Quantum computing with topological codes
Logical quantum information can be stored nonlocally in stabilizer-code degrees of freedom.
$$\bar X\bar Z=-\bar Z\bar X$$
What this means
Logical quantum information can be stored nonlocally in stabilizer-code degrees of freedom.
Deep dive: mathematical and physical mechanism
In surface codes, data qubits and repeated local parity checks detect error syndromes. Logical operators form extended strings or loops; increasing code distance raises the minimum number of physical faults needed for an undetectable logical error.
How it appears in quantum phenomena
Superconducting and other quantum processors investigate surface-code error correction.
Assumptions, caveats and limitations
Error correction requires repeated high-fidelity measurements and decoding; threshold depends on the noise model.
Connect the ideas
For context, see the Quantum Phenomena and Applications topic guide and the reading references.