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).

28 pages, 24 figures. Comments welcome! V2 Contains a more detailed FPGA analysis

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• Artificial Intelligence for Quantum Computing
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Neural network decoder for near-term surface-code experiments
• Artificial Neural Network Syndrome Decoding on IBM Quantum Processors
• Mitigating errors in logical qubits
• Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction
• Spatially parallel decoding for multi-qubit lattice surgery
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Pinball: A Cryogenic Predecoder for Surface Code Decoding Under Circuit-Level Noise
• Neural Decoders for Universal Quantum Algorithms