  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. % One of the challenges of QEC is its high
complexity and computational demand. 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 uW 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.
