A lower bound on the overhead of quantum error correction in low dimensions

• URL: http://arxiv.org/abs/2302.04317v1
• Date: Wed, 8 Feb 2023 20:19:28 GMT
• Title: A lower bound on the overhead of quantum error correction in low dimensions
• Authors: Nou\'edyn Baspin and Omar Fawzi and Ala Shayeghi
• Abstract summary: We show that a quantum architecture with an error correction procedure limited to geometrically local operations incurs an overhead that grows with the system size. In particular, we prove that in order to operate a quantum error correcting code in 2D at a logical error rate of $delta$, a space overhead of $Omega(sqrtlog(1/delta))$ is needed.
• Score: 9.797319790710711
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that a quantum architecture with an error correction procedure limited to geometrically local operations incurs an overhead that grows with the system size, even if arbitrary error-free classical computation is allowed. In particular, we prove that in order to operate a quantum error correcting code in 2D at a logical error rate of $\delta$, a space overhead of $\Omega(\sqrt{\log(1/\delta)})$ is needed for any constant depolarizing noise $p > 0$.

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