Handle impossible factories in RE API

[msoeken]

Currently, the factory builder API returns a vector of factories for space-time evaluation. However, returning no factory may mean that the algorithm was too fast, and the optimizer will continue to search for some. But there are some cases in which no factory can be found given the input parameters, no matter of the duration of the algorithm.

This PR changes the API to allow to indicate if no magic factories can be computed by returning Option<Vec<...>> instead of Vec<...>.

[github-actions]

Benchmark for 851f8fc

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Test	Base	PR	%
Array append evaluation	340.7±2.28µs	341.6±3.36µs	+0.26%
Array literal evaluation	178.2±1.45µs	194.0±7.44µs	+8.87%
Array update evaluation	421.2±5.45µs	424.5±2.84µs	+0.78%
Core + Standard library compilation	16.6±0.04ms	17.0±0.48ms	+2.41%
Deutsch-Jozsa evaluation	5.1±0.05ms	5.1±0.04ms	0.00%
Large file parity evaluation	33.7±0.16ms	33.8±0.61ms	+0.30%
Large input file compilation	11.3±0.12ms	11.5±0.20ms	+1.77%
Large input file compilation (interpreter)	46.3±1.78ms	43.7±1.48ms	-5.62%
Large nested iteration	33.1±0.13ms	33.5±0.25ms	+1.21%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1490.7±30.66µs	1488.3±36.29µs	-0.16%
Perform Runtime Capabilities Analysis (RCA) on large file sample	7.6±0.10ms	7.6±0.10ms	0.00%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1405.4±31.56µs	1399.7±36.09µs	-0.41%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	21.1±0.18ms	21.3±0.31ms	+0.95%
Teleport evaluation	89.0±4.08µs	88.9±3.34µs	-0.11%

[ivanbasov]

Is there any semantic difference in the case between returning an empty array vs returning None?

[msoeken]

Is there any semantic difference in the case between returning an empty array vs returning None?

Yes, there is. In case of an empty array, we would increase the number of cycles and continue trying, see here:

https://github.com/microsoft/qsharp/blob/95019fd19483697037e24c19cfcbc6cead13a7f9/resource_estimator/src/estimates/physical_estimation.rs#L639C17-L641C18

and

https://github.com/microsoft/qsharp/blob/main/resource_estimator/src/estimates/physical_estimation.rs#L674

But, there are situations in which there aren't just any factories for the provided output error rate, then the factory has the chance to return None.