I ran the following circuit to calculate the real part of the Bargmann Invariant of a system of quantum states. The invariant is defined as
Re[BI_m] = Re[<a_1|a_2> <a_2|a_3>… <a_m|a_1>]
Circuit for m = 3 (The gates to the left of the dotted line for qreg 1-3 are just to set up sample quantum states to test the circuit on):
Circuit for m = 4 (The gates to the left of the dotted line for qreg 1-4 are just to set up sample quantum states to test the circuit on):
Basically the BI real part is equal to the probability of getting 0 and so by running the circuit 1000 times, we can get a good estimate of it.
Because of that, I thought that in theory, it’s like flipping a coin multiple times to figure out the bias of the coin. And so regardless of the number of bits (m) that we use, we should only need to run the circuit the same number of times to get the same accuracy.
This however was not the case. When I ran it for m=4 vs m=3, I had to run the circuit almost 10 times more to get similar accuracy to the theoretical values. Why is this? Is it because of some limitations in the simulation done by qiskit, or have I conceptually misunderstood what is happening in this circuit?
