Fix global phase for PauliI rotation and DumpRegister

[swernli]

This change introduces a new, stdlib-only intrinsic for applying global phase during simulation to make phase behavior more consisten and fixes #1450. This intrinsic only applies the global phase during simulation; the new GlobalPhase intrinsic is a no-op for QIR generation, circuit generation, and resource estimation. The change also includes updates to the stdlib and associated tests to account for the corrected global phase behavior.

This also fixes a bug in DumpRegister related to iteration through the state vector that ensures the "base" amplitude used for separating the state is consistently chosen, which avoids corner cases that could introduce a phase in the displayed output that wasn't present in the underlying state.

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Change in memory usage detected by benchmark.

Memory Report for 05e923e

Test	This Branch	On Main	Difference
compile core + standard lib	15892349 bytes	15969785 bytes	-77436 bytes

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Benchmark for 05e923e

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Test	Base	PR	%
Array append evaluation	341.3±2.21µs	363.4±3.40µs	+6.48%
Array literal evaluation	192.3±0.51µs	195.3±1.95µs	+1.56%
Array update evaluation	424.4±2.74µs	429.1±1.91µs	+1.11%
Core + Standard library compilation	16.6±0.20ms	17.7±0.72ms	+6.63%
Deutsch-Jozsa evaluation	5.1±0.05ms	5.0±0.04ms	-1.96%
Large file parity evaluation	33.7±0.07ms	33.5±0.25ms	-0.59%
Large input file compilation	11.2±0.30ms	12.0±0.15ms	+7.14%
Large input file compilation (interpreter)	43.2±1.13ms	47.7±1.37ms	+10.42%
Large nested iteration	33.4±0.09ms	33.5±0.13ms	+0.30%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1490.0±26.95µs	1480.4±29.15µs	-0.64%
Perform Runtime Capabilities Analysis (RCA) on large file sample	7.8±0.14ms	7.6±0.09ms	-2.56%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1401.4±29.61µs	1403.1±43.75µs	+0.12%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	21.0±0.28ms	21.3±0.25ms	+1.43%
Teleport evaluation	89.1±3.52µs	87.4±3.71µs	-1.91%

[swernli]

@tcNickolas Ok, with the combination of these changes and the teleport sample update from #1456, I've confirmed a few things of note:

• The teleportation sample now always returns consistent before and after dumps with the expected phases.
• R(PauliI) behaves as an application of global phase consistent with how it is documented.
• R1 no longer introduces an extra global phase and is consistent with the other rotations like Z and S rather than being off by a phase (and introduced unit tests to make sure it stays that way).
• Application of controlled global phase behave as expected in simulation and introduce calls to Rz where appropriate so that execution on physical systems is consistent.
• The updated state preparation tests confirm that calls PreparePureStateD now results in states without complex phase that match the inputs provided.
• The fixes to R1 exposed a bug in the ApplyQFT test cases that, when corrected, confirms the Fourier transform is being performed as expected.

There is still one other issue remaining from #1317 that will require changes to the internals of the simulator, which will be in another PR (hopefully out soon).

[minestarks]

The actual global phase fix is beyond my knowledge, but the evaluator/backend bits LGTM

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Change in memory usage detected by benchmark.

Memory Report for 329443a

Test	This Branch	On Main	Difference
compile core + standard lib	15892349 bytes	15969785 bytes	-77436 bytes

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Benchmark for 329443a

Click to view benchmark

Test	Base	PR	%
Array append evaluation	340.4±4.39µs	332.0±15.24µs	-2.47%
Array literal evaluation	173.9±3.30µs	177.6±6.84µs	+2.13%
Array update evaluation	422.8±19.40µs	411.3±8.78µs	-2.72%
Core + Standard library compilation	17.9±0.74ms	19.0±0.83ms	+6.15%
Deutsch-Jozsa evaluation	5.1±0.06ms	4.9±0.12ms	-3.92%
Large file parity evaluation	33.8±0.23ms	33.1±0.75ms	-2.07%
Large input file compilation	12.0±0.48ms	12.2±0.51ms	+1.67%
Large input file compilation (interpreter)	47.4±1.75ms	48.7±1.39ms	+2.74%
Large nested iteration	33.2±0.46ms	32.6±0.73ms	-1.81%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1493.8±65.37µs	1494.4±57.27µs	+0.04%
Perform Runtime Capabilities Analysis (RCA) on large file sample	7.8±0.18ms	7.5±0.24ms	-3.85%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1407.1±65.00µs	1389.3±96.96µs	-1.27%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	21.3±0.49ms	22.1±0.60ms	+3.76%
Teleport evaluation	88.5±3.87µs	87.6±5.08µs	-1.02%

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Change in memory usage detected by benchmark.

Memory Report for ea0a767

Test	This Branch	On Main	Difference
compile core + standard lib	15889189 bytes	15966617 bytes	-77428 bytes

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Benchmark for ea0a767

Click to view benchmark

Test	Base	PR	%
Array append evaluation	350.8±7.96µs	341.1±2.67µs	-2.77%
Array literal evaluation	189.4±0.73µs	179.7±3.37µs	-5.12%
Array update evaluation	424.3±3.64µs	421.5±1.63µs	-0.66%
Core + Standard library compilation	20.0±0.67ms	20.1±0.65ms	+0.50%
Deutsch-Jozsa evaluation	5.2±0.06ms	5.1±0.07ms	-1.92%
Large file parity evaluation	33.6±0.08ms	33.8±0.24ms	+0.60%
Large input file compilation	13.1±0.39ms	12.8±0.33ms	-2.29%
Large input file compilation (interpreter)	50.4±2.35ms	48.8±0.96ms	-3.17%
Large nested iteration	33.6±0.13ms	33.4±0.39ms	-0.60%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1526.9±85.55µs	1519.7±108.51µs	-0.47%
Perform Runtime Capabilities Analysis (RCA) on large file sample	8.1±0.10ms	8.0±0.08ms	-1.23%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1442.6±101.34µs	1442.8±134.36µs	+0.01%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	21.5±0.22ms	21.1±0.20ms	-1.86%
Teleport evaluation	90.6±5.60µs	88.3±3.63µs	-2.54%