Quantum error-correcting codes, systolic geometry, and quantitative embeddings

Abstract: There have been several recent breakthroughs constructing good quantum codes which have N qubits with distance and dimension Ω(N). However, these codes cannot be implemented in 3 dimensions - there is no way to place the qubits on a lattice so that every check only involves the qubits in some small ball. Bravyi and Terhal have shown that such 3d codes with qubits can have distance at most O(N^2/3) and dimension at most O(N^1/3), given that distance. In this talk I'll discuss how to construct 3d codes with parameters that match these bounds. This relies on the known good codes, a connection between codes and systolic geometry made by Freedman-Hastings, and a quantitative embedding theorem.

quantum computing and informationMathematicsPhysics

Audience: researchers in the topic

Comments: Passcode: 657361

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