  Color code is a promising topological code for fault-tolerant quantum
computing. Insufficient research on the color code has delayed its practical
application. In this work, we address several key issues to facilitate
practical fault-tolerant quantum computing based on color codes. First, by
introducing decoding graphs with error-rate-related weights, we obtained the
threshold of $0.47\%$ of the 6,6,6 triangular color code under the standard
circuit-level noise model, narrowing the gap to that of the surface code.
Second, our work firstly investigates the circuit-level decoding of color code
lattice surgery, and gives an efficient decoding algorithm, which is crucial
for performing logical operations in a quantum computer with two-dimensional
architectures. Lastly, a new state injection protocol of the triangular color
code is proposed, reducing the output magic state error rate in one round of 15
to 1 distillation by two orders of magnitude compared to a previous rough
protocol. We have also proven that our protocol offers the lowest logical error
rates for state injection among all possible CSS codes.
