Learning to decode logical circuits

Area of Science:

• Quantum Information Science
• Quantum Error Correction
• Computational Complexity

Background:

• Advancing quantum hardware necessitates efficient decoding algorithms for error-corrected quantum circuits.
• Correlated errors from entangling gates challenge conventional quantum memory decoding methods.
• A polynomial-time decoding algorithm is critical for realizing fault-tolerant quantum computation.

Purpose of the Study:

• To introduce a novel, data-centric, modular decoder framework for deep logical quantum circuits.
• To address the bottleneck of decoding correlated errors introduced by entangling gates.
• To develop a noise-model-agnostic decoding solution for scalable quantum computing.

Main Methods:

• Developed the Multi-Core Circuit Decoder (MCCD) framework with modular components for each logical operation.
• Trained MCCD using mirror-symmetric random Clifford circuits to learn correlated error patterns.
• Evaluated MCCD performance on deep circuits, comparing accuracy and decoding time against MWPM, MLE, and BP-OSD.

Main Results:

• MCCD effectively learns and decodes correlated errors in quantum circuits.
• Maintained high logical accuracy on circuits deeper than those used for training.
• Achieved competitive accuracy with significantly improved time efficiency, especially for circuits with entangling gates.

Conclusions:

• The MCCD framework provides an efficient and accurate solution for decoding deep logical quantum circuits.
• This approach overcomes limitations of traditional decoders, particularly in handling correlated errors.
• MCCD represents a significant step towards fault-tolerant quantum computation by addressing a critical decoding bottleneck.