Fault-tolerant quantum algorithm for dual-threshold image segmentation

Abstract The intrinsic high parallelism and entanglement characteristics of quantum computing have made quantum image processing techniques a focus of great interest. One of the most widely used techniques in image processing is segmentation, which in one of their most basic forms can be carried out using thresholding algorithms. In this paper, a fault-tolerant quantum dual-threshold algorithm has been proposed. This algorithm is based on Clifford+T gates. Because T gates add fault tolerance but have the trade-off of having a much higher cost than other quantum gates,our focus has been on reducing the number of T gates. This has allowed adding noise tolerance, computational cost reduction and fault toleranceto the state-of-the-art dual-threshold segmentation circuits. Sincethe dual-threshold image segmentation involves the comparison operation,as part of this work we have implemented two comparator circuits.These circuits optimise the metrics T-count and T-depth with respect to the best circuit comparators currently available in the literature.