Improving threshold for fault-tolerant color code quantum computing by flagged weight optimization
arxiv(2024)
摘要
Color codes are promising quantum error correction (QEC) codes because they
have an advantage over surface codes in that all Clifford gates can be
implemented transversally. However, thresholds of color codes under
circuit-level noise are relatively low mainly because measurements of their
high-weight stabilizer generators cause an increase in a circuit depth, and
thus, substantial errors are introduced. This makes color codes not the best
candidate. Here, we propose a method to suppress the impact of such errors by
optimizing weights of decoders using flag qubits and reducing the circuit depth
using cat states. We set the weights based on conditional error probabilities
conditioned on the measurement outcomes of flag qubits. In numerical
simulations, we improve the threshold of the (4.8.8) color code under the
circuit-level noise from 0.14
integer programming decoder. Furthermore, in the (6.6.6) color code, we
achieved a circuit-level threshold of around 0.36
value as the highest value in the previous studies employing the same noise
model. In both cases, the achieved logical error rates at low physical error
rates are almost one order of magnitude lower than a conventional method that
uses a single ancilla qubit for each stabilizer measurement. This method can
also be applied to other weight-based decoders, making the color codes more
promising for the candidate of experimental implementation of QEC. Furthermore,
one can utilize this approach to improve a threshold of wider classes of QEC
codes, such as high-rate quantum low-density parity check codes.
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