quantum computing

• 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}

• 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

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

• qubits
• quantum gates