0
$\begingroup$

I am starting to study quantum error correction and it's the first time that I see the operators (usually Pauli) as projective measurements which seem to just identify a syndrome but do not destroy the quantum information.

I'm used to figure out a quantum evolution with the standard circuit model and I can't really imagine how this works and how to represent it.

For example, when reading about the basic example of bit-flip error correction, one can state that the measurements $\sigma^z_1\otimes\sigma^z_2$ and $\sigma^z_2\otimes\sigma^z_3$, won't affect the logical state but give us the syndrome. However to represent this syndrome with the circuit model, ancillary qubits come in play and a destructive measurement on those ancillas occurs. Are this ancillas necessary? If yes, why?

$\endgroup$

1 Answer 1

1
$\begingroup$

The correction of errors during computations is required for large-scale quantum information processing. A qubit is encoded in a subspace of many physical qubits in quantum error correction so that faults can be actively rectified without altering the stored data. We must account for the fact that errors occur not only when something like a gate or measurement is applied on the qubit, but also while the qubits are idle. The solution is to keep measuring all the time. No qubit is ever left unattended for an extended period of time. Rather, data is continually pulled from the system in order to maintain track of any faults that have happened. However, this is not always practical and is an inefficient approach.

For example, measuring a superposition state would lead to collapsing it into a single state. In this case, we have not destroyed the error but we have used a wrong approach i.e. the superposition needed to be preserved. To avoid destroying states and still correct errors, QEC codes were created.

Feedback based on multi-qubit measurements, also known as stabilizer measurements, is a promising technique to repair faults in encoded quantum states. You can read more about this here: https://www.nature.com/articles/ncomms11526

So, in a nutshell, non-destructive measurement refers to a method of not damaging the state of our qubit as a result of measurement in order to correct errors.

$\endgroup$
1
  • $\begingroup$ I see what you mean. Thank you! What makes me confused is reading about a measurement such as $\sigma_z$, claimed to be non destructive, but I don't understand why it is not. I understand that one can simulate that by mean of a CNOT over an ancilla, but maybe I'd like to understand what it means besides that implementation. $\endgroup$ Jan 21, 2022 at 14:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.