From f6e357c684e7eeb363dd7bf4159c65423666f7ac Mon Sep 17 00:00:00 2001
From: Dennis Kobert <dennis@kobert.dev>
Date: Sat, 30 Nov 2019 12:22:57 +0100
Subject: Change gnuplot appearance

---
 gnuplot.plt | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/gnuplot.plt b/gnuplot.plt
index 635bd3e..ea5e043 100644
--- a/gnuplot.plt
+++ b/gnuplot.plt
@@ -1,7 +1,7 @@
 set view equal xyz
 set parametric
-set isosamples 10,10
-splot cos(u)*cos(v),cos(u)*sin(v),sin(u)
-replot 'data'
+set isosamples 34,34
+splot cos(u)*cos(v),cos(u)*sin(v),sin(u) w l lc rgb "#42a4f5"
+replot 'data' w points palette pointsize 2 pointtype 7 
 ;
 pause mouse close
-- 
cgit v1.2.3-54-g00ecf


From f3988902b014da58eb8c6a1914312721b0b59f86 Mon Sep 17 00:00:00 2001
From: Dennis Kobert <dennis@kobert.dev>
Date: Sat, 30 Nov 2019 12:52:41 +0100
Subject: Fix bloch_map

---
 single_dequantify.py | 21 +++++++++++----------
 1 file changed, 11 insertions(+), 10 deletions(-)

diff --git a/single_dequantify.py b/single_dequantify.py
index 43c256d..44f2190 100644
--- a/single_dequantify.py
+++ b/single_dequantify.py
@@ -9,10 +9,10 @@ alpha = 1 / npy.sqrt(2)
 beta  = 1 / npy.sqrt(2)
 state = npy.array([alpha, beta])
 
-dt = 0.2
-iterations = 20
+dt = 0.067
+iterations = 41
 
-H = npy.array([[2,-2j],[2j,3]])
+H = npy.array([[2,-1j],[1j,3]])
 
 
 def time_evolution(state, dt = dt):
@@ -20,19 +20,20 @@ def time_evolution(state, dt = dt):
 
 def bloch_map(state):
     temp  = npy.conj(state[0] / state[1])
-    phi   = 2 * npy.arctan(1 / abs(temp))
-    theta = npy.arctan(temp.imag / temp.real)
+    theta = 2 * npy.arctan(abs(temp) / 2)
+    phi = cmt.phase(temp)
+
     return npy.array([phi, theta])
 
 def sphere2cart(phi, theta):
         return [
-             mth.sin(theta) * mth.cos(phi),
-             mth.sin(theta) * mth.sin(phi),
-             mth.cos(theta)
+             mth.cos(theta) * mth.cos(phi),
+             mth.cos(theta) * mth.sin(phi),
+             mth.sin(theta)
         ]
 
 historie = npy.array([bloch_map(state)])
-f = open("data", "a")
+f = open("data", "w")
 
 for i in range(iterations):
     state = time_evolution(state)
@@ -40,7 +41,7 @@ for i in range(iterations):
     historie = npy.vstack([historie,bloch_map(state)])
     coords = bloch_map(state)
     coords = sphere2cart(coords[0], coords[1])
-    f.write(f"{coords[0]}; {coords[1]}; {coords[2]}\n")
+    f.write(f"{coords[0]}; {coords[1]}; {coords[2]}; {(i + 1) / iterations}\n")
 
 f.close()
 subprocess.run(["gnuplot", "gnuplot.plt"])
-- 
cgit v1.2.3-54-g00ecf


From 98c588bbb04f11b05324b6e415ec358305f06f7a Mon Sep 17 00:00:00 2001
From: Dennis Kobert <dennis@kobert.dev>
Date: Sat, 30 Nov 2019 13:15:01 +0100
Subject: Normalize alpha and beta

---
 single_dequantify.py | 30 +++++++++++++++++-------------
 1 file changed, 17 insertions(+), 13 deletions(-)

diff --git a/single_dequantify.py b/single_dequantify.py
index 44f2190..fa5f017 100644
--- a/single_dequantify.py
+++ b/single_dequantify.py
@@ -5,14 +5,18 @@ import cmath as cmt
 import numpy as npy
 import scipy.linalg as sla
 
-alpha = 1 / npy.sqrt(2)
-beta  = 1 / npy.sqrt(2)
-state = npy.array([alpha, beta])
+#alpha = 1 / npy.sqrt(2)
+alpha = 1
+#beta  = 1 / npy.sqrt(2)
+beta  = 1
 
-dt = 0.067
-iterations = 41
+norm  = npy.linalg.norm([alpha, beta])
+state = npy.array([alpha / norm, beta / norm])
 
-H = npy.array([[2,-1j],[1j,3]])
+dt = 0.1
+iterations = 61
+
+H = npy.array([[2,0],[0,3]])
 
 
 def time_evolution(state, dt = dt):
@@ -20,16 +24,16 @@ def time_evolution(state, dt = dt):
 
 def bloch_map(state):
     temp  = npy.conj(state[0] / state[1])
-    theta = 2 * npy.arctan(abs(temp) / 2)
+    theta = 2 * npy.arctan(abs(temp))
     phi = cmt.phase(temp)
 
-    return npy.array([phi, theta])
+    return (phi, theta)
 
 def sphere2cart(phi, theta):
         return [
-             mth.cos(theta) * mth.cos(phi),
-             mth.cos(theta) * mth.sin(phi),
-             mth.sin(theta)
+             mth.sin(theta) * mth.cos(phi),
+             mth.sin(theta) * mth.sin(phi),
+             mth.cos(theta)
         ]
 
 historie = npy.array([bloch_map(state)])
@@ -39,8 +43,8 @@ for i in range(iterations):
     state = time_evolution(state)
     h = npy.dot(state, state)
     historie = npy.vstack([historie,bloch_map(state)])
-    coords = bloch_map(state)
-    coords = sphere2cart(coords[0], coords[1])
+    (phi, theta) = bloch_map(state)
+    coords = sphere2cart(phi, theta)
     f.write(f"{coords[0]}; {coords[1]}; {coords[2]}; {(i + 1) / iterations}\n")
 
 f.close()
-- 
cgit v1.2.3-54-g00ecf