From 8296b8c24689525509778d0f0659dbc8eede471a Mon Sep 17 00:00:00 2001
From: Anton Quelle <anton.quelle@pasqal.com>
Date: Wed, 16 Nov 2022 16:02:23 +0100
Subject: [PATCH] created solutions notebook

---
 tensor_networks.ipynb | 128 +++---------------------------------------
 1 file changed, 8 insertions(+), 120 deletions(-)

diff --git a/tensor_networks.ipynb b/tensor_networks.ipynb
index 1c5e767..8aba644 100644
--- a/tensor_networks.ipynb
+++ b/tensor_networks.ipynb
@@ -122,18 +122,6 @@
     "hint: there is an inbuilt kron function in the language"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "0ae71ba7",
-   "metadata": {},
-   "source": [
-    "solution:\n",
-    "\n",
-    "function tensor(a,b)\n",
-    "    return kron(a,b)\n",
-    "end"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "ed16c698",
@@ -233,22 +221,6 @@
     "hint: recursively call tensor, for example by using foldl(tensor, .)"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "8da9b908",
-   "metadata": {},
-   "source": [
-    "solution:\n",
-    "\n",
-    "function ghz_state(n)\n",
-    "    return foldl(tensor, [[1,0] for _ in 1:n]) + foldl(tensor, [[0,1] for _ in 1:n])\n",
-    "end\n",
-    "\n",
-    "function hadamard_state(n)\n",
-    "    return foldl(tensor, [[1,1] for _ in 1:n])\n",
-    "end"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "6d698325",
@@ -428,7 +400,8 @@
     "    @assert elt(ψ, [1,2,1,2,2]) ≈ 1\n",
     "\n",
     "    return nothing\n",
-    "end"
+    "end\n",
+    "test_tn_states()"
    ]
   },
   {
@@ -440,31 +413,6 @@
     "        https://itensor.github.io/ITensors.jl/stable/examples/MPSandMPO.html"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "4fcdd292",
-   "metadata": {},
-   "source": [
-    "solution:\n",
-    "\n",
-    "function tn_ghz_state(n)\n",
-    "    sites = siteinds(\"S=1/2\", n)\n",
-    "    states_up = [\"Up\" for _ in 1:n]\n",
-    "    states_dn = [\"Dn\" for _ in 1:n]\n",
-    "    return MPS(sites, states_dn) + MPS(sites, states_up)\n",
-    "end\n",
-    "\n",
-    "function tn_hadamard_state(n)\n",
-    "    sites = siteinds(\"S=1/2\", n)\n",
-    "    state = randomMPS(sites) #this constructs a randomly initialized product wave-function in TN form\n",
-    "    for s in 1:n    #manually set each qubit to the [1, 1] state\n",
-    "        state[s][1] = 1\n",
-    "        state[s][2] = 1\n",
-    "    end\n",
-    "    return state\n",
-    "end"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "d9665529",
@@ -601,12 +549,15 @@
     "        return scalar(V)\n",
     "    end\n",
     "    sites = siteinds(\"S=1/2\", N)\n",
-    "    state = MPS(sites, [\"Up\"])\n",
+    "    in = MPS(sites, [\"Dn\", \"Up\", \"Dn\"])\n",
     "    hwa = hwa_layer(sites, [pi/2, pi/2, -pi/2, pi/2, pi/2, -pi/2, pi/2, pi/2, -pi/2])\n",
-    "    @assert elt(out,[2,2,1]) ≈ sqrt(2)+im*sqrt(2)\n",
+    "    out = apply(hwa, in)\n",
+    "    @assert elt(out,[2,2,1]) ≈ (sqrt(2)+im*sqrt(2))/2\n",
     "    \n",
     "    return nothing\n",
-    "end"
+    "end\n",
+    "\n",
+    "test_hwa_layer()"
    ]
   },
   {
@@ -618,27 +569,6 @@
     "hint2: In the above file look at layer, variational_circuit, and lines 77-79"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "7f9f4508",
-   "metadata": {},
-   "source": [
-    "Solution:\n",
-    "Ry(theta) = cos(theta/2)*[1 0; 0 1] + im*sin(theta/2)*[0 -im; im 0]\n",
-    "Rx(theta) = cos(theta/2)*[1 0; 0 1] + im*sin(theta/2)*[0 1; 1 0]\n",
-    "ITensors.op(::OpName\"rotations\", ::SiteType\"Qubit\"; t1::Number, t2::Number, t3::Number) = Ry(t3)*Rx(t2)*Ry(t1)\n",
-    "\n",
-    "function hwa_layer(sites, angles::Vector{<:Number})\n",
-    "  layer = Prod{Op}()\n",
-    "  for i in 1:length(sites)\n",
-    "    layer = Op(\"rotations\", i; t1=angles[1+3*(i-1)],  t2=angles[2+3*(i-1)],  t3=angles[3+3*(i-1)])*layer\n",
-    "  end\n",
-    "  layer = Op(\"CNOT\", 1, 2)*layer\n",
-    "  layer = Op(\"CNOT\", 2, 3)*layer\n",
-    "  return Prod{ITensor}(layer, sites)\n",
-    "end"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "003a4139",
@@ -704,24 +634,6 @@
     "call orthogonalize or orthogonalize!"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "0f40edd1",
-   "metadata": {},
-   "source": [
-    "solution:\n",
-    "\n",
-    "sites = siteinds(2, 5)\n",
-    "ψ = randomMPS(sites; linkdims = 5)\n",
-    "print(ψ)\n",
-    "orthogonalize!(ψ, 3)\n",
-    "print(ψ)\n",
-    "a = matrix(ψ[1], inds(ψ[1]))\n",
-    "print(a)\n",
-    "b = array(ψ[2], inds(ψ[2]))\n",
-    "print(b)"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "e4dd25b9",
@@ -784,30 +696,6 @@
     "you can copy any tensor, and then prime some of its indexes. Contracting the tensor with its copy will contract along the unprimed indices. https://itensor.github.io/ITensors.jl/stable/ITensorType.html#Priming_and_tagging_ITensor"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "bbd01772",
-   "metadata": {},
-   "source": [
-    "solution:\n",
-    "\n",
-    "sites = siteinds(2, 5)\n",
-    "ψ = randomMPS(sites; linkdims = 5)\n",
-    "orthogonalize!(ψ, 3)\n",
-    "println(ψ)\n",
-    "a = ψ[1]\n",
-    "b = deepcopy(a)\n",
-    "prime!(b; tags=\"l=1\")\n",
-    "c = matrix(a*b)\n",
-    "println(c)\n",
-    "d = ψ[2]\n",
-    "e = deepcopy(d)\n",
-    "prime!(e; tags=\"l=2\")\n",
-    "f = matrix(d*e)\n",
-    "println(f)\n",
-    "#etc."
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "d4edeb9e",