Efficient real-time decoder for 2D-local phase-flip LDPC (cellular automaton) codes

Develop an efficient syndrome decoder that can be integrated into the quantum processor to perform real-time decoding for the 2D-local phase-flip LDPC cellular automaton codes with low-weight X-type stabilizers proposed for concatenation with cat qubits, capable of processing repeated rounds of stabilizer measurements during operation.

Background

The paper proposes a hardware-efficient architecture that concatenates cat qubits with high-rate 2D-local phase-flip LDPC codes, many of which are cellular automaton (fractal) codes with weight-4 X-type stabilizers. Performance is evaluated using a BP+OSD decoder in numerical simulations, but practical deployment requires fast decoding compatible with code-cycle times.

The authors emphasize that a decoder suitable for real-time integration into the processor remains to be developed and note in an appendix that identifying a faster or more efficient decoder for these highly structured codes is an unresolved task.

References

Finally, the construction of an efficient decoder for our codes that could be integrated into the architecture of the quantum processor to decode syndromes in real-time is still an open research problem.

— LDPC-cat codes for low-overhead quantum computing in 2D (2401.09541 - Ruiz et al., 17 Jan 2024) in Conclusion (Section: Conclusion)