Transversal non-Clifford gates for quantum LDPC codes on sheaves

Understand

A major goal in quantum computing is to build a fault-tolerant quantum computer.

• One approach involves quantum low-density parity-check (qLDPC) codes that support transversal non-Clifford gates.
• In this work, we provide a large family of such codes.
• The key insight is to interpret the logical operators of qLDPC codes as geometric surfaces and use the intersection number of these surfaces to define the non-Clifford operation.