Gate Decomposition
Decomposition rewrites an unsupported gate as a sequence of native ones, either exactly (up to an unmeasurable global phase) or approximately within a declared tolerance. Equivalent decompositions can trade gate count against depth and calibration quality, so shorter is not automatically better.
What is gate decomposition?
Decomposition rewrites one gate the target does not support as a sequence of gates it does. The thing being preserved is the gate's unitary — the exact, reversible input-to-output transformation it performs on the quantum state; think of it as the gate's complete truth table, including amplitudes and signs, not just bit values.
Two grades exist. Exact decomposition reproduces the unitary perfectly, up to global phase (an overall factor no measurement can detect — worked through below). Approximate synthesis reproduces it within a declared error tolerance, trading accuracy for shorter sequences. That tolerance is part of the result: a report that says "equivalent" when it means "equivalent within one part in a million" is hiding a number you may care about.
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