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Error correction can fix bit flips, but how can it help if qubits loose entanglement?
by sesm 3y ago
Error correction can fix bit flips, but how can it help if qubits loose entanglement?
- sebzim4500 3y agoIt's an unintuitive theorem in quantum computation that as long as you can protect against two types of errors (bit flips and sign flips) you are protected against almost all errors.
- sesm 3y agoWhen qbits are not entangled, quantum computer doesn't exist anymore, this is not a kind of error that you can correct.
- eigenket 3y agoThere isn't a good non-technical answer to your previous question but lemma 3.3 of this paper [1] says that if you can correct a finite set of errors for each qubit individually then you can also (essentially for free) correct all other errors. Specifically if you correct a set of errors which spans the set of possible errors (for example the Pauli errors on each qubit do this) then you correct all errors. This is essentially the reason people are still interested in quantum computing, and why quantum error correction is viable at all. You can protect highly entangled crazy states from highly non-local complicated errors using only the resources needed to correct simple local errors. [1] Key ideas in quantum error correction, Raussendorf 2012: https://royalsocietypublishing.org/doi/10.1098/rsta.2011.0494 https://royalsocietypublishing.org/doi/10.1098/rsta.2011.049...
- fxj 3y agoCan you also compensate against decoherence? I thought this is the magic limit when the QC breaks. See also: https://blogs.scientificamerican.com/observations/decoherence-is-a-problem-for-quantum-computing-but/ https://blogs.scientificamerican.com/observations/decoherenc...
- eigenket 3y agoDecoherence here pretty much just means "enough individual errors that you can't recover from them anymore". Theoretically yes, it is quite clear that you can protect against this. Practically doing so at the scale you need for a real, useful computer is very hard.
- deleted 3y ago[deleted]
- Strilanc 3y agoQuantum error correction corrects more than just bit flips. It corrects phase flips, accidental measurement, qubit erasure, small global rotations... lots of stuff. I don't know exactly what you have in mind as "loss of entanglement"... But quantum error correction will very much preserve entanglement at the logical level against decay of entanglement at the physical level.