Techniques for combining fast local decoders with global decoders under circuit-level noise

Abstract

Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying these requirements. We then introduce the construction of local neural network (NN) decoders using three-dimensional convolutions. These local decoders are adapted to circuit-level noise and can be applied to surface code volumes of arbitrary size. Their application removes errors arising from a certain number of faults, which serves to substantially reduce the syndrome density. Remaining errors can then be corrected by a global decoder, such as Blossom or Union Find, with their implementation significantly accelerated due to the reduced syndrome density. However, in the circuit-level setting, the corrections applied by the local decoder introduce many vertical pairs of highlighted vertices. To obtain a low syndrome density in the presence of vertical pairs, we consider a strategy of performing a syndrome collapse which removes many vertical pairs and reduces the size of the decoding graph used by the global decoder. We also consider a strategy of performing a vertical cleanup, which consists of removing all local vertical pairs prior to implementing the global decoder. Lastly, we estimate the cost of implementing our local decoders on Field Programmable Gate Arrays (FPGAs).

Real-time decoding for fault-tolerant quantum computing: progress, challenges and outlook

“…For superconducting and photonic qubits, a high operational rate implies that the decoding throughput and latency are paramount [21,42]. Throughput (defined as the time it takes the decoder coprocessor to perform the decoding once it receives the measurement outcomes) is even more important than latency (defined as the time it takes to send the measurement outcomes to the decoder coprocessor) [41,43]. In recent superconducting-qubit experiments, QEC rounds were performed every ∼1 µs [21][22][23][24], leading to an estimate that a utility-scale quantum computer would generate a few tens of Mbps of syndrome data per logical qubit, for a total of many Tbps [44].…”

“…Besides being fast, a decoder must also be accurate, scalable with respect to the number of physical qubits, able to tackle complex noise models and compatible with lattice surgery. In those respects, neural-network decoders are promising candidates for real-time decoding, thanks to their constant inference time, the inherent ability to learn any error model, the scalability to large code distances [34,43,83] and compatibility with lattice surgery [34,43,84]. Nevertheless, several challenges must be overcome before seeing neural-network hardware decoders in a practical quantum computer, such as finding the optimal neural-network architecture able to address complex error models, and quantifying the trade-offs between the hardware costs and the decoder performance.…”

“…Hardware-based decoder implementations have been proposed as alternative to software decoders to keep the (expected) decoding times below the 1 µs target, e.g. employing FPGAs [25,26,28,29,32,43], ASICs [27,32] or single-flux-quantum logic (SFQ) [38][39][40]84]. In the case of neural-network-based decoders, implementing them in hardware can exploit the advances in the field of hardware accelerators for neural networks for classical applications, such as image and voice recognition.…”

“…Many proposals [30,33,34,43,69,84,103,104] have been put forward where decoding occurs in two stages, with a first, computationally-simple local decoder and a second, more-complex global decoder. The first stage can either be a pre-processing stage whose outcome is passed anyway to the global decoder [69], or it can try to correct all errors (if the pattern is 'simple' enough) and call the global decoder only when it fails.…”

Scalable surface code decoders with parallelization in time

“…On the other hand, local decoding schemes [12][13][14][15][16][17][18][19] are fast and scalable to a certain degree, but their speed comes at the expense of accuracy. The accuracy of local decoders can be improved by appending a global decoder [20][21][22][23][24][25] while still pursuing relatively high decoding throughputs. Other schemes based on specialized hardware [26][27][28][29] have also been proposed.…”