Efficient LDPC Codes: Simulating Generalized Bicycle Codes for Atom Arrays

Achieving error rates necessary for disruptive quantum algorithms will likely require fault tolerance, incurring large qubit overheads for quantum error correction. Families of quantum LDPC codes have provided promising results for minimizing this overhead via good encoding rates, but are often difficult to implement in hardware due to the requirement of long range interactions. In this work we present a protocol for efficiently implementing stabilizer circuits of generalized bicycle codes in atom array devices. Our protocol identifies a good match between the cyclic structure of these codes and qubit movement in atom arrays via acousto-optic deflectors (AODs). We validate our protocol with circuit-level simulations and examine the impact of stabilizer weight on code performance.