In this work, we discuss the realization of Grover’s quantum search algorithm using a set of given gates which can be implemented in the QED circuit for two superconducting qubits of transmon type. In this realization, we employ the X-rotation gate, instead of Hadamard transformation, and we implement the phase oracle. We show that a probability of success greater than $\frac {1}{2}$ can be reached. We propose also an effective way to implement the two-qubit Grover’s search algorithm based on qubit-qubit interaction via a circuit QED for two different situations. In this sense, we use two transmon qubits that are coupled capacitively to a resonator driven by a strong microwave field. The capacitive coupling in dispersive regime gives a X-rotation gate for two qubits during an appropriate interaction time. This given gate allows us to generate the states of Bell type. The obtained numerical results show that our proposal is feasible with a high fidelity.

中文翻译：

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Grover搜索算法在两个超导量子比特的QED电路中的实现

在这项工作中，我们讨论了使用一组给定门的 Grover 量子搜索算法的实现，这些门可以在 QED 电路中实现，用于两个 transmon 类型的超导量子位。在这个实现中，我们使用 X 旋转门，而不是哈达玛变换，我们实现了相位预言机。我们表明可以达到大于 $\frac {1}{2}$ 的成功概率。我们还提出了一种有效的方法来实现基于量子位-量子位交互的双量子位格罗弗搜索算法，通过电路 QED 针对两种不同情况。从这个意义上说，我们使用两个 transmon 量子位，它们电容耦合到由强微波场驱动的谐振器。色散状态下的电容耦合在适当的交互时间内为两个量子位提供了 X 旋转门。这个给定的门允许我们生成贝尔类型的状态。获得的数值结果表明我们的建议是可行的，具有很高的保真度。