Periodic Reporting for period 4 - StrEnQTh (Strong Entanglement in Quantum many-body Theory)
Período documentado: 2022-11-01 hasta 2023-12-31
The microscopic constituents of matter obey the counterintuitive laws of quantum mechanics, which are fundamentally different from the classical laws that we are used to in our macroscopic world. One far-reaching consequence of quantum mechanics is the existence of “entangled states” formed by groups of quantum components (particles). In such a state, the individual components relinquish their identity, and every component "knows" the behavior of the others across any distance. In recent years, major experimental strides in ultracold atomic gases and other platforms have made it possible to manipulate and design complex materials at the single-component level. We know that entanglement at this fundamental level plays a major role. Yet, until now, entanglement is fully understood only if very few particles are involved, and no concise theoretical framework exists for entanglement involving large groups of particles. Even more, it is very difficult, even for the best state of art experiments, to detect entanglement that is shared between many particles. These constitute paramount obstacles for further theoretical and technological progress in quantum matter and quantum technologies.
The "Strong Entanglement in Quantum Many-body Theory" (StrEnQTh) project aimed to overcome these hurdles, following three main objectives.
(i) The design of novel mathematical frameworks for many-particle entanglement, which is notoriously challenging to classify.
(ii) The development of novel methods for studying many-body quantum systems, in particular, for understanding the role that entanglement plays during their time evolution away from thermal equilibrium. Our main focus lied on gauge theories, which form the theoretical basis for describing fundamental particles of nature and describe emergent exotic phases of matter.
(iii) The exploitation of the untapped potential of engineered quantum dynamics, such as by perturbing the quantum system in a controlled manner, in order to design protocols for accessing many-particle entanglement and other key signatures of quantumness in state-of-the-art experiments.
By uniting these three aspects, this project addressed a key frontier of modern physics at the interfaces of quantum computing, quantum information theory, atomic physics, high-energy physics, quantum chemistry, and computational biophysics. The results achieved provide us with new fundamental frameworks to classify entangled matter, furthered our understanding of quantum many-body systems in and out of equilibrium, and generated new methodology to treat them in theoretical analyses as well as in laboratory experiments. The implications and further applications range from novel computing and simulation algorithms, over the design of new materials, to quantum-enhanced sensors.
The "Strong Entanglement in Quantum Many-body Theory" (StrEnQTh) project aimed to overcome these hurdles, following three main objectives.
(i) The design of novel mathematical frameworks for many-particle entanglement, which is notoriously challenging to classify.
(ii) The development of novel methods for studying many-body quantum systems, in particular, for understanding the role that entanglement plays during their time evolution away from thermal equilibrium. Our main focus lied on gauge theories, which form the theoretical basis for describing fundamental particles of nature and describe emergent exotic phases of matter.
(iii) The exploitation of the untapped potential of engineered quantum dynamics, such as by perturbing the quantum system in a controlled manner, in order to design protocols for accessing many-particle entanglement and other key signatures of quantumness in state-of-the-art experiments.
By uniting these three aspects, this project addressed a key frontier of modern physics at the interfaces of quantum computing, quantum information theory, atomic physics, high-energy physics, quantum chemistry, and computational biophysics. The results achieved provide us with new fundamental frameworks to classify entangled matter, furthered our understanding of quantum many-body systems in and out of equilibrium, and generated new methodology to treat them in theoretical analyses as well as in laboratory experiments. The implications and further applications range from novel computing and simulation algorithms, over the design of new materials, to quantum-enhanced sensors.
The StrEnQTh project has been extremely productive. At the initial stages, a substantial effort has been put into the team creation, the selection of the team members, and formation of a collaborative team spirit. Throughout, the team was formed by 8 PhD students, 4 postdoctoral fellows, 2 senior researchers, the principal investigator, and two administrative staff. Team members hailed from Brazil, China, Germany, India, Italy, Lebanon, Namibia, and Switzerland. The team has held more than 65 presentations disseminating the aims and results of the project and published 54 peer-reviewed journal articles, 21 preprints, and 1 general-science publication. The website disseminated results and the group required about 650 followers on X.
Almost all of the major milestones of the project have been achieved.
The mathematical basis for objective (i) has been laid. Among central achievements of StrEnQTh, we have developed novel ways to classify the number of particles that are entangled with each other if they have fermionic statistics, and developed frameworks for characterizing entanglement in systems that are subject to constraints or governed by a non-Hermitian model Hamiltonian. In an interesting sidetrack, we also made progress in understanding the role of entanglement for solving hard combinatorial problems, and designed algorithms to exploit quantum effects for solving outstanding problems from computational biophysics and soft matter.
Regarding objective (ii), we developed highly performant numerical and analytical methods, which enabled us to identify and study a variety of novel phenomena in strongly-correlated quantum matter, including dynamical critical behavior, new types of universality, or staircase-like prethermalization. Moreover, we designed new methods to study such highly interacting systems directly in experimental platforms, such as cold atomic gases and superconducting quantum chips. These have lead to first laboratory studies of important gauge-theory phenomena such as Coleman's phase transition, certification of gauge symmetry, or confinement in presence of a topological theta term.
Regarding objective (iii), we have established paradigmatically new experimentally-friendly detection tools for many-body entanglement, the quantum fluctuation-dissipation theorem, exotic quantum phases of matter, particle currents, and many other effects of quantum correlations.
These achievements were enabled by an exceptional degree of cross- and interdisciplinarity, involving collaborations with experimentalists working on a range of quantum-device platforms as well as experts in quantum information theory, high-energy and nuclear physics, cosmology, computational biophysics, soft-matter theory, and quantum chemistry.
Almost all of the major milestones of the project have been achieved.
The mathematical basis for objective (i) has been laid. Among central achievements of StrEnQTh, we have developed novel ways to classify the number of particles that are entangled with each other if they have fermionic statistics, and developed frameworks for characterizing entanglement in systems that are subject to constraints or governed by a non-Hermitian model Hamiltonian. In an interesting sidetrack, we also made progress in understanding the role of entanglement for solving hard combinatorial problems, and designed algorithms to exploit quantum effects for solving outstanding problems from computational biophysics and soft matter.
Regarding objective (ii), we developed highly performant numerical and analytical methods, which enabled us to identify and study a variety of novel phenomena in strongly-correlated quantum matter, including dynamical critical behavior, new types of universality, or staircase-like prethermalization. Moreover, we designed new methods to study such highly interacting systems directly in experimental platforms, such as cold atomic gases and superconducting quantum chips. These have lead to first laboratory studies of important gauge-theory phenomena such as Coleman's phase transition, certification of gauge symmetry, or confinement in presence of a topological theta term.
Regarding objective (iii), we have established paradigmatically new experimentally-friendly detection tools for many-body entanglement, the quantum fluctuation-dissipation theorem, exotic quantum phases of matter, particle currents, and many other effects of quantum correlations.
These achievements were enabled by an exceptional degree of cross- and interdisciplinarity, involving collaborations with experimentalists working on a range of quantum-device platforms as well as experts in quantum information theory, high-energy and nuclear physics, cosmology, computational biophysics, soft-matter theory, and quantum chemistry.
The project has gone significantly beyond the state of art in various aspects. The following are examples of key breakthroughs:
- It is now possible to classify entanglement in situations that reach beyond the standard paradigm of Hermitian models with bosonic statitistics, including fermions, lattice gauge theories, and non-Hermitian systems. These are important for manifold situations in nature, including elementary particles and systems coupled to a bath.
- We have established a fully new research line of using quantum computing to solve problems of computational biophysics.
- Novel schemes to experimentally realize lattice gauge theories in cold atomic gases have opened the door for microscopic in-depth investigations of gauge theory dynamics. First applications have been demonstrated and many further investigations into these important but hard-to-compute model systems are now possible.
- We have made significant progress in understanding the role of perturbations on the dynamics of gauge theories and how to protect against them, furthering our understanding of the workings of nature as well as enabling more precise quantum-simulation algorithms.
- Thanks to novel protocols based on engineered quantum dynamics, observables that have hitherto been unreachable now become accessible, enabling unprecedented access to microscopic quantum effects.
In total, the project has developed new mathematical frameworks for many-body entanglement as well as a range of theoretical and experimental tools to systematically study quantum dynamics in regimes that previously were out of reach. Thanks to these, a much clearer picture of the role of entanglement in quantum many-body systems is emerging, with fundamental implications into interactions of many particles as well as applications in harnessing and certifying quantum devices.
- It is now possible to classify entanglement in situations that reach beyond the standard paradigm of Hermitian models with bosonic statitistics, including fermions, lattice gauge theories, and non-Hermitian systems. These are important for manifold situations in nature, including elementary particles and systems coupled to a bath.
- We have established a fully new research line of using quantum computing to solve problems of computational biophysics.
- Novel schemes to experimentally realize lattice gauge theories in cold atomic gases have opened the door for microscopic in-depth investigations of gauge theory dynamics. First applications have been demonstrated and many further investigations into these important but hard-to-compute model systems are now possible.
- We have made significant progress in understanding the role of perturbations on the dynamics of gauge theories and how to protect against them, furthering our understanding of the workings of nature as well as enabling more precise quantum-simulation algorithms.
- Thanks to novel protocols based on engineered quantum dynamics, observables that have hitherto been unreachable now become accessible, enabling unprecedented access to microscopic quantum effects.
In total, the project has developed new mathematical frameworks for many-body entanglement as well as a range of theoretical and experimental tools to systematically study quantum dynamics in regimes that previously were out of reach. Thanks to these, a much clearer picture of the role of entanglement in quantum many-body systems is emerging, with fundamental implications into interactions of many particles as well as applications in harnessing and certifying quantum devices.