PAR Class 19, Mon 2019-03-25

The book that I like most (today) is this:

1. Quantum Computing for Computer Scientists 1st Edition ( recommended in Microsoft talk)

   Example of superimposition: 2 slit experiment, page 93. Weights of either slit: 1/sqrt(2). Spread out weights for each slit (all /sqrt(6)): -1+i, -1-i, 1-i.

My summary so far.

1. Qbit.
2. Its state is 0 or 1.
3. Several qbits.
4. The combined state is the tensor product of the individual qbits.
5. For $n$ qbits, the tensor product is a vector with $2^n$ elements, one element for each possible value of each qbit.
6. Each element of the tensor product has a complex weight.
7. The physical meaning is that the system is simultaneously in a superimposition of all the possible combos of values of the component qbits.
8. It is wrong to think that the system is really in one of the states, but you don't know which one. This is the hidden variable theory. It has been proved experimentally to be false.
9. The probability of it being in a particular single state is proportional to the squared magnitude of its complex weight.
10. For some sets of weights, the combined state cannot be separated into a tensor product of individual qbits. In this case, the individual qbits are entangled.
11. You transform a state by multiplying it by a matrix.
12. The matrix is invertible.
13. The transformation doesn't destroy information.
14. When you measure a state, it collapses into one of the component states. (This may be inaccurate.)
15. The probability of collapsing into a particular state is the squared magnitude of its complex weight.