Synthesis of Deutsch-Jozsa Circuits and Verification by IBM Q

Deutsch-Jozsa algorithm first realized the exponential acceleration of classical algorithm and it solved the Deutsch problem of n qubits. The implementation of this algorithm embodies the characteristics of quantum superposition and quantum parallelism. Deutsch-Jozsa algorithm has not completely been implemented on any quantum platform so far. In this paper, a synthesis algorithm is proposed which can automatically generate all 8 truth tables and quantum circuits of 2-bit Deutsch-Jozsa algorithm. Two methods are also proposed that can synthesize f(x) when the quantum circuit of f(x) is not given. The correctness of the quantum circuits and Deutsch-Jozsa algorithm is verified by IBM Q Experience.

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