Update ClassicalSimulator to use simulation infrastructure #14467

Job	Run time
Misc check	4s
Format check	7s
Packaging test	1m 16s
Type check	1m 16s
Changed files test	1m 10s
Build protos	8s
Coverage check	1m 9s
Doc test	1m 16s
Isolated pytest Ubuntu	1m 16s
Lint check	1m 14s
Pytest MacOS (3.9)	1m 15s
Notebook formatting	14s
Pytest MacOS (3.10)	52s
Notebook Tests against PR	1m 3s
Changed Notebooks Isolated Test against Cirq stable (partition-0)	47s
Pytest MacOS (3.11)	1m 7s
Changed Notebooks Isolated Test against Cirq stable (partition-1)	48s
Check consistency of requirements	28s
Changed Notebooks Isolated Test against Cirq stable (partition-2)	47s
Pytest Ubuntu (3.9)	1m 15s
Shell check	9s
Changed Notebooks Isolated Test against Cirq stable (partition-3)	55s
Pytest Ubuntu (3.10)	1m 14s
Pytest Ubuntu (3.11)	1m 16s
Bundle file consistency	42s
Typescript lint check	29s
Typescript tests coverage	36s
Typescript tests	37s
Pytest Windows (3.9)	58s
Pytest Windows (3.10)	1m 1s
Pytest Windows (3.11)	1m 0s
	26m 29s

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