Deutsch-Jozsa算法首次实现了对经典算法的指数级加速, 解决了n个量子比特的Deutsch问题,奠定了量子算法的基本思想,体现了量子叠加性和并行性的特征。 首次提出了一种综合算法,可自动生成2比特Deutsch-Jozsa算法的全部8个真值表与量子电路。并给出了 一种综合方法,可在f(x)对应电路未知的情况下构建量子电路。通常用经典算法解决该问题最多 需要执行2n－1+1次判断,而Deutsch-Jozsa算法只需要一步就可以完成,虽然新提出的方法需要两步,但为 实际应用中不同问题的解决提供了另一种可能的途径。进一步通过IBM Q Experience平台运行生成的量子 电路,验证了量子电路和Deutsch-Jozsa算法的正确性。

Deutsch-Jozsa algorithm realizes the exponential acceleration of classical algorithm for the first time, and solves the Deutsch problem of n qubits. The algorithm establishes the basic idea of quantum algorithms, and the implementation of which embodies the characteristics of quantum superposition and parallelism. A comprehensive algorithm is proposed for the first time, which can automatically generate all eight truth tables and quantum circuits of two-bit Deutsch-Jozsa algorithm. A synthesis method is given further to judge the properties of f(x) by constructing quantum circuit when the corresponding circuit is unknown. Generally, to solve this problem, a typical classical algorithm needs to do 2n+1+1 times of judgement and the Deutsch-Jozsa algorithm only needs one time. Although the new approach requires two steps to solve the problem, it provides another possible way to solve the problems with specific requirements in practical application. In addition, the correctness of the quantum circuits and Deutsch-Jozsa algorithm is verified by IBM Q Experience platform.