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arXiv · 2302.04317

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

Nouédyn Baspin·Omar Fawzi·Ala Shayeghi
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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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Nouédyn Baspin, Omar Fawzi, Ala Shayeghi. 2023-02-08. A lower bound on the overhead of quantum error correction in low dimensions. https://arxiv.org/abs/2302.04317

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