Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, potentially enabling low-overhead fault-tolerant quantum computing. However, implementing qLDPC codes involves nonlocal operations that require long-range connectivity between qubits. This makes their physical realization challenging in comparison to geometrically local codes, such as the surface code. Here we propose a hardware-efficient scheme for fault-tolerant quantum computation with high-rate qLDPC codes that is compatible with the recently demonstrated capabilities of reconfigurable atom arrays. Our approach utilizes the product structure inherent in many qLDPC codes to implement the nonlocal syndrome extraction circuit through atom rearrangement, resulting in an effectively constant overhead. We prove the fault tolerance of these protocols, and our simulations show that the qLDPC-based architecture starts to outperform the surface code with as few as several hundred physical qubits. We further find that quantum algorithms involving thousands of logical qubits can be performed using less than 105 physical qubits. Our work suggests that low-overhead quantum computing with qLDPC codes is within reach using current experimental technologies. Quantum low-density parity-check codes are highly efficient in principle but challenging to implement in practice. This proposal shows that these codes could be implemented in the near term using recently demonstrated neutral-atom arrays.