An Accurate Union Find Decoder for Quantum Error Correction on the Toric Code

Quantum computing represents an exciting computing paradigm that promises to solve problems untractable for a classical computer. One main limiting factor is the noise impacting qubits, which hinders the superpolynomial speedup promise. Thus, although Quantum Error Correction (QEC) mechanisms are paramount, QEC demands high speed and low latency to scale quantum computations. Within this context, hardware accelerators, such as FPGAs, represent a valuable approach to fulfilling the QEC requirements. Nevertheless, the literature falls short in proposing solutions optimized for the toric code, which is capable of encoding two logical qubits and, therefore, requires fewer qubits to correct errors. This manuscript presents QUEKUF, an FPGA-based QEC dataflow architecture dealing with toric code. QUEKUF disposes of parallel processing units to spatially parallelize QEC that a centralized controller orches-trates for data movement and operation decisions. Experimental results show that our design attains up to 20.14 × improvement in execution time over a C++ implementation while keeping a high accuracy, similar to the theoretical framework.