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Despite the necessity of fault-tolerant quantum systems built on errorcorrecting codes, many popular codes, such as the surface code, haveprohibitively large overheads. This has spurred significant interest in quantumLDPC codes which can reduce this overhead by an order of magnitude.Unfortunately, this reduction comes at the cost of many long rangeinteractions. The difficulty in implementing these long range interactionsraises questions about the practical viability of quantum LDPC codes.  In this work we identify quantum LDPC codes that can be used in practice bycarefully matching their features with underlying hardware. We target aspecific family, known as generalized-bicycle codes, which have the favorableproperty of repeated check structure. We find this property can be exploited byquantum computers made from atom arrays, enabling an efficient implementation.Using numerical simulations, we evaluate the performance of generalized-bicyclecodes in atom arrays and find comparable logical error rates to surface codes,but with an order of magnitude lower qubit overhead.  We then quantify the utility of this implementation in the context of acomplete fault tolerant architecture. We compare the cost of implementingbenchmark programs in a standard, surface code only architecture and a recentlyproposed mixed architecture where data is stored in qLDPC memory but is loadedto surface codes for computation. We treat the mixed architecture as a simplememory hierarchy and analyze the dependence of performance on program structureand compilation. Overall, for most programs of interest we find the mixedarchitecture leads to reduced costs compared to a standard, surface code onlyarchitecture. Additionally, we point out important compiler optimizations thatemphasize qubit reuse and perform data prefetching to further improve theperformance of the mixed architecture.

Matching Generalized-Bicycle Codes to Neutral Atoms for Low-Overhead Fault-Tolerance