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To assess whether a gate-based quantum algorithm can be executed successfully on a noisy intermediate-scale quantum (NISQ) device, both complexity and actual value of quantum resources should be considered carefully. Based on quantum phase estimation, we implemente arbitrary controlled rotation of quantum algorithms with a proposed modular method. The proposed method is not limited to be used as a submodule of the HHL algorithm and can be applied to more general quantum machine learning algorithms. Compared with the polynomial-fitting function method, our method only requires the least ancillas and the least quantum gates to maintain the high fidelity of quantum algorithms. The method theoretically will not influence the acceleration of original algorithms. Numerical simulations illustrate the effectiveness of the proposed method. Furthermore, if the corresponding diagonal unitary matrix can be effectively decomposed, the method is also polynomial in time cost.
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We experimentally constructed an all-microwave scheme for the controlled-NOT (cNOT) gate between two superconducting transmon qubits in a three dimensional cavity. Our cNOT gate is based on the microwave-activated phase (MAP) gate, which requires an additional procedure to compensate the accumulated phases during the operation of the MAP gate. We applied Z-axis phase gates using microwave hyperbolic secant pulse on both qubits with adequate rotation angles systematically calibrated by separate measurements.We evaluated the gate performance of the constructed cNOT gate by performing two-qubit quantum process tomography (QPT). Finally, we present the experimental implementation of Deutsch-Jozsa algorithm using the cNOT gate.
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