Embedded within the general objective of the project, the work
perfomed in MaBoQuaCo revolved around four more specific research
directions.
1) The first objective was to explore applications of quantum typicality for
simulations on NISQ devices. Here, the notion of quantum typicality refers to
the fact that certain properties of large quantum systems can be approximated
by individual random pure quantum states. This direction builds on previous work
by the researcher in the context of quantum-hydrodynamics simulations, which
appeared to be promising candidates for early robust NISQ simulations. As a
first step, random Clifford circuits with a conservation law were studied. Such
Clifford circuits are particularly useful for benchmarking quantum simulations
thanks to their comparatively simple implementation on NISQ devices and their
efficient simulability on digital NISQ devices. Secondly, long-range quantum
systems with higher-order conservation laws where studied, where the competing
tendencies of long-range interactions and restraining symmetries leads to
interesting dynamics. By combining analytical arguments with simulations of
classical toy models as well as typicality-based simulations of spin chains,
different hydrodynamic regimes were unveiled with distinct dynamical exponents.
These results will guide experiments in trapped-ion and Rydberg-atom platform
which are also key technology candidates in the maturation of NISQ platforms.
2) The second objective was to understand the impact of the environment, for
instance in the form of measurements and decoherence, on certain types of
quantum dynamics. Here, two different directions were followed.
First, boundary-driven systems described by Lindblad master equations were
studied regarding their transport properties. In particular, it was
demonstrated that open-system Lindblad dynamics is in certain cases
describable by properties of the bare closed system. This novel connection was
established by analyzing individual quantum trajectories thanks to a
typicality-based pure-state approach. These typicality relations are not only
of fundamental importance to understand transport in open systems, they are
also practically relevant as efficient simulation tools. Moreover, as a second
direction, non-Hermitian quantum systems were studied more broadly with
respect to their integrability and their dynamics. Using a newly developed
framework for correlation functions in open systems, the transport properties
were analyzed and signatures of fast ballistic transport were observed even in
nonintegrable models, which is in stark contrast to the common knowledge from
standard Hermitian models.
3) Here, the goal was to simulate many-body localization dynamics in
disordered systems coupled to a bath and to understand the stability of
localization in such systems. To this end, newly adapted typicality-based
methods were applied to a realistic scenario of a disordered spin chain, where
the decay of magnetization acts as a proxy for localization. As a main result,
it was found that under certain driving protocols, the decay of magnetization
can become notably slower, allowing to draw conclusions on the amount of
disorder present in the system. These findings may guide simulations on noisy
quantum computers or in more traditional solid-state experiments. Moreover, in
a different strand of research, many-body localization was studied in one- and
two-dimensional Clifford circuits. These studies unveiled that localization is
absolutely robust in one dimension, which might be interesting for applications
on NISQ devices to control the proliferation of errors.
4) Finally, inspired by progress in NISQ simulations, the goal was to
develop new efficient classical simulation schemes. In particular, a hybrid
Schrödinger-Feynman simulation was implemented which is memory efficient and,
thanks to large-scale parallelization, was shown to be able to address quantum
systems significantly larger than other common techniques. The method was
specifically applied to study slow thermalization in moderately disordered
quantum systems, which is known to be an extremely challenging problem due
to strong finite-size effects.
