Add benchmark tracking

.github/workflows/Benchmarks.yml

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+name: Benchmark Tracking
+on:
+  push:
+    branches:
+      - main
+  pull_request:
+    branches:
+      - main
+
+permissions:
+    contents: write
+    deployments: write
+
+concurrency:
+    # Skip intermediate builds: always.
+    # Cancel intermediate builds: only if it is a pull request build.
+    group: ${{ github.workflow }}-${{ github.ref }}
+    cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  benchmark:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: '1'
+          arch: x64
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: Run benchmark
+        run: |
+          cd benchmarks
+          julia --project --threads=2 --color=yes -e '
+            using Pkg;
+            Pkg.develop(PackageSpec(path=joinpath(pwd(), "..")));
+            Pkg.instantiate();
+            include("runbenchmarks.jl")'
+
+      - name: Store benchmark result
+        uses: benchmark-action/github-action-benchmark@v1
+        with:
+          name: Julia benchmark result
+          tool: "julia"
+          output-file-path: benchmarks/benchmarks_output.json
+          github-token: ${{ secrets.GITHUB_TOKEN }}
+          auto-push: ${{ github.event_name != 'pull_request' }}
+          # Show alert with commit comment on detecting possible performance regression
+          alert-threshold: "200%"
+          comment-on-alert: true
+          fail-on-alert: true
+          alert-comment-cc-users: "@ktrz,@findmyway"

benchmarks/.gitignore

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+/benchmarks_output.json

benchmarks/Project.toml

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+[deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"

benchmarks/runbenchmarks.jl

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+using BenchmarkTools
+using QuantumToolbox
+
+fib(n) = n <= 1 ?  1 : fib(n - 2) + fib(n - 1)
+
+suite = BenchmarkGroup()
+
+suite["steadystate"] = BenchmarkGroup(["steadystate"])
+
+
+## steadystate ##
+
+N = 50
+Δ = 0.1
+F = 2
+γ = 1
+a = destroy(N)
+H = Δ * a' * a + F * (a + a')
+c_ops = [sqrt(γ) * a]
+
+suite["steadystate"]["driven-dissipative harmonic oscillator"] = @benchmarkable steadystate($H, $c_ops)
+
+## end ##
+
+
+tune!(suite)
+results = run(suite, verbose = true)
+
+BenchmarkTools.save("benchmarks_output.json", mean(results))