benchmark against QuantumAlgebra

[oameye]

Docs preview: https://qojulia.github.io/SecondQuantizedAlgebra.jl/previews/PR163/comparison/

Adds a cross-package benchmark suite and a "Comparison with other packages" docs page that pit SecondQuantizedAlgebra.jl (SQA) against four other symbolic second-quantized algebra packages, across three languages: QuantumAlgebra.jl, SymPy (sympy.physics.quantum), OpenFermion, and sneg (Mathematica).

Fairness contract

Every row times each package producing the same canonical (normal-ordered) result from the same physical input, written idiomatically in that package.

• Eager packages (SQA, sneg) canonicalize on every *, so the operation itself is timed. Lazy packages (QuantumAlgebra, SymPy, OpenFermion) are timed through their normalization call.
• Products of 3+ factors use the eager workflow on the lazy side too (normalize after each multiply), so we measure the algorithm, not a workflow footgun.
• Before timing, each script verifies textbook identities in its own package (a a† = 1 + a†a, a a a† = a†a a + 2a, two-level completeness). A failing check aborts that package's run. Any single trial over 3 s is reported as capped.
• Cross-language ratios are order-of-magnitude indicators (BenchmarkTools median / Python timeit / Mathematica RepeatedTiming). The Julia-vs-Julia column is precise.

Results

Single Linux workstation, 2026-07-17: SQA 0.9.0 and QuantumAlgebra 1.6.0 on Julia 1.12.6, SymPy 1.14.0 and OpenFermion 1.8.1 on Python 3.14.6, sneg 2.0.21 on Mathematica 14.2. The SQA column is absolute time; every other cell shows that package's time with its ratio to SQA in parentheses. n/a means the scenario is not expressible in that package.

[github-actions]

Benchmark Results

Details

Benchmark suite	Current: bc413da	Previous: 5a37827	Ratio
Accumulation/Many-mode H/foldl M=16	9551 ns	10870 ns	0.88
Accumulation/Many-mode H/foldl M=24	20844 ns	24726 ns	0.84
Accumulation/Many-mode H/foldl M=8	2299.1111111111113 ns	2800.8888888888887 ns	0.82
Accumulation/Many-mode H/sum M=16	1311 ns	1683.1 ns	0.78
Accumulation/Many-mode H/sum M=24	1810.4 ns	2298.777777777778 ns	0.79
Accumulation/Many-mode H/sum M=8	534.0752688172043 ns	713.2805755395683 ns	0.75
Accumulation/Same-site/foldl	5138 ns	6229.6 ns	0.82
Accumulation/Same-site/sum	1604.8 ns	2101.777777777778 ns	0.76
Commutator/Nested JC/depth=1	1214.4 ns	1678.1 ns	0.72
Commutator/Nested JC/depth=2	13475 ns	18254 ns	0.74
Commutator/Nested JC/depth=3	49280 ns	68689 ns	0.72
Commutator/Nested JC/depth=4	122277 ns	170841 ns	0.72
Commutator/Nested JC/depth=5	265554 ns	377859 ns	0.70
Commutator/Schrieffer-Wolff/[S, V]	128500 ns	201047 ns	0.64
Commutator/Schrieffer-Wolff/[S, [S, H0]]	237861 ns	375935 ns	0.63
Indexing/Diagonal collapse/[H_Dicke, S_j]	30140 ns	43342 ns	0.70
Indexing/Diagonal collapse/[H_JC, σ_j]	40410 ns	61826 ns	0.65
Indexing/Simplify/double-sum spin-spin	10693 ns	16030 ns	0.67
Indexing/Simplify/indexed JC H	1085 ns	1135.1 ns	0.96
Indexing/Sum construction/double Σ_ij(J_ij*S_i*S_j)	5884.6 ns	8596.333333333334 ns	0.68
Indexing/Sum construction/single Σ_i(σ_i*σ_j)	7137.5 ns	11642 ns	0.61
Normal Order/Fock (c*c')^n/n=2	486.4948979591837 ns	602.224043715847 ns	0.81
Normal Order/Fock (c*c')^n/n=3	726.5644171779142 ns	869 ns	0.84
Normal Order/Fock (c*c')^n/n=4	997.7777777777778 ns	1154.2 ns	0.86
Normal Order/Fock (c*c')^n/n=5	1326.1 ns	1539.9 ns	0.86
Normal Order/Ground state/3-level rewrite	652.5204678362574 ns	818.7183098591549 ns	0.80
Normal Order/Multi-mode/2-mode 6-op chain	817.6518518518518 ns	957.578947368421 ns	0.85
Simplify/Jaynes-Cummings/H	845.0727272727273 ns	1057 ns	0.80
Simplify/Jaynes-Cummings/H²	1788.3 ns	2381.1111111111113 ns	0.75
Simplify/Two cavities/H	876.0333333333333 ns	1083.1 ns	0.81
Simplify/Two cavities/H²	3521.25 ns	4564.285714285715 ns	0.77
Simplify/Λ-system/H	998.6 ns	1350.5 ns	0.74
Simplify/Λ-system/H²	1709.4 ns	2286.5555555555557 ns	0.75

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