Add CI Benchmark Suite

[dorephysicsresearcher]

Resolves #407.

This PR introduces an automated benchmark suite utilizing BenchmarkTools.jl. It tests the Schroedinger, Lindblad, and MCWF time evolution solvers. A GitHub Action workflow has been added to automatically trigger these benchmarks on new commits to track performance regressions.

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	55154eb...	master / 55154eb...
master/base array types/1//2	29.3 ± 6.8 μs	29.4 ± 6.9 μs	0.995 ± 0.33
master/base array types/100//1	24.3 s	24.9 s	0.977
master/base array types/20//1	0.0463 ± 0.00075 s	0.0466 ± 0.0008 s	0.994 ± 0.023
master/base array types/50//1	1.37 ± 0.0057 s	1.38 ± 0.009 s	0.989 ± 0.0077
master/qo types/1//2	0.0328 ± 0.0073 ms	0.0334 ± 0.0072 ms	0.981 ± 0.3
master/qo types/100//1	20.9 s	21.2 s	0.988
master/qo types/20//1	0.04 ± 0.0013 s	0.04 ± 0.0011 s	1 ± 0.043
master/qo types/50//1	1.2 ± 0.021 s	1.22 ± 0.0098 s	0.978 ± 0.019
schroedinger/base array types/1//2	5.8 ± 0.32 μs	5.77 ± 0.32 μs	1 ± 0.078
schroedinger/base array types/100//1	3.33 ± 0.04 ms	3.32 ± 0.037 ms	1 ± 0.016
schroedinger/base array types/20//1	0.137 ± 0.0041 ms	0.137 ± 0.0041 ms	1 ± 0.042
schroedinger/base array types/50//1	0.705 ± 0.0098 ms	0.704 ± 0.0099 ms	1 ± 0.02
schroedinger/qo types/1//2	6.36 ± 0.36 μs	6.32 ± 0.35 μs	1.01 ± 0.08
schroedinger/qo types/100//1	3.09 ± 0.023 ms	3.03 ± 0.023 ms	1.02 ± 0.011
schroedinger/qo types/20//1	0.214 ± 0.005 ms	0.213 ± 0.0053 ms	1 ± 0.034
schroedinger/qo types/50//1	0.758 ± 0.0081 ms	0.746 ± 0.0084 ms	1.02 ± 0.016
stochastic master/base array types/1//2	0.244 ± 0.045 ms	0.237 ± 0.047 ms	1.03 ± 0.28
stochastic master/base array types/100//1	0.483 ± 0.022 s	0.467 ± 0.012 s	1.03 ± 0.053
stochastic master/base array types/20//1	31.3 ± 2.8 ms	28.8 ± 2.1 ms	1.09 ± 0.13
stochastic master/base array types/50//1	0.134 ± 0.0038 s	0.12 ± 0.0079 s	1.11 ± 0.08
stochastic master/qo types/1//2	0.286 ± 0.037 ms	0.276 ± 0.038 ms	1.03 ± 0.19
stochastic master/qo types/100//1	0.73 ± 0.016 s	0.706 ± 0.01 s	1.03 ± 0.028
stochastic master/qo types/20//1	25.4 ± 1.9 ms	25.5 ± 1.9 ms	0.996 ± 0.1
stochastic master/qo types/50//1	0.159 ± 0.0015 s	0.157 ± 0.0042 s	1.01 ± 0.029
stochastic schroedinger/base array types/1//2	0.0476 ± 0.00077 ms	0.0449 ± 0.0011 ms	1.06 ± 0.031
stochastic schroedinger/base array types/100//1	1.37 ± 0.1 ms	1.42 ± 0.1 ms	0.967 ± 0.1
stochastic schroedinger/base array types/20//1	0.267 ± 0.0061 ms	0.267 ± 0.0065 ms	0.998 ± 0.033
stochastic schroedinger/base array types/50//1	0.643 ± 0.01 ms	0.644 ± 0.011 ms	0.999 ± 0.023
stochastic schroedinger/qo types/1//2	0.0535 ± 0.0052 ms	0.0532 ± 0.0051 ms	1 ± 0.14
stochastic schroedinger/qo types/100//1	1.49 ± 0.22 ms	1.46 ± 0.22 ms	1.02 ± 0.21
stochastic schroedinger/qo types/20//1	0.334 ± 0.0088 ms	0.335 ± 0.0086 ms	0.998 ± 0.037
stochastic schroedinger/qo types/50//1	0.774 ± 0.026 ms	0.764 ± 0.036 ms	1.01 ± 0.059
time_to_load	2.96 ± 0.011 s	2.98 ± 0.038 s	0.993 ± 0.013

Memory benchmarks

	master	55154eb...	master / 55154eb...
master/base array types/1//2	0.52 k allocs: 29.3 kB	0.52 k allocs: 29.3 kB	1
master/base array types/100//1	0.135 M allocs: 11.6 GB	0.135 M allocs: 11.6 GB	1
master/base array types/20//1	7.96 k allocs: 29.6 MB	7.96 k allocs: 29.6 MB	1
master/base array types/50//1	0.0375 M allocs: 0.817 GB	0.0375 M allocs: 0.817 GB	1
master/qo types/1//2	0.647 k allocs: 31.8 kB	0.647 k allocs: 31.8 kB	1
master/qo types/100//1	0.155 M allocs: 11.7 GB	0.155 M allocs: 11.7 GB	1
master/qo types/20//1	9.19 k allocs: 29.9 MB	9.19 k allocs: 29.9 MB	1
master/qo types/50//1	0.043 M allocs: 0.819 GB	0.043 M allocs: 0.819 GB	1
schroedinger/base array types/1//2	0.069 k allocs: 3.78 kB	0.069 k allocs: 3.78 kB	1
schroedinger/base array types/100//1	0.085 k allocs: 0.0531 MB	0.085 k allocs: 0.0531 MB	1
schroedinger/base array types/20//1	0.069 k allocs: 14.3 kB	0.069 k allocs: 14.3 kB	1
schroedinger/base array types/50//1	0.069 k allocs: 31 kB	0.069 k allocs: 31 kB	1
schroedinger/qo types/1//2	0.08 k allocs: 4.28 kB	0.08 k allocs: 4.28 kB	1
schroedinger/qo types/100//1	0.094 k allocs: 0.0474 MB	0.094 k allocs: 0.0474 MB	1
schroedinger/qo types/20//1	0.08 k allocs: 13.5 kB	0.08 k allocs: 13.5 kB	1
schroedinger/qo types/50//1	0.08 k allocs: 28.1 kB	0.08 k allocs: 28.1 kB	1
stochastic master/base array types/1//2	3.85 k allocs: 0.207 MB	3.85 k allocs: 0.207 MB	1
stochastic master/base array types/100//1	2.69 k allocs: 0.218 GB	2.69 k allocs: 0.218 GB	1
stochastic master/base array types/20//1	4.31 k allocs: 15.4 MB	4.31 k allocs: 15.4 MB	1
stochastic master/base array types/50//1	3.11 k allocs: 0.0643 GB	3.09 k allocs: 0.064 GB	1
stochastic master/qo types/1//2	4.81 k allocs: 0.227 MB	4.81 k allocs: 0.227 MB	1
stochastic master/qo types/100//1	5.46 k allocs: 0.389 GB	5.46 k allocs: 0.389 GB	1
stochastic master/qo types/20//1	5.46 k allocs: 16.8 MB	5.46 k allocs: 16.8 MB	1
stochastic master/qo types/50//1	5.46 k allocs: 0.0984 GB	5.46 k allocs: 0.0984 GB	1
stochastic schroedinger/base array types/1//2	0.072 k allocs: 3.94 kB	0.072 k allocs: 3.94 kB	1
stochastic schroedinger/base array types/100//1	0.265 k allocs: 0.0649 MB	0.265 k allocs: 0.0649 MB	1
stochastic schroedinger/base array types/20//1	0.072 k allocs: 14.4 kB	0.072 k allocs: 14.4 kB	1
stochastic schroedinger/base array types/50//1	0.072 k allocs: 31.2 kB	0.072 k allocs: 31.2 kB	1
stochastic schroedinger/qo types/1//2	0.403 k allocs: 19.5 kB	0.403 k allocs: 19.5 kB	1
stochastic schroedinger/qo types/100//1	0.419 k allocs: 0.0684 MB	0.419 k allocs: 0.0684 MB	1
stochastic schroedinger/qo types/20//1	0.403 k allocs: 30 kB	0.403 k allocs: 30 kB	1
stochastic schroedinger/qo types/50//1	0.403 k allocs: 0.0456 MB	0.403 k allocs: 0.0456 MB	1
time_to_load	0.149 k allocs: 11.1 kB	0.149 k allocs: 11.1 kB	1

[dorephysicsresearcher]

I did notice that the quantumoptics-tests-amdgpu check failed, but since this PR only adds the benchmark script and the workflow file, I'm guessing it might be an unrelated flaky test or a timeout on the server side.

Could a maintainer take a look or re-trigger the checks when you have a minute? Let me know if you need me to make any tweaks to the benchmark script!