QECOOL: On-Line Quantum Error Correction with a Superconducting Decoder for Surface Code

Due to the low error tolerance of a qubit, detecting and correcting errors on it is essential for fault-tolerant quantum computing. Surface code (SC) associated with its decoding algorithm is one of the most promising quantum error correction (QEC) methods. QEC needs to be very power-efficient since the power budget is limited inside of a dilution refrigerator for superconducting qubits by which one of the most successful quantum computers (QCs) is built. In this paper, we propose an online-QEC algorithm and its hardware implementation with SFQ based superconducting digital circuits. We design a key building block of the proposed hardware with an SFQ cell library and evaluate it by the SPICE-level simulation. Each logic element is composed of about 3000 Josephson junctions and power consumption is about $2.78 \mu \mathrm{W}$ when operating with 2 GHz clock frequency which meets the required decoding speed. Our decoder is simulated on a quantum error simulator for code distances 5 to 13 and achieves a 1.0% accuracy threshold.