Scalable Neural Network Decoders for Higher Dimensional Quantum Codes

Abstract

Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that they can be evaluated by dedicated hardware which is very fast and consumes little power. Machine learning has been previously applied to decode the surface code. However, these approaches are not scalable as the training has to be redone for every system size which becomes increasingly difficult. In this work the existence of local decoders for higher dimensional codes leads us to use a low-depth convolutional neural network to locally assign a likelihood of error on each qubit. For noiseless syndrome measurements, numerical simulations show that the decoder has a threshold of around 7.1% when applied to the 4D toric code. When the syndrome measurements are noisy, the decoder performs better for larger code sizes when the error probability is low. We also give theoretical and numerical analysis to show how a convolutional neural network is different from the 1-nearest neighbor algorithm, which is a baseline machine learning method.

Quantum error correction for the toric code using deep reinforcement learning

“…Finding better performing decoders has been the topic of many studies, using methods such as renormalization group [31,32], cellular automata [33,34], and a number of neural network based decoders [19,[35][36][37][38][39][40][41][42][43]. The decoder presented in this paper does not outperform state of the art decoders, it's value lies in showing that it is possible to use reinforcement learning to achieve excellent performance on a minimal model.…”

Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes

“…In this article, we use this strategy for the decoding of quantum LDPC codes. Neural-networkbased decoders for quantum error-correcting codes have attracted great interest recently, particularly in the context of topological codes [16][17][18][19][20][21][22][23][24][25][26][27]. But near optimal (or very fast suboptimal) decoding algorithms are already proposed for these codes [28][29][30][31], which exploit their regular lattice structure.…”

Optimizing Quantum Error Correction Codes with Reinforcement Learning

“…For the problem of finding optimized QEC strategies for near-term quantum devices, adaptive machine learning [11] approaches may succeed where brute force searches fail. In fact, machine learning has already been applied to a wide range of decoding problems in QEC [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Efficient decoding is of central interest in any fault-tolerant scheme.…”