Fault-Tolerant Compilation of Classically Hard IQP Circuits on Hypercube Quantum Codes

The authors propose a hardware-efficient, fault-tolerant approach to realizing complex sampling circuits by co-designing the circuits with appropriate quantum error correcting codes. They focus on a family of high-dimensional color codes that support transversal non-Clifford gates, enabling the efficient implementation of classically hard instantaneous quantum polynomial (IQP) circuits.