Error-rate-agnostic decoding of topological stabilizer codes
Journal article, 2022

Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold maximum-likelihood decoders require an explicit error model for Pauli errors to decode a specific syndrome, whereas lower-threshold heuristic approaches such as minimum-weight matching are error agnostic. Here we consider an intermediate approach, formulating a decoder that depends on the bias, i.e., the relative probability of phase-flip to bit-flip errors, but is agnostic to error rate. Our decoder is based on counting the number and effective weight of the most likely error chains in each equivalence class of a given syndrome. We use Metropolis-based Monte Carlo sampling to explore the space of error chains and find unique chains that are efficiently identified using a hash table. Using the error-rate invariance, the decoder can sample chains effectively at an error rate which is higher than the physical error rate and without the need for thermalization between chains in different equivalence classes. Applied to the surface code and the XZZX code, the decoder matches maximum-likelihood decoders for moderate code sizes or low error rates. We anticipate that, because of the compressed information content per syndrome, it can be taken full advantage of in combination with machine-learning methods to extrapolate Monte Carlo-generated data.

Author

Karl Hammar

University of Gothenburg

Alexei Orekhov

Student at Chalmers

Patrik Wallin Hybelius

University of Gothenburg

Anna Katariina Wisakanto

University of Gothenburg

Basudha Srivastava

University of Gothenburg

Anton Frisk Kockum

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Mats Granath

University of Gothenburg

Physical Review A

24699926 (ISSN) 24699934 (eISSN)

Vol. 105 4 042616

Subject Categories

Telecommunications

Computational Mathematics

Probability Theory and Statistics

DOI

10.1103/PhysRevA.105.042616

More information

Latest update

5/31/2022