Explicit construction of time-dependent MPOs

Construct exact time-dependent matrix-product-operator representations explicitly for the Yang–Baxter brickwork circuits whose operator-Schmidt rank is known only through bounded or polynomial upper bounds.

Background

Polynomial operator-Schmidt-rank bounds imply the existence of exact matrix-product-operator representations with polynomial bond dimension, but the bounds alone do not provide the local tensors of those representations. The paper identifies the explicit construction of such time-dependent MPOs as a separate unresolved problem, particularly for slowly growing families.