Reducing circuit initialization complexity

Question

I'm encoding data into a QuantumCircuit via the Initialize method for QFTs. In doing this and transpiling for IonQ backends, I'm getting rather complex circuits. Is there a way to encode this data more efficiently for IonQ backends or a method to approximate this circuit? Thanks in advance!

Answer 1

I think that the QuantumCircuit.initialize() method isn't always providing the most efficient state preparations.

I have tried to initialize some very simple states, like $|11⟩$ for 2-qubits system:

1. In the first case I just used simple 2 NOT gates (which are also native gates in all the quantum computers that I know), so the the transpiled version is pretty much the same:

2. In the second case I have used qc.initialize([0,0,0,1]) to initialize the same $|11⟩$ state and the results are very ugly:

Along with this talking I can infer that QuantumCircuit.initialize() isn't providing always the most efficient method for setting a desired state. And that's probably the reason that so many gates are used in order to set the 8-qubits state above.

Try to set up the desired state manually (I don't understand exactly which state you are trying to initialize here so I can't tell you exactly how to do it for now).

Answer 2

Try using isometry instead of initialize:

qc.isometry(y/np.linalg.norm(y), [*range(n_qubits)], [])

Also, try setting optimization_level to 3 for transpile method. Most of the time this will reduce number of gates.

qc1 = transpile(circuits=qc, backend=backend, optimization_level=3)