[feature request] Ask user to specify path in CFG

[ellishg]

I had an idea for a feature that might be useful. Since we are already building the control flow graph, we can display it to the user and ask them to specify a path by listing the order of the basic blocks to execute. We can then change the program to be (almost) linear and the wavefunction should be a pure state. We won't be able to get rid of measurements and so if the measurement gives the wrong outcome we need to restart the program.

Here's an example.

H 0
CNOT 0 1
MEASURE 0
JUMP-WHEN @END 0
X 1
@END 

If the user wants to ignore the if statement, we can change this to

@START
H 0
CNOT 0 1
MEASURE 0
JUMP-WHEN @END 0
# Reset all qubits to 0
JUMP @START
@END 
# Do tomography

[ellishg]

After talking with Will we realized that this method works well except in the case when the desired branch is very unlikely. When that happens the tomography will take a long time since it has to try many times before it finds the right outcome. If the probability we take a branch is p, then the expected number of trials is 1/p. If we know p, maybe we can use this to determine if this is a good idea.