Figure 4.

(a) Quantum forking to reduce the number of QRAM calls for evaluating the functions of inner products. The swap operation is represented by two × symbols connected with a vertical line. (b) Quantum forking circuit for evolving the target state $|\mathrm{\Phi }\rangle$ under three different unitary operations in each branch (subspace). Thicker horizontal lines indicate multi-qubit channels, $|a\rangle$ is an arbitrary ancilla state, and H (H₃) represents the Hadamard gate on a qubit (qutrit).