  We introduce a class of quantum non-Markovian processes -- dubbed process
trees -- that exhibit polynomially decaying temporal correlations and memory
distributed across time scales. This class of processes is described by a
tensor network with tree-like geometry whose component tensors are (1)
{causality-preserving} maps (superprocesses) and (2) {locality-preserving}
temporal change of scale transformations. We show that the long-range
correlations in this class of processes tends to originate almost entirely from
memory effects, and can accommodate genuinely quantum power-law correlations in
time. Importantly, this class allows efficient computation of multi-time
correlation functions. To showcase the potential utility of this model-agnostic
class for numerical simulation of physical models, we show how it can
approximate the strong memory dynamics of the paradigmatic spin-boson model, in
term of arbitrary multitime features. In contrast to an equivalently costly
matrix product operator (MPO) representation, the ansatz produces a fiducial
characterization of the relevant physics. Our work lays the foundation for the
development of more efficient numerical techniques in the field of strongly
interacting open quantum systems, as well as the theoretical development of a
temporal renormalization group scheme.
