Benchmarks

Symmetry-resolved basis construction and representative-state lookup speed, compared against XDiag.jl and QuSpin. SymBasis is benchmarked against its own dev checkout; XDiag.jl and QuSpin are whatever their latest released versions were at the time this page was generated. Regenerated automatically on every SymBasis release.

Threads are left at each library's own defaults (JULIA_NUM_THREADS=auto, OMP_NUM_THREADS unset) rather than pinned to 1 – these numbers reflect out-of-the-box performance, not a strictly single-threaded comparison.

Sweep: BENCH_SWEEP=quick

Spin-1/2 — basis construction

plot_construction("spin", "Spin-1/2")

N	config	dim	SymBasis	XDiag	QuSpin	XDiag/SymBasis	QuSpin/SymBasis
8	U1	70	3.173e-05 ± 3.3e-05 s	4.152e-06 ± 6.8e-06 s	3.941e-05 ± 1.7e-05 s	0.13x	1.24x
8	U1+T(k=0)	10	0.0001782 ± 0.00019 s	5.22e-05 ± 3e-05 s	5.045e-05 ± 1.2e-05 s	0.29x	0.28x
8	U1+T(k=0)+P(p=1)	8	0.0001123 ± 7e-05 s	0.0001265 ± 3.1e-05 s	5.276e-05 ± 1.2e-05 s	1.13x	0.47x
10	U1	252	3.948e-05 ± 3.6e-05 s	4.265e-06 ± 6.5e-06 s	3.464e-05 ± 7.1e-06 s	0.11x	0.88x
10	U1+T(k=0)	26	6.188e-05 ± 3.1e-05 s	9.97e-05 ± 2.5e-05 s	5.248e-05 ± 9.3e-06 s	1.61x	0.85x
10	U1+T(k=0)+P(p=1)	16	0.000216 ± 0.00027 s	0.0002221 ± 2.4e-05 s	6.385e-05 ± 9.3e-06 s	1.03x	0.30x
12	U1	924	0.0004061 ± 0.00027 s	4.548e-06 ± 6.5e-06 s	4.746e-05 ± 1.2e-05 s	0.01x	0.12x
12	U1+T(k=0)	80	8.604e-05 ± 3.2e-05 s	0.0002646 ± 3.1e-05 s	9.072e-05 ± 1.2e-05 s	3.08x	1.05x
12	U1+T(k=0)+P(p=1)	50	0.0001552 ± 2.6e-05 s	0.0004887 ± 2.2e-05 s	0.0001213 ± 1.4e-05 s	3.15x	0.78x
14	U1	3432	0.0002003 ± 0.00017 s	5.092e-06 ± 6.2e-06 s	6.802e-05 ± 8.6e-06 s	0.03x	0.34x
14	U1+T(k=0)	246	0.0001784 ± 3.2e-05 s	0.0009059 ± 4.2e-05 s	0.0002242 ± 1.3e-05 s	5.08x	1.26x
14	U1+T(k=0)+P(p=1)	133	0.0003197 ± 6.7e-05 s	0.00128 ± 5.6e-05 s	0.0003295 ± 1.3e-05 s	4.00x	1.03x
16	U1	12870	0.0005674 ± 0.00032 s	6.782e-06 ± 7.7e-06 s	0.0001479 ± 9.1e-06 s	0.01x	0.26x
16	U1+T(k=0)	810	0.0005136 ± 5.9e-05 s	0.003611 ± 2.7e-05 s	0.0007325 ± 1.6e-05 s	7.03x	1.43x
16	U1+T(k=0)+P(p=1)	440	0.0009558 ± 0.00054 s	0.00444 ± 6.3e-05 s	0.001148 ± 2.5e-05 s	4.65x	1.20x

Spin-1/2 — representative lookup (seconds/call, amortized over batch)

N	config	nsamples	SymBasis	XDiag	QuSpin
16	U1+T(k=0)+P(p=1)	10000	3.103e-07 ± 2.8e-08 s	N/A (no decoupled API)	1.795e-07 ± 3.2e-09 s

Spinless fermion — basis construction

plot_construction("fermion", "Spinless fermion")

N	config	dim	SymBasis	XDiag	QuSpin	XDiag/SymBasis	QuSpin/SymBasis
8	U1	70	2.727e-05 ± 3.8e-05 s	4.102e-06 ± 6.2e-06 s	5.022e-05 ± 1.4e-05 s	0.15x	1.84x
8	U1+T(k=0)	9	4.993e-05 ± 2.3e-05 s	5.208e-05 ± 2.7e-05 s	6.349e-05 ± 1.3e-05 s	1.04x	1.27x
8	U1+T(k=0)+P(p=1)	6	6.931e-05 ± 3.1e-05 s	0.0001261 ± 3.3e-05 s	7.244e-05 ± 1.2e-05 s	1.82x	1.05x
10	U1	252	4.106e-05 ± 3.4e-05 s	4.573e-06 ± 6.5e-06 s	5.296e-05 ± 1e-05 s	0.11x	1.29x
10	U1+T(k=0)	26	0.000192 ± 2.8e-05 s	0.000109 ± 3.2e-05 s	7.799e-05 ± 1.3e-05 s	0.57x	0.41x
10	U1+T(k=0)+P(p=1)	16	0.0001181 ± 3.8e-05 s	0.0002278 ± 2.7e-05 s	9.259e-05 ± 1.1e-05 s	1.93x	0.78x
12	U1	924	5.739e-05 ± 4e-05 s	4.853e-06 ± 6.6e-06 s	6.239e-05 ± 1.2e-05 s	0.08x	1.09x
12	U1+T(k=0)	76	0.0001379 ± 4.3e-05 s	0.0002948 ± 2.2e-05 s	0.0001193 ± 3.1e-05 s	2.14x	0.87x
12	U1+T(k=0)+P(p=1)	33	0.00027 ± 4.5e-05 s	0.0005051 ± 2.1e-05 s	0.0001217 ± 1e-05 s	1.87x	0.45x
14	U1	3432	0.0002793 ± 2.7e-05 s	5.454e-06 ± 7.2e-06 s	6.463e-05 ± 8.2e-06 s	0.02x	0.23x
14	U1+T(k=0)	246	0.0003876 ± 3.3e-05 s	0.001024 ± 3.1e-05 s	0.0002237 ± 1e-05 s	2.64x	0.58x
14	U1+T(k=0)+P(p=1)	113	0.0007973 ± 6e-05 s	0.001431 ± 8.2e-05 s	0.0003248 ± 1.5e-05 s	1.79x	0.41x
16	U1	12870	0.0004991 ± 0.00045 s	7.169e-06 ± 9e-06 s	0.0001502 ± 1e-05 s	0.01x	0.30x
16	U1+T(k=0)	809	0.001517 ± 0.00035 s	0.00407 ± 3.8e-05 s	0.0007362 ± 8.6e-06 s	2.68x	0.49x
16	U1+T(k=0)+P(p=1)	422	0.003208 ± 0.00047 s	0.005042 ± 0.00026 s	0.001122 ± 9.7e-06 s	1.57x	0.35x

Spinless fermion — representative lookup (seconds/call, amortized over batch)

N	config	nsamples	SymBasis	XDiag	QuSpin
16	U1+T(k=0)+P(p=1)	10000	1.815e-06 ± 1.9e-09 s	N/A (no decoupled API)	1.868e-06 ± 3e-09 s

Boson (d=3) — basis construction

plot_construction("boson", "Boson (d=3)")

N	config	dim	SymBasis	XDiag	QuSpin	XDiag/SymBasis	QuSpin/SymBasis
6	U1	141	7.806e-05 ± 7.8e-05 s	4.444e-06 ± 6.2e-06 s	6.074e-05 ± 1.3e-05 s	0.06x	0.78x
6	U1+T(k=0)	26	0.000133 ± 6.9e-05 s	5.597e-05 ± 2.6e-05 s	7.975e-05 ± 1.2e-05 s	0.42x	0.60x
6	U1+T(k=0)+P(p=1)	18	0.0002299 ± 5.4e-05 s	0.0001059 ± 3.2e-05 s	8.912e-05 ± 1.8e-05 s	0.46x	0.39x
8	U1	1107	0.0003047 ± 0.00022 s	7.102e-06 ± 7.4e-06 s	9.74e-05 ± 1e-05 s	0.02x	0.32x
8	U1+T(k=0)	142	0.000506 ± 6.8e-05 s	0.000252 ± 3.7e-05 s	0.0002314 ± 1.5e-05 s	0.50x	0.46x
8	U1+T(k=0)+P(p=1)	84	0.0008095 ± 0.00015 s	0.0003862 ± 3.6e-05 s	0.0002262 ± 1.6e-05 s	0.48x	0.28x
10	U1	8953	0.001359 ± 0.00013 s	1.528e-05 ± 2.1e-05 s	0.0002916 ± 1.1e-05 s	0.01x	0.21x
10	U1+T(k=0)	902	0.004391 ± 0.00027 s	0.00195 ± 4.3e-05 s	0.001504 ± 9.5e-06 s	0.44x	0.34x
10	U1+T(k=0)+P(p=1)	486	0.00722 ± 0.00043 s	0.002477 ± 3.2e-05 s	0.001833 ± 2.5e-05 s	0.34x	0.25x
12	U1	73789	0.01077 ± 0.00053 s	2.804e-05 ± 9.2e-06 s	0.002088 ± 3.3e-05 s	0.00x	0.19x
12	U1+T(k=0)	6166	0.04925 ± 0.0021 s	0.01823 ± 0.00013 s	0.01413 ± 3.3e-05 s	0.37x	0.29x
12	U1+T(k=0)+P(p=1)	3179	0.07985 ± 0.0023 s	0.02173 ± 0.00014 s	0.01707 ± 7.8e-05 s	0.27x	0.21x

Boson (d=3) — representative lookup (seconds/call, amortized over batch)

N	config	nsamples	SymBasis	XDiag	QuSpin
12	U1+T(k=0)+P(p=1)	10000	6.818e-06 ± 4.8e-08 s	N/A (no decoupled API)	3.167e-07 ± 8.7e-10 s