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A general theory of quantum codes connecting quantum computation, complexity and physics

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Nature Physics, Published online: 18 September 2024; doi:10.1038/s41567-024-02622-w

Approximate notions of quantum error-correcting codes hold wide importance across quantum information and physics, but are not cohesively understood. Now, general rigorous connections established between approximate quantum error correction and quantum circuit complexity reveal a ‘complexity phase diagram’ for generalized quantum codes — and create a new unifying lens on complex quantum systems.