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I need to construct a universal quantum circuit decomposition for a three-qubit operation where one qubit is the control bit, and a two-qubit unitary operator acts on the other two depending on the control bit. I can do the decomposition when there's a one-qubit unitary operation with as many control bits as needed; this two-qubit unitary with one control bit I am not clear about. Anyone has any clue what the recipe for this construction is?

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Can you provide a little more detail in your question? The answer is going to depend on a number of factors: the form of your 2-qubit unitary, the set of gates you are allowing in the final circuit, and whether you want an exact or approximate solution. There are "recipes" for a number of decompositions, but for a three qubit operation these might give you a circuit with hundreds of gates. I do not believe there is a recipe, at this time, for an optimal decomposition. – John Schanck Jun 6 '11 at 16:07

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