Parallel window decoding enables scalable fault tolerant quantum computation

• URL: http://arxiv.org/abs/2209.08552v1
• Date: Sun, 18 Sep 2022 12:37:57 GMT
• Title: Parallel window decoding enables scalable fault tolerant quantum computation
• Authors: Luka Skoric, Dan E. Browne, Kenton M. Barnes, Neil I. Gillespie, Earl T. Campbell
• Abstract summary: We present a methodology that parallelizes the decoding problem and achieves almost arbitrary syndrome processing speed. Our parallelization requires some classical feedback decisions to be delayed, leading to a slow-down of the logical clock speed. Using known auto-teleportation gadgets the slow-down can be eliminated altogether in exchange for increased qubit overhead.
• Score: 2.624902795082451
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum Error Correction (QEC) continuously generates a stream of syndrome data that contains information about the errors in the system. Useful fault-tolerant quantum computation requires online decoders that are capable of processing this syndrome data at the rate it is received. Otherwise, a data backlog is created that grows exponentially with the $T$-gate depth of the computation. Superconducting quantum devices can perform QEC rounds in sub-1 $\mu$s time, setting a stringent requirement on the speed of the decoders. All current decoder proposals have a maximum code size beyond which the processing of syndromes becomes too slow to keep up with the data acquisition, thereby making the fault-tolerant computation not scalable. Here, we will present a methodology that parallelizes the decoding problem and achieves almost arbitrary syndrome processing speed. Our parallelization requires some classical feedback decisions to be delayed, leading to a slow-down of the logical clock speed. However, the slow-down is now polynomial in code size and so an exponential backlog is averted. Furthermore, using known auto-teleportation gadgets the slow-down can be eliminated altogether in exchange for increased qubit overhead, all polynomially scaling. We demonstrate our parallelization speed-up using a Python implementation, combining it with both union-find and minimum weight perfect matching. Furthermore, we show that the algorithm imposes no noticeable reduction in logical fidelity compared to the original global decoder. Finally, we discuss how the same methodology can be implemented in online hardware decoders.

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