Surface Codes with Biased-Noise Qubits | Seminar Series with Shruti Puri

[@muddassirghoorun4322]

Interesting talk but I'm sorry for this dumb question: How do you simulate depolarizing noise on the surface code? And how do you get the syndrome?

[@ton2079]

Hello there! You can simulate depolarizing noise on the surface code through Monte Carlo methods. By establishing a probability distribution within the data qubits (e.g. p = 5%, px = py = pz = p/3), you can simulate error strings of size n. Afterwards, through the application of the stabilizers of the surface code you will reach a syndrome. Lastly, you should use a decoding method in order to recover the original simulated error. If you succeed, the surface code will recover its original state once applying the recovered error, if not, the state of the surface code will still be affected. After many simulations such as the one I described, you can stablish a ratio of the surface code failing (number of attempts in which the original state is not recovered / number of total attempts).

[@muddassirghoorun4322]

​@@ton2079 Thanks for the reply. I found the answer last year as well. We got depolarizing noise, amplitude damping, phase damping type of channels we could use as well. But as an engineer beginning in the topic that was not clear in the beginning. A question which I still have in my mind is how to know the exact sequence of the CNOT gates based on the stabilizers.

[@ton2079]

​@@muddassirghoorun4322 Hello, the CNOT gates are done so that the measured state of the measurement qubits result in a partial collapse of the surface code quantum state. That is, that the data qubits can only experience pauli gate operators (X, Y, Z, I), and so an error like (1/sqrt(2)(X+Y)) cannot occur, that is called the digitization of errors. You can see why their sequence stabilizes the code by considering an arbitrary qubit in a state |psi> = alpha * |0> + beta * |1> ana having it interacting with its 4 nearest measurement qubits following the circuit of FIG.1 in arxiv.org/ftp/arxiv/papers/1208/1208.0928.pdf . Afterwards, measure the measuring qubits. Do the same for X|psi>, Y|psi> and Z|psi>, and you will notice that different errors yield different measurement results. Best wishes