Initial lectures still need to be added

Lecture 5: Stabilizer code, Stabilizer state, Stabilizer group

  • Exam
    • Present the Toric code from the perspective of group theory β†’ surfaces β†’ fundamental group β†’ error correction. Potentially finish by comparing fundamental groups with homology classes.
    • Define as looking at the expectation of the sum of small squares?

Lecture 7 notes ( WIP )

Claim:
Proof: Letting , we have . Taking the derivative to obtain the probability distribution function, we get . The created Random variable has the properties:

  • : This follows from the kurtosis of the normal distribution. I need to understand how to build this connection more directly. Help me ❓

Alternative proof:

  • Let
  • are independent
  • By the Central Limit Theorem, Their sum converges to .

Lecture 9

Keywords: Stochastic Differential Equation, Ito Isometry

We define , where

  • for an appropriately defined .
  • . Also where

We get this weird result, where

  • . More formally,
  • Extract this result into it’s own note

Changing Differential Equations

Let , and define . We want to define the Stochastic Differential Equation that defines . We have