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Towards an Efficient Decoder for Quantum LDPC Codes

Jonas Anderson, Université de Sherbrooke

(Session 9a : Friday from 5:30pm - 6:00pm)

Quantum low-density parity-checking (LDPC) codes can greatly reduce the overhead associated with fault-tolerant quantum computation (FTQC) by providing a nonzero-rate code family with low-weight stabilizer generators. In principle this means that as the code distance grows so does the number of encoded qubits thus allowing FTQC with constant overhead [1]. Exact decoding of classical LDPC codes is computationally difficult, but approximate decoders such as the belief propagation (BP) decoder are known to work well. For quantum LDPC codes much less is known and BP without modifications is plagued with issues due to degeneracy and short cycles in the Tanner graph. Here we improve upon the work of Poulin and Chung [2] by modifying BP to correct for some of the effects of message passing on a Tanner graph with cycles. Our technique uses nonlinear message weights to offset the additional correlations picked up due to cycles. For physical error rates an order of magnitude below pseudothreshold, arguably the most important regime for FTQC, we improve upon the best-known decoding schemes by an order of magnitude. We will also discuss ideas to further improve upon these schemes. [1] Daniel Gottesman, “What is the Overhead Required for Fault-Tolerant Quantum Computation?” arxiv.org/1310.2984. [2] David Poulin and Yeojin Chung, “On the iterative decoding of sparse quantum codes” Quantum Information and Computation, Vol. 8, No. 10 (2008) 0987–1000.