CSS Circuits: useful quantum circuits that can be simulated with $O(1)$ cost per gate

arXiv:2611.14944v1 Announce Type: new Abstract: "CSS circuits" are quantum circuits generated by $X$, $Z$, $M_X$, $M_Z$, and CNOT gates. Although CSS circuits are extremely restrictive, they can implement important quantum protocols like teleportation, error correction, and entanglement purification. We present a simple CSS circuit simulator that uses $O(1)$ work per gate. The simulator corresponds to a local hidden variable model, so we use Bell inequalities to prove the simulator can't also support Hadamard gates, CZ gates, or S gates. We note that CSS circuits appear ideal for benchmarking quantum error correction in the presence of atom loss errors.