quantum theory allows us to understand physics; it reconciliations the classical world with the quantum world.

1. Classical particles, in the double slit experiment, would just straight go through and bounce off
2. Actual particles (quantum) like light, under quantum theory, would actually exhibit interference via wave-like hebahior

The measurement of quantum theory is done via quantum information theory.

A little endeavor to learn about Lambek Calculus, quantum information theory, and linguistics I guess.

Courses to Take for QNLP

Categorical Grammars Index

A qubit is a two-layer quantum theory system.

A classical bit is something that can be set between two values, a qubit between a much higher dimension.

Week 9

• isn’t \(P^{\text{SAT}}\) just \(\text{SAT}\) with more steps? i.e., because an “oracle” for \(\text{SAT}\) is just a system that checks SAT, and we know that can be done in P no it isn’t because checking requires a witness
• can we use CLIQUE in pset

Week 8

• ask Omer to go over subset sum

Week 7

• so in NP, “nondeterministically guess” happens in order-1 time for all possible choices?

Week 6

• interpreter arguments: why is that changing \(K(x)\) up to a constant? i.e. for instance doesn’t the choice of \(K_{p}(x)\) matter?
• Godel’s consistency: why does the

imply that \(\neg S_{G,\varepsilon}\) is true?

a quotient group is a group which is the product of mapping things out.

subgroups

The set of integers \(\mathbb{Z}\) is obviously a group. You can show it to yourself that multiples of any number in the group is a subgroup of that group.

For instance:

\(3 \mathbb{Z}\), the set \(\{\dots -6, -3, 0, 3, 6, \dots\}\) is a subgroup

actual quotient groups

We can use the subgroup above to mask out a group. The resulting product is NOT a subgroup, but its a new group with individual elements being subsets of our original group.