It is my understanding that, given a quantum computer with $n$ qubits and a way to apply $m$ single- and 2-qubit gates, quantum supremacy experiments
- Initialize the $n$ qubits into the all-zero's ket $|000\cdots\rangle$
- Generate a random unitary $U$ of $m$ gates
- Apply the quantum gate $U$ to these qubits, e.g. produce the state $|\Psi\rangle=U|000\cdots\rangle$
- Measure $|\Psi\rangle$ to produce an $n$-bit classical string
- Measure some property the sampled string, such as a cross-entropy, and determine if quantum supremacy is achieved based on the sampled string, as compared to, say, the uniform distribution.
This can be repeated multiple times.
- Would a claim of quantum supremacy require applying the same random unitary $U$ each time, for each sample? Or is there a different pseudo-random $U$ for each sample?
I think I'm reading that $U$ is broken up into a set of pseudo-random single-qubit gates, followed by a set of 2-qubit gates. Are either or both of these fixed, or do they change for each sample?