Hey, I’ve got a sudden question for you.
Probability distribution on a set of binary variables is to a quantum state
as ??? is to a unitary linear operator.
What should ??? be replaced with?
Here’s why I have this question. Somehow I was thinking about Normalizing flows, which are invertible functions which, when applied to a sample from an N-dimensional probability distribution, transform it into a sample from another N-dimensional probability distribution. And then I thought: isn’t this similar to how quantum operator is always unitary? Maybe then I can combine encoding an image as a pure state (like in Stoudenmire 2016 - Supervised learning with quantum-inspired tensor networks with representing quantum operators as tensor networks to get a quantum-inspired generative model similar to normalizing flows.
Would it be correct to say that (2) and (3) can be replaced with just “apply any linear operator”?
Also, what advantages does working with amplitudes have compared to working with probabilities? Why don’t we just use probability theory?
Any unitary linear operator (to make sure squared amplitudes still sum to 1). To your second question, I’ll post a toplevel comment.
Hey, I’ve got a sudden question for you. Probability distribution on a set of binary variables is to a quantum state as ??? is to a unitary linear operator.
What should ??? be replaced with?
Here’s why I have this question. Somehow I was thinking about Normalizing flows, which are invertible functions which, when applied to a sample from an N-dimensional probability distribution, transform it into a sample from another N-dimensional probability distribution. And then I thought: isn’t this similar to how quantum operator is always unitary? Maybe then I can combine encoding an image as a pure state (like in Stoudenmire 2016 - Supervised learning with quantum-inspired tensor networks with representing quantum operators as tensor networks to get a quantum-inspired generative model similar to normalizing flows.
Maybe stochastic matrix?