We present a circuit design realizing Grover’s algorithm based on 1-bit unitary gates and 2-bit quantum phase gates implementable with cavity QED techniques. In the first step, we express the circuit block which performs a key unitary transformation that flips only the sign of the state |11 · · · 11〉 using 1-bit and 2-bit gates. The Grover’s iteration operator can then be constructed using this key unitary transformation twice, plus other operations involving only 1-bit unitary gates on each qubit. Mathematical proofs are given to justify that the cricuiting satisfies the desired operator properties.
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