Neural network decoder for topological color codes with circuit level noise

P. Baireuther*, M. D. Caio, B. Criger, C. W.J. Beenakker, T. E. O'Brien

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)
78 Downloads (Pure)


A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a way to tailor such an algorithm to the specific error processes of an experiment - without the need for a priori knowledge of the error model. Here, we apply this technique to topological color codes. We demonstrate that a recurrent neural network with long short-term memory cells can be trained to reduce the error rate L of the encoded logical qubit to values much below the error rate phys of the physical qubits - fitting the expected power law scaling , with d the code distance. The neural network incorporates the information from 'flag qubits' to avoid reduction in the effective code distance caused by the circuit. As a test, we apply the neural network decoder to a density-matrix based simulation of a superconducting quantum computer, demonstrating that the logical qubit has a longer life-time than the constituting physical qubits with near-term experimental parameters.

Original languageEnglish
Article number013003
Number of pages13
JournalNew Journal of Physics
Issue number1
Publication statusPublished - 8 Jan 2019


  • machine learning
  • quantum error correction
  • recurrent neural network
  • topological color codes


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