving potential well. We can describe the position of a spin carrier (electron or holes), as a function of time $x(t)$. Such a trajectory will determine a route-specific projection on the 2D field $W(t, x(t))$ which gives the noise experienced by the spin. 
+
+```julia
+L=10; σ =sqrt(2)/20; M=5000; N=501; T1=100; T0=25; κₜ=1/20; κₓ=1/0.1;
+
+B=OrnsteinUhlenbeckField(0,[κₜ,κₓ],σ)
+model=TwoSpinSequentialModel(T0, T1, L, N, B)
+
+Ψ= model.Ψ
+ρ=Ψ*Ψ'
+w=dephasingmatrix(model)
+
+ρt=w.*ρ
+
+println(ρ)
+```
+
+```
+f1=statefidelity(model)
+f2, f2_err=sampling(model, statefidelity, M)
+f3=1/2*(1+W(T0, T1, L,B))
+
+println("NI:", f1)
+println("MC:", f2)
+println("TH:", f3)
+```
+
 ![Sequential shuttling of a pair of entangled qubit](./docs/src/assets/animation2spins.gif)