Method for 3D structure of measurement-free fault tolerant surface code

Abstract Quantum error correction (QEC) is essential for mitigating decoherence in quantum computations, but many QEC schemes rely heavily on mid-circuit measurements, which introduce significant noise due to their high error rates in current hardware. To overcome this limitation, we propose a measurement-free QEC scheme based on the surface code, leveraging its topological robustness while eliminating the need for physical measurements during error correction. Our key innovation is a three-dimensional patch-based architecture that interlinks three logical qubit patches, enabling coherent error extraction and feedback without measurements. By transforming syndrome information into geometric correlations across patches, our design inherently suppresses measurement-induced errors while preserving the surface code’s fault-tolerant thresholds. We analyze the scheme’s performance under realistic noise models and demonstrate its advantages over traditional flag-based or Steane-type QEC in regimes where measurements dominate error rate. This work bridges the gap between measurement-free QEC and scalable surface code architectures, offering a path toward fault-tolerant quantum computing in systems where fast, high-fidelity measurements remain impractical.