Multiple Qubits errors for Shor's 9 qubits code

Hi, I was trying to realize the Shor’s 9 qubits code by pennylane. However, I have a question about that code. As we all learned in the articles, Shor’s code is mainly work for single-qubit error. How about two or three-qubit errors Is it possible?

Hi @learnerSWE,

Welcome to the PennyLane community! :rocket: :tada:

This 9-qubit code can only correct one bit flip error, one phase flip error, or one of each, on any of the physical qubits. It won’t correct errors on multiple qubits. It was an important result because it was I believe the first demonstration of how error correction could work on superposition states, but since then several better codes have been developed that can correct more errors using fewer qubits.

Perhaps you know it already, but I personally like this review on quantum error correction.

Hope that helps!

Juan Miguel

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Thank you @jmarrazola! I think the concatenation of Shor’s 9 qubits codes can correct multiple qubit errors. Am I right?


You’re welcome!

I’m not an expert in quantum error correction, but yes, I believe that code concatenation can be used to increase the number of errors that can be corrected.

I’m not sure what is the scope of your project, but keep in mind that there are better codes than the Shor code, for example the [5,1,3] stabilizer code.


Juan Miguel