Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes

Abstract

Belief-propagation (BP) decoders play a vital role in modern coding theory, but they are not suitable to decode quantum error-correcting codes because of a unique quantum feature called error degeneracy. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check (LDPC) codes with a loss function tailored to error degeneracy. Training substantially improves the performance of BP decoders for all families of codes we tested and may solve the degeneracy problem which plagues the decoding of quantum LDPC codes.

Pseudocodeword-based Decoding of Quantum Stabilizer Codes

“…4 shows some simulation results of SPA+LPPCWD decoding of toric codes described in Algorithm 2, where we use at most 100 iterations of SPA to obtain SPA pseudocodewords. According to the simulation results in [4], the performance of the original SPA gets worse as the code block length of toric codes increases. As shown in Fig.…”

“…The task of analyzing the behavior of SPA decoding for quantum stabilizer codes is more challenging, especially because the degeneracy of quantum stabilizer codes needs to be taken into account. Despite these challenges, being able to understand and improve the behavior of the SPA is highly desirable, since it has been observed that the performance of the SPA is far from satisfactory when decoding quantum stabilizer codes of high degeneracy (see, e.g., the discussion of simulation results of various massage-passing iterative decoding algorithms and LP decoders in [2]- [4]).…”

“…The maximum number of iterations of SPA is 100 and the maximum number of IMR trials is 10. The IMR-SPA achieves lower WER at around p = 10 −2 compared with the the neural belief-propagation decoder [4] for MacKay's bicycle codes with the same parameters.…”

“…{Remove isolated checks.} 8: end while in [4] and the Markov chain Monte Carlo algorithm in [14]. Fig.…”

Generation of ice states through deep reinforcement learning

“…Reinforcement learning has demonstrated remarkable abilities in achieving better than human performances on video games [22], and the game of Go [23,24]. Recently it has also been applied to quantum physics research such as quantum control [25], quantum error correction [26][27][28], quantum experiment design [29]. In a reinforcement learning setup, a machine agent interacts with its environment.…”