>[!warning] >This content has not been peer reviewed. # Entanglement protects information from noise **Quantum error correction (QEC):** Quantum information is fragile: decoherence and noise erase it. **QEC** encodes logical qubits into a larger number of physical qubits in an **entangled** state, so that local errors (bit flips, phase flips) can be detected and corrected without measuring (and thus destroying) the logical state. The **surface code** (Kitaev 2003; Fowler et al. 2012) is a leading scheme: logical qubits live in the **global** entanglement structure; local noise is correctable because the information is **non-local** (Bravyi & Kitaev 1998; Dennis et al. 2002). --- ## What it is - **Idea:** Encode one logical qubit in many physical qubits. The code is chosen so that **syndrome** measurements (parity checks) reveal errors without revealing the logical state. Correction restores the logical qubit. - **Surface code:** Qubits sit on a 2D lattice; stabilisers are local (nearest-neighbour). The logical information is stored in the **topological** (global) degrees of freedom — so it is **protected** from local noise. Threshold: below a certain physical error rate, logical error rate can be made arbitrarily small by increasing code distance. - **Implication:** **Entanglement** is not just correlation; it is a **mechanism for protecting information** from the environment. The substrate can “hold” information in a form that is robust to local fluctuations. --- ## How RRT/RST uses it - **Hardware implementation of A3:** **[[Translation]]** (A3) is the irreversible mechanism of change; every change costs energy (Landauer). In a quantum substrate, **erasure** is the default (decoherence, noise). QEC is the **hardware** that implements **persistence despite noise**: the substrate “uses” entanglement (non-local encoding) to keep logical information from being erased by local fluctuations. So **[[The minimum cost to erase a bit]]** still applies — but the cost of *erasing a logical bit* is now the cost of corrupting a whole *code block*; the surface code **raises** that cost by spreading the bit non-locally. - **Space as QEC:** If “space” is the relational network ([[Format]], A1), then the **geometry of space** can be interpreted as the **architecture of an error-correcting code**: distance ([[Relational distance]], A5) and connectivity determine how information is spread and how much noise can be tolerated. So “Space” is not just a distance; it is the **quantum error-correcting structure** the substrate uses to keep the “signal” of matter from being erased by vacuum fluctuations. This bridges the **Relational Landauer Principle** and **quantum mechanics**: persistence in a quantum world requires something like QEC; the substrate’s geometry may be that code. --- ## Links | Concept | Note | |:---|:---| | Cost per bit, erasure | **[[The minimum cost to erase a bit]]** | | Irreversible change, A3 | **[[Translation]]** | | Substrate, A1 | **[[Format]]** | | Axioms | **[[Relational Resolution Theory (RRT)]]** | --- ## References - Bravyi, S. B. & Kitaev, A. Y. (1998). *Quantum codes on a lattice with boundary.* [arXiv:quant-ph/9811052](https://arxiv.org/abs/quant-ph/9811052) - Kitaev, A. Y. (2003). *Fault-tolerant quantum computation by anyons.* Ann. Phys. **303**, 2–30. [DOI](https://doi.org/10.1016/S0003-4916(02)00018-0) - Dennis, E. et al. (2002). *Topological quantum memory.* J. Math. Phys. **43**, 4452–4505. [DOI](https://doi.org/10.1063/1.1499754) [arXiv:quant-ph/0110143](https://arxiv.org/abs/quant-ph/0110143) - Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. (2012). *Surface codes: Towards practical large-scale quantum computation.* Phys. Rev. A **86**, 032324. [DOI](https://doi.org/10.1103/PhysRevA.86.032324) [arXiv:1208.0928](https://arxiv.org/abs/1208.0928)