Abstract

From quantum computing, the theory of thermalization to the impurity physics,
the dynamics of quantum many-body systems out-of-equilibrium is at the
forefront of several fields. Fundamentally, the numerical study of larger
quantum systems is challenging due to the exponential number of parameters
necessary to describe the wavefunction. If their entanglement is low,
wavefunctions can be approximated with relatively few parameters using tensor
networks. Since equilibrium wavefunctions have low entanglement, this makes
computations viable. However, when simulating dynamics, entanglement grows
rapidly with the evolution time. Here we discuss a new approach to many-body
dynamics, by using insights from the field of open quantum systems. We consider
dynamics of a subsystem, and view the rest of the many-body system as a bath.
The bath's properties are encoded in the influence functional (IF) on the space
of trajectories. Treating the IF as a "wave function" in the temporal domain,
we introduced the concept of Temporal Entanglement (TE) which can be
interpreted as the "quantum memory" of the bath. We show that in several broad
and relevant classes of systems, such as proximity to dissipative, integrable,
many-body localized or dual unitary phases, TE exhibits favorable scaling. This
allows the IF to be efficiently compressed as tensor network, opening the door
to a new family of computational methods based on low temporal rather than
spatial entanglement. For baths consisting of free fermions, we introduce a
procedure to obtain the IF directly from the spectral density. This allows us
to compute dynamics of impurity problems, such as the Single Impurity Anderson
model, achieving state of the art accuracy and time scales. We also discuss how
this algorithm can be applied to correlated matter in the context of dynamic
mean field theory. Finally I will show preliminary results demonstrating that
the IF can be also reconstructed directly from physical measurements on a
quantum computer. This potentially allows for predictions even in the absence
of a microscopic theory.