Benchmarks

The benchmark scripts live in benches/ and need the bench dependency group. Each folder's README holds the full tables and the commands to reproduce them.

PrimitivesCopy Anchor Link

benches/primitives compares the MPO-MPO product against quimb's contract-then-compress on one Booster node of the Leonardo supercomputer at CINECA (32 cores, one A100-64GB). One MPO is random, the other a slightly perturbed identity, so the product is highly compressible.

At small $\chi$ the CPU is faster than the GPU, which has too little work to fill it. At $\chi = 1000$ SRC uses about a seventh of the peak host memory of quimb, and single precision (complex64) brings the GPU time to 1.90 s and 3.03 s.

Quench dynamicsCopy Anchor Link

benches/stack evolves 50 and 100 qubits of the non-integrable mixed-field Ising chain from $|0\dots0\rangle$ to $t = 8$ (80 Trotter steps), on one A100, fusing $k$ steps per stack sweep. Errors are against a $\chi = 1024$ reference.

• Exact SVD truncation (quimb) is more accurate at equal $\chi$, and SRC at twice the bond dimension is more accurate than quimb. The timings compare a GPU with 32 CPU cores, and the quimb time looks inflated by how it is called, so they are not a speed-up; a comparison on the same hardware is still to do.
• Fusing two or four steps per sweep is 1.8-2.8x faster than one at a time, for at most 7 % more infidelity.

Out-of-coreCopy Anchor Link

benches/large compresses a stack whose middle MPO is read from disk. On one A100, a 50-site stack with $D_M = 1000$ compressed to $\chi = 500$ gives bit-identical results under a 4 GB and a 60 GB GPU budget, which keep 49 and 0 of the 50 environments on the host; spilling costs 18 % of the wall time.

Stack depthCopy Anchor Link

benches/stack also compares one sweep over a stack, src(A_1, ..., A_k, psi), with pairwise application truncating after every product, as a function of the number of trains, on small chains on a laptop.

• One sweep over the whole stack is at best moderately more accurate. For random stacks ending in an MPS it has about 20 % lower median error at depth 4; for random MPO products the gain is at most 8 %; for Trotter layers there is no systematic difference.
• Both methods sit 2-15x above the best possible error at the same bond dimension, so the randomized sketch, not compounding across layers, dominates the error.
• The per-site cost grows with $\chi^2$ times the product of the layer bonds. Thin Trotter layers run at 0.6-1.4x the pairwise time up to depth 5, while random MPOs of bond 8 and 16 at depth 4 are 30x and 136x slower.