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 portc 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 the sketch size squared 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. Oversampling reduces that error for both the one-shot and pairwise approaches.

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.