When Fewer Gates Is Not the Whole Story
Total gate count is a single number that hides gate type, parallelism, duration, and error rates, so the candidate with the fewest gates can lose on estimated fidelity or runtime. Choosing between compiled circuits requires an explicit objective function — and different reasonable objectives rank the same candidates differently.
Why isn't gate count enough?
Gate count compresses a whole circuit into one number, and the compression throws away what matters. Gates are not interchangeable: on typical superconducting hardware a two-qubit gate takes roughly ten times longer than a one-qubit gate and fails roughly ten times more often. A count that adds a 30-nanosecond, 0.05%-error gate and a 300-nanosecond, 1%-error gate as "1 + 1" is measuring with a broken ruler.
An objective function is the explicit formula a compiler uses to score candidates — for example "minimize two-qubit gate count", or "maximize the product of per-gate success probabilities". Writing the objective down is not bureaucracy: as this lesson shows with arithmetic, changing the objective changes which candidate wins.
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