Skip to content

Typos week2 #4

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
wants to merge 2 commits into
base: gh-pages
Choose a base branch
from
Open

Typos week2 #4

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
f36d774
Corrected typos week 1
Feb 13, 2024
e0c61cb
Typos week 2
Feb 13, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
8 changes: 4 additions & 4 deletions doc/pub/week1/ipynb/week1.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -659,7 +659,7 @@
"id": "f60e43ec",
"metadata": {},
"source": [
"For two arbitrary vectors $\\vert x\\rangle$ and $\\vert y\\rangle$ with the same lentgh, we have the\n",
"For two arbitrary vectors $\\vert x\\rangle$ and $\\vert y\\rangle$ with the same length, we have the\n",
"general expression"
]
},
Expand Down Expand Up @@ -1414,7 +1414,7 @@
"metadata": {},
"source": [
"## Examples of tensor products\n",
"If we now go back to our original one-qubit basis states, we can form teh following tensor products"
"If we now go back to our original one-qubit basis states, we can form the following tensor products"
]
},
{
Expand Down Expand Up @@ -1981,7 +1981,7 @@
"\n",
"Since our original basis $\\vert \\psi\\rangle$ is orthogonal and normalized with $\\vert\\alpha\\vert^2+\\vert\\beta\\vert^2=1$, the new basis is also orthogonal and normalized, as we can see below here.\n",
"\n",
"Since the inverse of a hermitian matrix is equal to its hermitian\n",
"Since the inverse of a unitary matrix is equal to its hermitian\n",
"conjugate/adjoint), unitary transformations are always reversible.\n",
"\n",
"Why are only unitary transformations allowed? The key lies in the way the inner product tranforms.\n",
Expand All @@ -2004,7 +2004,7 @@
"id": "1d1c60c1",
"metadata": {},
"source": [
"or in terms of a matrix-vector notatio we have"
"or in terms of a matrix-vector notation we have"
]
},
{
Expand Down
30 changes: 15 additions & 15 deletions doc/pub/week2/ipynb/week2.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -500,7 +500,7 @@
"source": [
"$$\n",
"\\boldsymbol{P}_a=\\vert \\psi_a\\rangle \\langle \\psi_a\\vert = \\begin{bmatrix} \\vert \\alpha_0\\vert^2 &\\alpha_0\\alpha_1^* \\\\\n",
" \\alpha_1\\alpha_0^* & \\vert \\alpha_1\\vert^* \\end{bmatrix},\n",
" \\alpha_1\\alpha_0^* & \\vert \\alpha_1\\vert^2 \\end{bmatrix},\n",
"$$"
]
},
Expand All @@ -519,7 +519,7 @@
"source": [
"$$\n",
"\\boldsymbol{P}_b=\\vert \\psi_b\\rangle \\langle \\psi_b\\vert = \\begin{bmatrix} \\vert \\beta_0\\vert^2 &\\beta_0\\beta_1^* \\\\\n",
" \\beta_1\\beta_0^* & \\vert \\beta_1\\vert^* \\end{bmatrix}.\n",
" \\beta_1\\beta_0^* & \\vert \\beta_1\\vert^2 \\end{bmatrix}.\n",
"$$"
]
},
Expand Down Expand Up @@ -558,8 +558,8 @@
"source": [
"$$\n",
"\\boldsymbol{A}=\\lambda_a\\begin{bmatrix} \\vert \\alpha_0\\vert^2 &\\alpha_0\\alpha_1^* \\\\\n",
" \\alpha_1\\alpha_0^* & \\vert \\alpha_1\\vert^* \\end{bmatrix} +\\lambda_b\\begin{bmatrix} \\vert \\beta_0\\vert^2 &\\beta_0\\beta_1^* \\\\\n",
" \\beta_1\\beta_0^* & \\vert \\beta_1\\vert^* \\end{bmatrix}.\n",
" \\alpha_1\\alpha_0^* & \\vert \\alpha_1\\vert^2 \\end{bmatrix} +\\lambda_b\\begin{bmatrix} \\vert \\beta_0\\vert^2 &\\beta_0\\beta_1^* \\\\\n",
" \\beta_1\\beta_0^* & \\vert \\beta_1\\vert^2 \\end{bmatrix}.\n",
"$$"
]
},
Expand Down Expand Up @@ -742,7 +742,7 @@
"metadata": {},
"source": [
"$$\n",
"\\sum_{i=0}^1\\boldsymbol{P}_i^{\\dagger}\\boldsymbol{P}_1=\\boldsymbol{I},\n",
"\\sum_{i=0}^1\\boldsymbol{P}_i^{\\dagger}\\boldsymbol{P}_i=\\boldsymbol{I},\n",
"$$"
]
},
Expand Down Expand Up @@ -1500,14 +1500,14 @@
"source": [
"## Simple Hamiltonian models\n",
"\n",
"In order to study get started with coding, we will study two simple Hamiltonian systems, one which we can use for a single qubit systems and one which has as basis functions a two-qubit system. These two simple Hamiltonians exhibit also something which is called level crossing, a feature which we will use in later studies of entanglement.\n",
"In order to get started with coding, we will study two simple Hamiltonian systems, one which we can use for a single qubit systems and one which has as basis functions a two-qubit system. These two simple Hamiltonians exhibit also something which is called level crossing, a feature which we will use in later studies of entanglement.\n",
"\n",
"We study first a simple two-level system. Thereafter we\n",
"extend our model to a four-level system which can be\n",
"interpreted as composed of two separate (not necesseraly identical)\n",
"subsystems.\n",
"\n",
"We let our hamiltonian depend linearly on a strength parameter $z$"
"We let our hamiltonian depend linearly on a strength parameter $\\lambda$"
]
},
{
Expand Down Expand Up @@ -1668,7 +1668,7 @@
"is $\\vert 0 \\rangle$. At $\\lambda=1$ the $\\vert 0 \\rangle$ mixing of\n",
"the lowest eigenvalue is $1\\%$ while for $\\lambda\\leq 2/3$ we have a\n",
"$\\vert 0 \\rangle$ component of more than $90\\%$. The character of the\n",
"eigenvectors has therefore been interchanged when passing $z=2/3$. The\n",
"eigenvectors has therefore been interchanged when passing $\\lambda=2/3$. The\n",
"value of the parameter $X$ represents the strength of the coupling\n",
"between the model space and the excluded space. The following code\n",
"computes and plots the eigenvalues."
Expand Down Expand Up @@ -1785,7 +1785,7 @@
"metadata": {},
"source": [
"$$\n",
"\\vert 10\\rangle = \\vert 1\\rangle_{\\mathrm{A}}\\otimes \\vert 0\\rangle_{\\mathrm{B}}=\\begin{bmatrix} 0 & 1 & 0 &0\\end{bmatrix}^T,\n",
"\\vert 01\\rangle = \\vert 0\\rangle_{\\mathrm{A}}\\otimes \\vert 1\\rangle_{\\mathrm{B}}=\\begin{bmatrix} 0 & 1 & 0 &0\\end{bmatrix}^T,\n",
"$$"
]
},
Expand All @@ -1803,7 +1803,7 @@
"metadata": {},
"source": [
"$$\n",
"\\vert 01\\rangle = \\vert 0\\rangle_{\\mathrm{A}}\\otimes \\vert 1\\rangle_{\\mathrm{B}}=\\begin{bmatrix} 0 & 0 & 1 &0\\end{bmatrix}^T,\n",
"\\vert 10\\rangle = \\vert 1\\rangle_{\\mathrm{A}}\\otimes \\vert 0\\rangle_{\\mathrm{B}}=\\begin{bmatrix} 0 & 0 & 1 &0\\end{bmatrix}^T,\n",
"$$"
]
},
Expand Down Expand Up @@ -1849,7 +1849,7 @@
"metadata": {},
"source": [
"$$\n",
"H_0\\vert 10 \\rangle = \\epsilon_{10}\\vert 10 \\rangle,\n",
"H_0\\vert 01 \\rangle = \\epsilon_{01}\\vert 01 \\rangle,\n",
Copy link
Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

These changes are strictly speaking not necessary, but I guess it makes sense to change the ordering, because of the correction above in the definition of |01> and |10>.

"$$"
]
},
Expand All @@ -1859,7 +1859,7 @@
"metadata": {},
"source": [
"$$\n",
"H_0\\vert 01 \\rangle = \\epsilon_{01}\\vert 01 \\rangle,\n",
"H_0\\vert 10 \\rangle = \\epsilon_{10}\\vert 10 \\rangle,\n",
"$$"
]
},
Expand Down Expand Up @@ -1914,8 +1914,8 @@
"source": [
"$$\n",
"\\boldsymbol{H}=\\begin{bmatrix} \\epsilon_{00}+H_z & 0 & 0 & H_x \\\\\n",
" 0 & \\epsilon_{10}-H_z & H_x & 0 \\\\\n",
"\t\t 0 & H_x & \\epsilon_{01}-H_z & 0 \\\\\n",
" 0 & \\epsilon_{01}-H_z & H_x & 0 \\\\\n",
"\t\t 0 & H_x & \\epsilon_{10}-H_z & 0 \\\\\n",
"\t\t H_x & 0 & 0 & \\epsilon_{11} +H_z \\end{bmatrix}.\n",
"$$"
]
Expand All @@ -1936,7 +1936,7 @@
"metadata": {},
"source": [
"$$\n",
"\\rho_0=\\left(\\alpha_{00}\\vert 00 \\rangle\\langle 00\\vert+\\alpha_{10}\\vert 10 \\rangle\\langle 10\\vert+\\alpha_{01}\\vert 01 \\rangle\\langle 01\\vert+\\alpha_{11}\\vert 11 \\rangle\\langle 11\\vert\\right),\n",
"\\rho_0=\\left(\\alpha_{00}\\vert 00 \\rangle\\langle 00\\vert+\\alpha_{01}\\vert 01 \\rangle\\langle 01\\vert+\\alpha_{10}\\vert 10 \\rangle\\langle 10\\vert+\\alpha_{11}\\vert 11 \\rangle\\langle 11\\vert\\right),\n",
"$$"
]
},
Expand Down