# quantum computing

### 0.1. note taking

- Emacs Org mode MathJax physics package
- M-x org-customize. Go to Org Export -> Org Export HTML -> Org HTML MathJax template
- mathjax braket

- Emacs Org mode Latex export
- See here

#+LATEX_HEADER: \usepackage{braket}

### 0.2. basic notation

- bilinear map (wikipedia)
- why antilinear in second argument? so the norm works out
- see bifunctors

- primer on bra ket
- basically gives us a nice way to write the inner product

- product of kets
- \(\ket{\phi}\ket{\psi}\)
- tensor product – see tensor product
- as far as I can tell, this is a generalization of the cartesian product between two vector spaces
- there is a bilinear map from the cartesian product of the vector spaces to yet another vector space

- why is the bilinear part important?
- we can apply a transform to only one of the qubits

- multiple qubits
- when you have multiple qubits enter a circuit, what is their state? it's the tensor product between the qubits

- The basic recipe for applying a gate to the \(k\) th qubit of a multi-qubit vector is to apply the gate to all the basis vectors that lie in the \(k\) th position and multiply by their amplitude

### 0.3. learning

- left off on page 35 of mike and ike – trying to understand the hadamard transform on multiple bits