Scalable surface code decoders with parallelization in time

Abstract

Fast classical processing is essential for most quantum fault-tolerance architectures. We introduce a sliding-window decoding scheme that provides fast classical processing for the surface code through parallelism. Our scheme divides the syndromes in spacetime into overlapping windows along the time direction, which can be decoded in parallel with any inner decoder. With this parallelism, our scheme can solve the decoding throughput problem as the code scales up, even if the inner decoder is slow. When using min-weight perfect matching and union-find as the inner decoders, we observe circuit-level thresholds of 0.68% and 0.55%, respectively, which are almost identical to 0.70% and 0.55% for the batch decoding.

Modular decoding: parallelizable real-time decoding for quantum computers

“…Our work was developed independently, but we note partial overlap with the recently published results in Refs. [13,14]. Furthermore, this article makes several contributions beyond existing literature.…”

“…More recently, in Refs. [13,14], a parallel approach to decoding is proposed and numerically benchmarked, showing that decoding can be parallelized without significant impact on accuracy (LER). We note that parallel decoders for some (non-topological) quantum LDPC codes have previously been proposed [15].…”

Robustness of Gauge Digitization to Quantum Noise

“…ZN number of physical qubits can scale from linearly to exponentially with logical qubits [37][38][39][40]. Phase transitions can separate theories with weak and strong gauge violations and different operators [58][59][60][61][62][63][64][65] so one can consider correcting only errors necessary to be in the same phase.…”

“…Different layouts and mixed architectures (combining qubits and qudits) are being investigated [20][21][22][23][24][25][26][27][28][29]. Further questions persist around the merits of quantum memory such as qRAM [30][31][32][33][34][35][36] and efficient quantum error correction (QEC) [37][38][39][40] where between O(10 1−5 ) physical qubits per logical qubit appear necessary for fault tolerance [41][42][43][44]. Meanwhile, quantum advantage for HEP problems may be possible by designing them to be robust to certain errors, using partial QEC [45][46][47][48][49][50][51], hardware-aware embeddings [52][53][54], or biased-noise qubits [55,56].…”

Sparse Blossom: correcting a million errors per core second with minimum-weight matching

“…When used for error correction simulations, we note that sparse blossom is already trivially parallelisable by splitting the simulation into batches of shots, and processing each batch on a separate core. However, parallelisation of the decoder itself is important for real-time decoding, to prevent an exponentially increasing backlog of data building up within a single computation [Ter15], or to avoid the polynomial slowdown imposed by relying on parallel window decoding instead [Sko+22;Tan+22]. Therefore, future work could explore combining sparse blossom with the techniques for parallelisation introduced in fusion blossom.…”