Let's assume that I have a density matrix $\rho$ that consists of $N$ qubits.

If this density matrix undergoes an error-channel that swaps any two qubits with an equal probability, i.e.

$$ \mathcal{E}(\rho)=(1-p)\rho + \frac{2p}{N(N-1)}\sum_{i=1}^{N-1}\sum_{j>i}^N \mathrm{SWAP}_{ij}\rho \mathrm{SWAP}_{ij} $$ where $p$ is the probability of an error.

Does there exist a quantum circuit/protocol that can detect and correct if a swap error has occurred?

  • $\begingroup$ Could you not just use a distance 5 error correcting code, since this can correct for any error on 2 or fewer sites? That presumably includes your swap case. Or are you hoping for something more specialised? $\endgroup$
    – DaftWullie
    Oct 20 at 13:13
  • $\begingroup$ Alternatively, perhaps you could encode in the fully symmetric subspace. That's a decoherence-free subspace for that noise, so you don't even have to apply any error correction. $\endgroup$
    – DaftWullie
    Oct 20 at 13:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.