Automated discovery of logical gates for quantum error correction

Hongxiang Chen, Michael Vasmer, Nikolas P. Breuckmann, Edward Grant

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Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimizations. We test the procedure by simulation on classical computers on small quantum codes of four qubits to fifteen qubits and show that it finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.
Original languageEnglish
Pages (from-to)947-964
Number of pages18
JournalQuantum Information and Computation
Issue number11-12
Publication statusPublished - 4 Aug 2022

Bibliographical note

Funding Information:
We wish to acknowledge the usage of high performance computing cluster from Department of Computer Science, University College London in completion of this project. H.C. acknowledges the support through a Teaching Fellowship from UCL. E.G. is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) [EP/P510270/1] M.V. at the Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade. N.P.B. is supported by the UCLQ Fellowship.

Publisher Copyright:
© Rinton Press.


  • Error correction
  • Machine learning
  • Quantum computation


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