Figure 1.
The quantum circuit implementation of quantum operations (33)–(41) that produce the output state . The controlled operation represents a series of 2𝒩 multi-qubit controlled operations according to the definition of in Eq. (36).
Figure 2.
Quantum circuit implementation of non-unitary operator in Eq. (49), following the procedure of Eq. (54). The measurement outcome in the first register is conditioned on the 0-bit value.
Figure 3.
The LCU quantum circuit of Eq. (60), implementing the non-unitary operator in Eq. (49).
Figure 4.
The implementation quantum circuit for the non-unitary operator in Eq. (62) with κ1 > 0. Notice that because the circuit is considerably simple.
Figure 5.
Synergistic quantum implementation of using the LCU and biorthogonal unitary implementations and for the non-unitary components and , respectively.