Factoring algorithm for resource estimation

[msoeken]

This adds a factoring algorithm based on work from Ekara-Hastad with optimizations to modular arithmetic subroutines based on work from Gidney (see https://arxiv.org/abs/1905.09749)

[github-actions]

Benchmark for 3ebfd30

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Test	Base	PR	%
Array append evaluation	880.1±12.68µs	863.9±6.51µs	-1.84%
Array update evaluation	952.2±6.81µs	938.1±5.06µs	-1.48%
Deutsch-Jozsa evaluation	31.4±0.29ms	31.3±0.23ms	-0.32%
Large file parity evaluation	36.2±0.09ms	36.1±0.16ms	-0.28%
Large input file	40.6±0.66ms	40.5±0.55ms	-0.25%
Standard library	21.7±0.28ms	21.9±0.42ms	+0.92%
Teleport evaluation	104.4±1.86µs	104.1±4.80µs	-0.29%

[github-actions]

Benchmark for b30d1f9

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Test	Base	PR	%
Array append evaluation	875.5±9.08µs	862.3±5.89µs	-1.51%
Array update evaluation	958.6±4.32µs	939.5±25.70µs	-1.99%
Deutsch-Jozsa evaluation	31.4±0.17ms	31.4±0.30ms	0.00%
Large file parity evaluation	36.0±0.05ms	35.9±0.35ms	-0.28%
Large input file	39.7±0.95ms	39.0±0.63ms	-1.76%
Standard library	21.1±0.38ms	21.1±0.25ms	0.00%
Teleport evaluation	105.3±1.87µs	102.9±2.46µs	-2.28%

[github-actions]

Benchmark for 9920117

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Test	Base	PR	%
Array append evaluation	861.0±5.11µs	863.2±8.21µs	+0.26%
Array update evaluation	935.8±6.80µs	935.8±6.80µs	0.00%
Deutsch-Jozsa evaluation	31.4±0.32ms	31.3±0.26ms	-0.32%
Large file parity evaluation	36.1±0.26ms	36.1±0.20ms	0.00%
Large input file	37.4±0.57ms	40.8±0.84ms	+9.09%
Standard library	20.8±0.20ms	23.0±1.42ms	+10.58%
Teleport evaluation	103.9±2.81µs	104.3±2.30µs	+0.38%

[github-actions]

Benchmark for 96a08db

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Test	Base	PR	%
Array append evaluation	762.9±7.00µs	778.1±5.89µs	+1.99%
Array literal evaluation	512.6±5.97µs	540.0±20.25µs	+5.35%
Array update evaluation	841.3±6.25µs	856.4±16.36µs	+1.79%
Deutsch-Jozsa evaluation	30.4±0.18ms	30.4±0.22ms	0.00%
Large file parity evaluation	35.4±0.13ms	35.5±0.19ms	+0.28%
Large input file	43.5±1.83ms	43.4±1.79ms	-0.23%
Standard library	25.1±1.62ms	25.2±1.41ms	+0.40%
Teleport evaluation	98.7±2.83µs	98.1±1.79µs	-0.61%

[tcNickolas]

I would add this sample to the readme at https://github.com/microsoft/qsharp/tree/main/samples/estimation, so that we document all samples uniformly.

Since this is a two-file sample (Jupyter notebook requires the .qs file to work), do we want to move both files to a separate subfolder to emphasize this? Not sure if the intent is to use them together only, or to allow using Q# file on its own as well - if it's the latter, we might want to keep them in this folder and document them separately in the README

[msoeken]

I would add this sample to the readme at https://github.com/microsoft/qsharp/tree/main/samples/estimation, so that we document all samples uniformly.

Since this is a two-file sample (Jupyter notebook requires the .qs file to work), do we want to move both files to a separate subfolder to emphasize this? Not sure if the intent is to use them together only, or to allow using Q# file on its own as well - if it's the latter, we might want to keep them in this folder and document them separately in the README

Thanks, I addresses this comment in a recent commit.

[github-actions]

Benchmark for 3939b7c

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Test	Base	PR	%
Array append evaluation	776.8±9.33µs	765.6±22.73µs	-1.44%
Array literal evaluation	530.5±10.51µs	601.0±46.21µs	+13.29%
Array update evaluation	855.3±14.36µs	841.3±6.60µs	-1.64%
Deutsch-Jozsa evaluation	30.4±0.18ms	30.6±1.11ms	+0.66%
Large file parity evaluation	35.4±0.10ms	35.4±0.25ms	0.00%
Large input file	43.2±2.33ms	42.5±2.28ms	-1.62%
Standard library	24.0±1.03ms	24.2±1.26ms	+0.83%
Teleport evaluation	98.7±7.23µs	97.8±1.83µs	-0.91%