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state, a well-defined desired state or a range of desired states, many paths to reach the desired<br />
state, and well-defined attributes of an optimal path.<br />
The quantum algorithmic solution to such problems requires the following steps:<br />
• Prepare the initial state in an equal superposition of all possible choices.<br />
• Use some reversible quantum arithmetic to compute the specialized property (makespan<br />
in our case) needed.<br />
• Construct the necessary oracle circuit.<br />
• Use Grover-type algorithms to search for the desired solution.<br />
The solution we propose based upon Grover’s algorithm is not universally applicable.<br />
Problem requiring specific optimization criteria may require quantum circuits that cannot be<br />
easily implemented with reversible quantum arithmetic. Moreover, Grover-type algorithms<br />
lead to a square-root improvement over the exhausting search, while many good classical<br />
algorithms may have better performance for some special problems.<br />
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