Stacks

src accepts any number of trains and compresses their whole product in one sweep, instead of compressing after every pairwise product:

import quimb.tensor as qtn

from src_method import apply, src

layers = [qtn.MPO_rand(10, bond_dim=2, seed=s) for s in range(3)]
psi = qtn.MPS_rand_state(10, bond_dim=8, seed=3)

# One sweep over U3 U2 U1 |psi>.
one_shot = src(*(U.arrays for U in layers), psi.arrays, chi_out=32, seed=0)

# The same product, truncating after every layer.
state = psi.arrays
for U in reversed(layers):
    state = apply(U.arrays, state, chi_out=32, seed=0)

The supported stacks are MPO^k, MPO^k . MPS and MPS . MPO^k; see Conventions for the order and the bra form.

When a single sweep pays offCopy Anchor Link

The per-site cost of the sweep grows with $\chi_{\text{out}}^2$ times the product of the bond dimensions of all layers, so it grows exponentially with the depth of the stack. In exchange, a single sweep truncates once instead of once per layer. In practice that buys at most a moderate gain in accuracy: the error of the randomized sketch dominates the error compounded across layers.

Compressing a whole stack at once pays off for shallow stacks of thin layers, such as two or three Trotter layers; apply anything else pairwise. The stack benchmarks measure both accuracy and time against the pairwise approach.