Comprehensive high-speed reconciliation for continuous-variable quantum key distribution

Reconciliation is currently the bottleneck of continuous-variable quantum key distribution systems for its great influence on the key rate and the distance of systems. In this paper, we address the increase in key rates by accelerating the speed of reconciliation algorithms based on the protocol of sliced error correction on a heterogeneous computing structure (a GPGPU card (general purpose graphics processing units will be abbreviated as GPU in this paper) and a general CPU) in the framework of Open Computing Language (OpenCL) (OpenCL is a programming framework based on C language). A block length of its component codes of low-density parity-check (LDPC) codes up to 2\(^{17}\) bits is employed in order to achieve a higher reconciliation efficiency. To meet the requirements of the OpenCL specifications, we designed a data structure, namely static cross bi-directional circular linked list, to store a super large sparse check matrix of the LDPC codes. Such a configuration ensures the practicability of our system, i.e. a better trade-off between the speed and net key rates of the reconciliation. The speed of the proposed reconciliation scheme reaches about 70.1 Mb/s with 512 codewords decoding in parallel, approximately 3600 times faster than that with the platform with only a CPU.