Periodic Reporting for period 2 - MaBoQuaCo (Quantum Many-Body Dynamics and Noisy Intermediate-Scale Quantum Computers: Interconnections, Near-Term Applications, and Novel Simulation Schemes)
Okres sprawozdawczy: 2024-05-01 do 2025-04-30
Quantum computing is at the forefront of modern scientific research, promising
to revolutionize technology by solving complex problems beyond the reach of
classical computers. Currently, the field is in the era of Noisy
Intermediate-Scale Quantum (NISQ) devices, which are limited by noise and
decoherence. Despite these limitations, NISQ devices hold significant potential
for simulating quantum many-body dynamics which is notoriously
challenging with classical computers. Crucially, at least for certain
problems, NISQ devices have started to challenge modern supercomputers.
Over the past two decades, the properties of quantum systems out of equilibrium
have experienced an upsurge of interest. Longstanding questions have received
renewed attention, e.g. regarding the origin of hydrodynamic transport under
unitary time evolution or the spreading of entanglement. Research on
strongly disordered quantum systems has unveiled the possibility of a many-body
localized (MBL) phase, where systems fail to reach thermal equilibrium under
their own dynamics. Moreover, the advent of NISQ devices has fueled efforts to
explore out-of-equilibrium phases of matter in monitored circuits consisting of
unitary gates interspersed with random measurements.
The project “MaBoQuaCo” seeks to bridge the gap between the theoretical
understanding of quantum many-body dynamics and the practical capabilities of
NISQ devices. It aims to deliver
important breakthroughs in both areas and its overarching goal is to explore
the connections between these two fields. In addition to studying fundamental
aspects of out-of-equilibrium quantum dynamics, the project will explore
avenues to leverage the capabilities of NISQ devices for this purpose and
develop efficient algorithms and simulation techniques inspired by and tailored
for NISQ hardware.
to revolutionize technology by solving complex problems beyond the reach of
classical computers. Currently, the field is in the era of Noisy
Intermediate-Scale Quantum (NISQ) devices, which are limited by noise and
decoherence. Despite these limitations, NISQ devices hold significant potential
for simulating quantum many-body dynamics which is notoriously
challenging with classical computers. Crucially, at least for certain
problems, NISQ devices have started to challenge modern supercomputers.
Over the past two decades, the properties of quantum systems out of equilibrium
have experienced an upsurge of interest. Longstanding questions have received
renewed attention, e.g. regarding the origin of hydrodynamic transport under
unitary time evolution or the spreading of entanglement. Research on
strongly disordered quantum systems has unveiled the possibility of a many-body
localized (MBL) phase, where systems fail to reach thermal equilibrium under
their own dynamics. Moreover, the advent of NISQ devices has fueled efforts to
explore out-of-equilibrium phases of matter in monitored circuits consisting of
unitary gates interspersed with random measurements.
The project “MaBoQuaCo” seeks to bridge the gap between the theoretical
understanding of quantum many-body dynamics and the practical capabilities of
NISQ devices. It aims to deliver
important breakthroughs in both areas and its overarching goal is to explore
the connections between these two fields. In addition to studying fundamental
aspects of out-of-equilibrium quantum dynamics, the project will explore
avenues to leverage the capabilities of NISQ devices for this purpose and
develop efficient algorithms and simulation techniques inspired by and tailored
for NISQ hardware.
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.
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.
The scientific results achieved over the course of the project extend our
knowledge of fundamental aspects of quantum dynamics in various ways. This
includes the dynamical phase diagram of long-range systems with higher-order
conservation laws realizable in analog quantum simulators, where a
comprehensive picture of the different transport regimes was provided.
Furthermore, the novel typicality-based connection between Lindbladian dynamics
and linear-response correlation functions enhances our understanding of the
limitations of state-of-the-art simulation techniques in open quantum systems.
In the context of open systems, the study of transport properties in
non-Hermitian Hamiltonians suggested the emergence of fast ballistic transport
which is another highly surprising result which will stimulate further
explorations in this direction. The project also achieved results beyond the
state of the art regarding questions related to many-body localization. On one
hand, the study of localization in one- and two-dimensional Clifford circuits
provided a new perspective on the possibility of using Clifford circuits to
simulate certain novel nonequilibrium quantum phenomena. Moreover, the
evaluation of the spectral form factor in these Clifford circuits highlighted
their hybrid nature between integrable and chaotic models, which warrants
further investigation. On the other hand, this project demonstrated the
successful implementation of a memory-efficient Schrödinger-Feynman-type
simulation which was able to address questions relevant to many-body
localization for remarkably large system sizes. This method should find various
other useful applications and we hope that our study will motivate its usage in
the quantum-dynamics community. In summary, the project significantly advanced
the state of the art, contributing both theoretical insights as well as
practical methodologies with relevance to future NISQ developments.
knowledge of fundamental aspects of quantum dynamics in various ways. This
includes the dynamical phase diagram of long-range systems with higher-order
conservation laws realizable in analog quantum simulators, where a
comprehensive picture of the different transport regimes was provided.
Furthermore, the novel typicality-based connection between Lindbladian dynamics
and linear-response correlation functions enhances our understanding of the
limitations of state-of-the-art simulation techniques in open quantum systems.
In the context of open systems, the study of transport properties in
non-Hermitian Hamiltonians suggested the emergence of fast ballistic transport
which is another highly surprising result which will stimulate further
explorations in this direction. The project also achieved results beyond the
state of the art regarding questions related to many-body localization. On one
hand, the study of localization in one- and two-dimensional Clifford circuits
provided a new perspective on the possibility of using Clifford circuits to
simulate certain novel nonequilibrium quantum phenomena. Moreover, the
evaluation of the spectral form factor in these Clifford circuits highlighted
their hybrid nature between integrable and chaotic models, which warrants
further investigation. On the other hand, this project demonstrated the
successful implementation of a memory-efficient Schrödinger-Feynman-type
simulation which was able to address questions relevant to many-body
localization for remarkably large system sizes. This method should find various
other useful applications and we hope that our study will motivate its usage in
the quantum-dynamics community. In summary, the project significantly advanced
the state of the art, contributing both theoretical insights as well as
practical methodologies with relevance to future NISQ developments.