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Why are phase bugs called 'the silent killer' when debugging quantum circuits, and where can you reliably catch them?
Phase errors always change the measurement probabilities, so they are obvious in the histogram but hidden in the amplitudes
Phase errors change the total probability so they show up as probabilities that do not sum to 1
Two states with identical |amplitude|^2 but different phases give the same computational-basis histogram, so phase errors are invisible there and must be caught by inspecting the amplitudes
Phase errors only occur on real hardware and can never appear in a state-vector simulator
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