High-rate quantum LDPC codes for long-range-connected neutral atom registers

Abstract

High-rate quantum error correcting (QEC) codes with moderate overheads in qubit number and control complexity are highly desirable for achieving fault-tolerant quantum computing. Recently, quantum error correction has experienced significant progress both in code development and experimental realizations, with neutral atom qubit architecture rapidly establishing itself as a leading platform in the field. Scalable quantum computing will require processing with QEC codes that have low qubit overhead and large error suppression, and while such codes do exist, they involve a degree of non-locality that has yet to be integrated into experimental platforms. In this work, we analyze a family of high-rate Low-Density Parity-Check (LDPC) codes with limited long-range interactions and outline a near-term implementation in neutral atom registers. By means of circuit-level simulations, we find that these codes outperform surface codes in all respects when the two-qubit nearest neighbour gate error probability is below $\sim 0.1\%$. By using multiple laser colors, we show how these codes can be natively integrated in two-dimensional static neutral atom qubit architectures with open boundaries, where the desired long-range connectivity can be targeted via the Rydberg blockade interaction.

16 pages, 7 figures. General revision, added references, added appendices

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Cited by in corpus (13)

• Architecture for fast implementation of qLDPC codes with optimized Rydberg gates
• Quantum Error Correction resilient against Atom Loss
• Error correction of transversal CNOT gates for scalable surface code computation
• A fiber array architecture for atom quantum computing
• Quantum error correction for long chains of trapped ions
• Adaptive Syndrome Extraction
• Quantum low-density parity-check codes for erasure-biased atomic quantum processors
• Low-depth quantum error correction via three-qubit gates in Rydberg atom arrays
• Enhanced Lieb-Robinson bounds for commuting long-range interactions
• Cavity polariton blockade for non-local entangling gates with trapped atoms
• Non-local resources for error correction in quantum LDPC codes
• Qudit low-density parity-check codes
• GPU-Accelerated Syndrome Decoding for Quantum LDPC Codes below the 63 $\mu$s Latency Threshold