Runtime reduction in lattice surgery utilizing time-like soft information

Optimizing the runtime of quantum computing within given computational resources is essential to achieve practical quantum advantage. This work proposes a runtime reduction protocol for lattice surgery, utilizing time-like soft information associated with logical measurement errors. Our proposal is a simple two-step protocol: first, operating lattice surgery with the reduced number of syndrome measurement cycles, and second, re-executing it with full syndrome measurement cycles when time-like soft information indicates logical measurement errors. We first discuss basic features of the time-like complementary gap, whose definition is inspired by existing works on its space-like counterpart [1,2]. Then, we demonstrate that our protocol surpasses the existing runtime reduction protocol, temporally encoded lattice surgery (TELS) [3], in most cases. Finally, we propose soft-information-accelerated TELS (STELS), a combination of our protocol and TELS. We confirm that STELS can further reduce the runtime, by over 50% compared to the naive lattice surgery under practical assumptions. The proposed protocol can be applied to any quantum computing architecture based on lattice surgery, and this is expected to be a fundamental building block for runtime optimization towards practical-scale quantum computing.



[1] C. Gidney et al., Nat Commun 16, 4498 (2025).

[2] H. Bombin et al., PRX Quantum 5, 010302 (2024)

[3] C. Chamberland and E. T. Campbell, PRX Quantum 3, 010331 (2022)