Module for arbitrary controlled rotation in gate-based quantum algorithms

Almost all gate-based quantum algorithms involving controlled rotation modules have faced the same challenges of limited quantum resources in the noisy intermediate-scale quantum (NISQ) era. Based on quantum phase estimation, this paper proposes a general module for arbitrary controlled rotation in gate-based quantum algorithms, which can be applied in the Harrow–Hassidim–Lloyd (HHL) algorithms and some other quantum algorithms. Numerical results show that the proposed module only requires a small number of auxiliary qubits to ensure the high fidelity of the HHL algorithm. Compared with the polynomial fitting function method, within a certain error range, the module only needs fewer quantum gates to realize the controlled rotation module of the HHL algorithm. Since the gate complexity of the module is associated with phase estimation, the gate complexity is also polynomial if the diagonal unitary matrix in phase estimation can be decomposed efficiently.