The dual-threshold quantum image segmentation algorithm and its simulation

Fault-tolerant quantum algorithm for dual-threshold image segmentation

“…Most of the Toffoli gates in the Yuan et al circuit (and in the Clifford+T version obtained from it) act on an auxiliary qubit and not on quantum states already initialized, so they can be directly replaced by Temporary-logical-AND operations. In particular, 3N − 1 Toffoli gates can be substituted, while 2N − 2 Toffoli gates act on existing states and cannot be replaced (at least not 3 Comparator circuit proposed by Yuan et al [7], for the case N = 3. It is optimized in terms of ancilla qubits.…”

“…Fig. 4 Comparator obtained from replacing the reset operations in the circuit of Yuan et al [7]. The uncomputation part consists of applying the same circuit, but in reverse order.…”

“…In the case of the number of ancilla qubits, the fault-tolerant proposals that obtain the best values are provided by the circuit of Yuan et al [7] without reset and our first comparator circuit design. Furthermore, in terms of T-count, the second circuit we have proposed in this work (16N ) substantially improves the values of the circuit of Yuan et al [7], both with and without reset operations (35N -21 and 70N -42). Lastly, if we compare the circuits of Wang et al [16] (original and without resets), both of them presents better results in terms of ancilla qubits.…”

“…If we focus on the quantum algorithm for dual-threshold image segmentation, a comparative analysis has been carried out in Table 2. The considered approaches have been: the proposed by Yuan et al [7] (Fig. 7), the proposed by Wang et al [16] and the implemented in this work (Fig.…”

“…Because the T gates are more expensive than other gates in terms of space and time cost [13][14][15], we have focused on minimized these type of gates. The two state-of-the-art algorithms that compute dual-threshold image segmentation are those proposed by Yuan et al [7] and Wang et al [16]. The former is based on full comparators and the latter on half comparators and is, therefore, more limited.…”