<tt>QUEKUF</tt> : An FPGA 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. The main limiting factor for quantum devices 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 to real-life-sized problems. Within this context, hardware accelerators, such as Field Programmable Gate Arrays (FPGAs), represent a valuable approach to fulfilling QEC requirements. Nevertheless, the literature falls short in proposing solutions targeting the toric code, a type of quantum Low-Density Parity Check code capable of encoding two logical qubits, thus requiring fewer physical qubits. This manuscript presents QUEKUF , an FPGA-based QEC dataflow architecture dealing with the toric code. QUEKUF disposes of parallel processing units to spatially parallelize QEC, which a centralized controller orchestrates for data movement and operation decisions. We also provide a latency-oriented resource optimization model to identify the best theoretical configuration of QUEKUF that minimizes latency and optimizes resource requirements based upon high-level quantum parameters. Experimental results show that QUEKUF attains up to \(7.30\times\) speedup and \(81.51\times\) improvement in energy efficiency over a C++ implementation with error-free syndromes while keeping high accuracy.