Automated discovery of logical gates for
quantum error correction
(pp947-964)
Hongxiang
Chen, Michael Vasmer,
Nikolas P. Breuckmann, and Edward Grant
Supplementary
(153 pages)
doi:
https://doi.org/10.26421/QIC22.11-12-3
Abstracts:
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 that 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
optimization. We test the procedure by simulating small quantum codes of
four to fifteen
qubits
showing that our procedure 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, the
[[8,3,2]] code, and the [[10,1,2]] code.
Key words:
Quantum computation,
Error correction, Machine learning |