Bump version to 0.16.0 #2870

Job	Run time
lint (3.10)	1m 18s
sdist (3.8, ubuntu-latest, x64)	2m 35s
sdist (3.9, ubuntu-latest, x64)	2m 52s
sdist (3.10, ubuntu-latest, x64)	2m 42s
sdist (3.11, ubuntu-latest, x64)	2m 42s
sdist (3.12.0, ubuntu-latest, x64)	2m 54s
tests-json-input (3.10, ubuntu-latest)	10m 13s
Windows Python 3.8	10m 8s
Linux Python 3.8	10m 40s
macOS Python 3.8	15m 8s
Windows Python 3.9	12m 44s
Linux Python 3.9	10m 37s
macOS Python 3.9	14m 0s
Windows Python 3.10	11m 4s
Linux Python 3.10	10m 16s
macOS Python 3.10	12m 23s
Windows Python 3.11	13m 16s
Linux Python 3.11	10m 3s
macOS Python 3.11	11m 52s
Windows Python 3.12.0	10m 50s
Linux Python 3.12.0	10m 22s
macOS Python 3.12.0	13m 35s
Linux Python 3.10 ('qiskit>=1.3.0b1')	12m 27s
	3h 34m 41s

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