Quantum Locally Testable Codes and Codes with Transversal Gates

Recent advancements in quantum error correction have led to breakthroughs in good quantum low-density parity-check (qLDPC) codes, which offer asymptotically optimal code rates and distances. However, several open questions remain, including the construction of quantum locally testable codes (qLTCs) and the construction of qLDPC codes with transversal gates. Interestingly, both questions can be approached through a higher-dimensional analog of the existing qLDPC code construction.

In this talk, I will review the constructions of good qLDPC codes and explain how to generalize them to higher dimensions. I will discuss methods for analyzing the code distance and local testability, as well as how the cup product structure on these codes enables transversal gates.

Based on joint work with Irit Dinur, Thomas Vidick, and Louis Golowich.