  Correlation functions of quantum systems -- central objects in quantum field
theories -- are defined in high-dimensional space-time domains. Their numerical
treatment thus suffers from the curse of dimensionality, which hinders the
application of sophisticated many-body theories to interesting problems. Here,
we propose a multi-scale space-time ansatz for correlation functions of quantum
systems based on quantics tensor trains (QTT), ``qubits'' describing
exponentially different length scales. The ansatz then assumes a separation of
length scales by decomposing the resulting high-dimensional tensors into tensor
trains (known also as matrix product states). We numerically verify the ansatz
for various equilibrium and nonequilibrium systems and demonstrate compression
rates of several orders of magnitude for challenging cases. Essential building
blocks of diagrammatic equations, such as convolutions or Fourier transforms
are formulated in the compressed form. We numerically demonstrate the stability
and efficiency of the proposed methods for the Dyson and Bethe-Salpeter
equations. {The QTT representation} provides a unified framework for
implementing efficient computations of quantum field theories.
