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

There have been several recent breakthroughs constructing good quantum codes which have Nqubits with distance and dimension \Omega(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 Nqubits 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.

*In-person and on Zoom*

https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09
Passcode: 657361
https://mathpicture.fas.harvard.edu/seminar