Non-equilibrium Many-body Physics Beyond the Floquet Paradigm

Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Because of the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension. Here, we show that prethermal nonequilibrium phases of matter are not restricted to the quantum domain. I will present different examples from periodically to aperiodically driven spin systems.

Superoscillation is a counterintuitive phenomenon for its mathematical feature of ”faster-than-Fourier”, which has allowed novel optical imaging beyond the diffraction limit. Here, we provide a superoscillating quantum control protocol realized by sequential selections in the framework of weak measurement, which drives the apparatus (target) by repeatedly applying optimal pre- and post-selections to the system (controller). Our protocol accelerates the adiabatic transport of trapped ions and adiabatic quantum search algorithm at a finite energy cost. We demonstrate the accuracy and robustness of the protocol in the presence of decoherence and fluctuating noise and elucidate the trade-off between fidelity and rounds of selections. Our findings provide avenues for quantum state control and wave-packet manipulation using superoscillation in various quantum platforms.

In this talk, we study the mean-field dynamics of a general class of quantum many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter $m(t)\sim t^{-\chi}$ with an exponent $\chi=\frac 13$ that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion constant which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.

Strongly driven systems of emitters offer an attractive source of light over broad spectral ranges up to the X-ray region. A key limitation of these systems is that the light they emit is mostly classical. We overcome this constraint by building a quantum-optical theory of strongly driven many-body systems, showing that the presence of correlations among the emitters creates emission of non-classical many-photon states of light. We consider the example of high-harmonic generation, by which a strongly driven system emits photons at integer multiples of the drive frequency. In the conventional case of uncorrelated emitters, the harmonics are in an almost perfectly multi-mode coherent state lacking any correlation between harmonics. By contrast, a correlation of the emitters before the strong drive is converted into non-classical features of the output light, including doubly peaked photon statistics, ring-shaped Wigner functions and correlations between harmonics. We propose schemes for implementing these concepts, creating the correlations between emitters via an interaction between them or their joint interaction with the background electromagnetic field. Our work paves the way towards the engineering of novel states of light over a broadband spectrum and suggests high-harmonic generation as a tool for characterizing correlations in many-body systems with attosecond temporal resolution.

Dynamical freezing refers to the phenomenon of perpetual but approximate freezing or conservation of certain local operators close to their initial values in a generic, disorder-free, quantum chaotic many-body system, under strong periodic drive. These conservation laws are "emergent", as they are not respected in the undriven system. This is a way to evade Thermalization at late times in the absence of disorder even in the thermodynamic system. We will conjecture a recipe for constructing the conservation laws and show that they are not necessarily protected by high energy costs that can be posed by the strong drive field. This provides a new route to stabilizing and engineering interacting quantum matter far from equilibrium, and also help quantum state preservation. It also raises new questions regarding mechanisms of stabilizing quantum of matter out of equilibrium, and formulating Statistical Mechanics with approximate but perpetual constraints.

The interplay between disorder and magnetic frustration in spin glasses keeps remaining one of the most prominent unsolved problems in statistical physics, with important applications in optimization, quantum annealing, and the fundamental research interest in the study of thermalization and ergodicity. An important subclass of these systems are dipolar interacting ones, where the existence of a spin glass phase in the strong diluted regime has been controversial over decades. In this talk, I will present two new protocols that we developed in order to characterize hysteresis, and possibly replica symmetry breaking, in an isolated dipolar system, which we realize on a Rydberg atom quantum simulation platform, where the spin degree of freedom is encoded in two different Rydberg states. Complementing other techniques that rely on a full measurement of the spin glass overlap, our techniques involve only global state preparation and measurements. The techniques show hysteresis both in a few particle finite size simulation as well as in a mesoscopic quantum simulation, giving a first indication of a possible quantum phase transition and replica symmetry breaking in a disordered dipolar Heisenberg spin system with a transverse field.

External coherent fields can drive quantum materials into non-equilibrium states, revealing exotic properties that are unattainable under equilibrium conditions -- an approach known as "Floquet engineering." While optical lasers have commonly been used as the driving fields, recent advancements have introduced nontraditional sources, such as coherent phonon drives. Building on this progress, we demonstrate that driving a metallic quantum nanowire with a coherent wave of terahertz phonons can induce an electronic steady state characterized by a persistent quantized current along the wire. The quantization of the current is achieved due to the coupling of electrons to the nanowire's vibrational modes, providing the low-temperature heat bath and energy relaxation mechanisms. Our findings underscore the potential of using non-optical drives, such as coherent phonon sources, to induce non-equilibrium phenomena in materials. Furthermore, our approach suggests a new method for the high-precision detection of coherent phonon oscillations via transport measurements.

There is a well-established principle and formalism for classifying ground state phases of gapped Hamiltonian systems - Hamiltonians which can be deformed into one another without closing the gap belong to the same topological phase. In the nonequilibrium context, topological phases of localized systems may be identified as sets of Hamiltonians which can be deformed into one another without going through a delocalization transition. For Floquet systems, it is known how to map the classification of such phases to a classification of locality preserving unitaries - called quantum cellular automata (QCA) - which characterize dynamics at the boundary of a sample. We show how to classify localized topological phases using QCAs beyond the context of periodic driving, including static and quasiperiodically driven systems. Further, we adapt many tools from the study of gapped ground states to the localized context, allowing for significant progress in the classification. Some of the localized topological phases so discovered are characterized by eigenstate order - eigenstates of the model are ordered like ground states of nontrivial gapped Hamiltonians. However, there are also anomalous localized topological phases (ALT phases), for which each eigenstate is trivial when regarded individually, but the system as a whole still cannot be deformed into an atomic insulator.

We study the effect of noise on two-dimensional periodically driven topological phases, focusing on two examples: the anomalous Floquet-Anderson insulator and the disordered Floquet-Chern insulator. We show that the former is substantially more robust against temporal noise than the latter, i.e. its initially populated topological modes undergo an algebraic decay as a function of time, instead of an exponential one. Using a combination of analytical results, phenomenological models, as well as full-scale numerical simulations, we find that this additional diffusive regime occurs at intermediate times, and that it is absent in the Floquet-Chern insulator, where the decay remains exponential throughout. Surprisingly, this is a consequence of a thermalization that occurs specifically among edge modes, separate from the bulk. Our findings indicate that anomalous phases, instead of Chern phases, are ideal candidates for potential applications of Floquet topology, given the unavoidable presence of both quenched disorder and decoherence in experiments.

Flocks of animals represent a fascinating archetype of collective behavior in the macroscopic classical world, where the constituents, such as birds, concertedly perform motions and actions as if being one single entity. Here, we address the outstanding question of whether flocks can also form in the microscopic world at the quantum level. For that purpose, we introduce the concept of active quantum matter by formulating a class of models of active quantum particles on a one-dimensional lattice. We provide both analytical and large-scale numerical evidence that these systems can give rise to quantum flocks. A key finding is that these flocks, unlike classical ones, exhibit distinct quantum properties by developing strong quantum coherence over long distances. We propose that quantum flocks could be experimentally observed in Rydberg atom arrays. Our work paves the way towards realizing the intriguing collective behaviors of biological active particles in quantum matter systems. We expect that this opens up a path towards a yet totally unexplored class of nonequilibrium quantum many-body systems with unique properties.

Active matter is an ensemble of self-propelled entities, such as flocks of birds and schools of fish, that has attracted much attention for its various phase transitions and pattern formations that are not present in equilibrium systems [1]. While the physics of active matter has been studied extensively in statistical physics and biophysics, most studies have been limited to classical systems, and the possibility of active matter in quantum systems has rarely been considered. However, recent developments in atomic-molecular-optical systems allow us to study the complex dynamics of quantum many-body systems in a highly controlled manner, and it may be possible to design quantum many-body systems that behave like active matter. Stimulated by this, the study of the quantum analog of active matter has been initiated very recently [2-6]. In particular, we have studied quantum phase transitions analogous to the nonequilibrium phase transitions of active matter [2,6]. In this presentation, we would like to present our work on quantum active matter. We have studied two-component (spin-1/2) hard-core bosons with spin-dependent asymmetric hopping corresponding to the motility of each active particle. This is expected to be realized with ultracold atoms with a dissipative optical lattice. We have shown that this model can be regarded as a quantum generalization of classical active matter models defined on a lattice, and that it exhibits various phase transitions, including nonequilibrium phase transitions unique to active matter, such as motility-induced phase separation [2]. In more recent work [6], we have shown that the combination of activity and repulsive interaction induces ferromangnetism, based on both numerical and analytical arguments. This activity-induced ferromangnetism can be considered as a quantum counterpart of flocking. While the flocking transition in classical systems requires a microscopic alignment interaction, this mechanism does not require such an interaction and thus may be unique to quantum active matter. We believe that our works extending active matter physics to quantum systems help to broaden the perspective on nonequilibrium phases of matter beyond conventional paradigms. [1] M. C. Marchetti et al., Rev. Mod. Phys. 85, 1143 (2013). [2] K. Adachi, KT, K. Kawaguchi, Phys. Rev. Research 4, 013194 (2022). [3] M. Yamagishi, N. Hatano, H. Obuse, arXiv: 2305.15319 [4] Y. Zheng, B. Liebchen, H. Löwen, arXiv: 2305.16131 [5] R. Khasseh, S. Wald, R. Moessner, C. A. Weber, M. Heyl, arXiv: 2308.01603 [6] KT*, K. Adachi*, K. Kawaguchi, Phys. Rev. Research 6, 023096 (2024). (*equally contributed)

Thermalization in a closed quantum system is defined by the dynamical approach of local observables toward universal expectation values, computed within a thermal Gibbs state. In this talk, I want to explain how a more refined notion of quantum equilibration can be studied by resolving the local state of a system via conditioning it on measurements of the complement (the “bath”). This yields an ensemble of pure conditional states — representing a physically motivated unraveling of the reduced density matrix — which describes a wavefunction distribution over the Hilbert space. I will show that for generic complex quantum dynamics, the ensemble tends toward universal distributions constrained only by global conservation laws, a process we dub "deep thermalization". Underpinning this phenomenon is a generalized maximum principle, which endows the limiting ensembles with the special quantum information-theoretic property of possessing minimal accessible information. I will show how this principle applies across physically distinct systems of discrete-variable spin systems as well as continuous-variable bosonic Gaussian systems. Our results demonstrate the power of quantum information theoretic frameworks in unveiling new physical phenomena and principles in quantum dynamics and statistical mechanics.

We discuss universal fluctuations that arise from natural quantum many-body dynamics. These fluctuations are unique to the statistics of global bitstring measurements and have been used in random circuit sampling tasks for recent quantum advantage claims. Based on such fluctuations, I will introduce a sample-efficient protocol which estimates the fidelity between an experimentally prepared state and an ideal target state, and is applicable to a wide class of analog quantum simulators. Finally, we apply this protocol in a 60-atom analog Rydberg quantum simulator, and further use our results to quantify the amount of mixed state entanglement present, as well as learning about the noise. We find that the experiment is competitive in this respect with state-of-the-art digital quantum devices performing random circuit evolution and we distinguish the proportion of local vs. global noise in the system.

Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry’s conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. Then, how can we define the ergodicity for quantum dynamics for which the notion of eigenstates does not exist? In this work, we introduce an alternative, stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. Such a phenomenon, called complete Hilbert-space ergodicity (CHSE) is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates. However, we show that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity — generated by the Fibonacci word and its generalizations — for which CHSE can be proven to occur. These results provide a basis for understanding thermalization in general time-dependent quantum systems. Based onPhys. Rev. Lett. 131, 250401 (2023)

We introduce a family of local models of dynamics based on ``word problems'' from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random circuit or local Hamiltonian dynamics, and include many familiar examples of constrained dynamics as special cases. The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must ``work out'' the other states in the sector to which they belong. When this problem has a high time complexity, relaxation is slow. In some of the cases we study, this problem also has high space complexity. When the space complexity is larger than the system size, an unconventional type of jamming transition can occur, whereby a system of a fixed size is not ergodic, but can be made ergodic by appending a large reservoir of sites in a trivial product state. This manifests itself in a new type of Hilbert space fragmentation that we call fragile fragmentation. We present explicit examples where slow relaxation and jamming strongly modify the hydrodynamics of conserved densities.

We study the role of time-translational symmetries in governing the temporal distributions of quantum states over the Hilbert space, by considering an aperiodic driving protocol derived from the Thue-Morse word. We show that the dynamics achieve complete Hilbert-space ergodicity (CHSE), meaning that any state uniformly visits the entire Hilbert space over time, yet, for systems of few-levels, it does so very slowly. This system exhibits steady states which are transient, but which survive for extremely long times. We find, invoking a mapping to a dynamical system of a classically chaotic map in the complex unit disk, that these are a result of emergent, yet transient time-translation symmetries. Our results showcase a physical system in which the expected outcome of thermalization happens, but which does so in an extremely slow fashion, much slower than would be expected of any natural time-scales of the system.

Measurement-induced phase transitions are novel classes of non-equilibrium dynamical phase transitions, resulting from the interplay between unitary time evolution and measurements. In this talk I will present a family of exactly solvable non-unitary circuits that lead to rich measurement-induced phase transitions, ranging from area to volume law scalings of the entanglement entropy. In the case of time-periodic non-unitary circuits, there exists a sharp transition from volume to area law. I will show how the full breaking of the time-translation symmetry in a class of quasiperiodic circuits leads to even richer entanglement transitions, with extended critical regions characterized by a fractal structure of entanglement separating area and volume law phases. I will finally comment on the case of a purely random non-unitary evolution. Work in collaboration with Shinsei Ryu, to appear.

Passive quantum memories are a way to passively protect quantum information using coupling that creates an "always-on'' decoder. In this talk, I will first discuss passive error correction (EC) using Lindbladian formalism for open quantum systems. I will show that how spontaneous symmetry breaking can be understood within this picture and point out the connection between passive EC and dissipative phases. Then I will discuss a concrete candidate for a passively protected quantum memory in 2D. The model consists of quantum harmonic oscillators with nearest-neighbour coupling and is robust against common bosonic noise. If time permits, I will then discuss our recent exploration of metastable passive quantum memories in 1D closed quantum systems subject to coherent perturbation, which arise from the phenomena of prethermalization.

Probing correlated states of many-body systems is one of the central tasks for quantum simulators and processors. I will discuss two of my recent publications on realizing such states as steady states of engineered dissipative evolution. The recent experimental work [X. Mi et al., Science 383, 1332 (2024)] on a Google superconducting quantum processor demonstrated cooling utilizing auxiliary degrees of freedom that are periodically reset to remove quasiparticles from the system, thereby driving it towards the ground state. In [arxiv:2404.12175] we develop a kinetic theory framework that describes the experiment and further suggests how to engineer more efficient cooling protocols. For examples of both integrable and non-integrable 1D quantum Ising models, we demonstrate high-fidelity preparation of ground states in different quantum phases. The effects of noise, which limits the efficiency of quantum algorithms on near-term quantum processors, can be naturally included in the kinetic theory framework and we establish thresholds for high-fidelity state preparation in the presence of noise.

Typically, dissipation relaxes a system to thermal equilibrium, while strong periodic driving causes it to heat up. I will describe an experimentally motivated setup in which time dependent dissipation arises naturally and stabilizes the Floquet states of the isolated system. I will present experimental data for a superconducting qubit coupled to a lossy cavity that demonstrates this effect, and discuss prospects to stabilize energy pumps with dissipation.

Entanglement entropy and its scaling with system size determine the complexity of quantum many-body states. Non-equilibrium many-body dynamics is often accompanied by rapid growth of entanglement, and is therefore challenging to simulate classically. I will describe an approach to a range of problems in quantum dynamics, based on viewing a many-body system as a quantum bath. The bath is characterized by the Feynman-Vernon influence functional. Viewing this object as a fictitious wave function in the temporal domain, I will characterise its complexity in terms of temporal entanglement. Temporal entanglement exhibits favorable, area-law scaling with evolution time for a range of important problems, including thermalization, quenches in integrable systems, and quantum impurity models. This observation yields rigorous bounds on simulation complexity of some of these problems, including the paradigmatic spin-boson model, and underlies a new family of efficient computational methods.

Trapped atomic ions serve as powerful digital, analog and hybrid quantum simulators for many-body quantum systems using their spin and motional degrees of freedom. Our system is based on a chain of 171Yb+ ions with individual laser beam addressing, creating a fully connected device capable of executing any sequence of single- and two-qubit gates, as well as continuous evolution. This makes it an arbitrarily programmable quantum computer and hybrid simulator. I will present simulation experiments using parallel and multi-qubit gates as well as spin-motional hybrid Hamiltonians. We also realize a new tomography method for imperfect measurement bases and use it to distinguish system errors. We further demonstrate the fitting of vibrionic molecular spectra in the same system.

A topological Thouless pump represents the quantised motion of atoms, electrons or, in general, quantum many-body states. This directional transport is enabled by a cyclic modulation of external control parameters or, to put it another way, it corresponds to a periodically driven system (in the adiabatic limit). Traditionally, Thouless pumping has been described in the language of free-fermion bandstructures, exhibiting non-trivial single-particle Chern numbers. In our lab, we have recently been able to engineer many-body pumps by combining a dynamical, single-wavelength optical lattice with tuneable interactions between fermionic potassium-40 atoms. In this talk, I will present three examples of novel many-body physics arising from topological pumps beyond the single-particle regime. Firstly, I discuss the role of confining potentials for pumping, giving rise to both interacting and non-interacting topological edge modes [1]. Secondly, our experiments demonstrate how the conjunction of strong interactions and specific lattice modulations can induce pumping, even in absence of an underlying sliding motion [2]. Lastly, I will demonstrate how pumping interacting fermions through a lattice gives rise to configurable shuttle and gate operations between particles, realising a new toolbox for quantum processing [3]. [1] Zhu et al. Science 384, 317 (2024) [2] Viebahn et al. PRX (in press) [3] Zhu et al. arXiv (in preparation)

Hamiltonian learning techniques represent a powerful tool for the verification and characterization of programmable quantum simulators. Recent investigations have shown that the system Hamiltonian can be efficiently extracted from local observables in single isolated eigenstates as well as from finite temperature Gibbs states. Furthermore, the Hamiltonian that governs the dynamics of a quantum quench can be obtained from measurements on the time-evolved many-body states. In the first part of this talk, I will present novel developments in Hamiltonian learning within the context of digital quantum simulation. I will discuss techniques for characterizing digital quantum devices by learning the individual orders of the Floquet Hamiltonian. Extensions towards the design of many-body quantum gates and the learning of dissipative processes will also be explored. In the second part of the talk, I will introduce ideas that combine Hamiltonian learning techniques with variational quantum algorithms, with a specific application to cold fermions in optical lattices.

Quantum scars are special eigenstates of many-body systems that evade thermalization. They were first discovered in the PXP model, a well-known effective description of Rydberg atom arrays. Despite significant theoretical efforts, the fundamental origin of PXP scars remains elusive. By investigating the discretized dynamics of the PXP model as a function of the Trotter step $\tau$, we uncover a remarkable correspondence between the zero- and two-particle eigenstates of the integrable Floquet-PXP cellular automaton at $\tau = \pi/2$ and the PXP many-body scars of the time-continuous limit. Specifically, we demonstrate that PXP scars are adiabatically connected to the eigenstates of the $\tau = \pi/2$ Floquet operator. Building on this result, we propose a protocol for achieving high-fidelity preparation of PXP scars in Rydberg atom experiments.

Free fermions have emerged as a versatile model system to study the impact of continuous measurements on the dynamics of entanglement, enabling both efficient numerical simulations and analytical progress using field theoretic methods. For one-dimensional free fermions, there are conflicting results concerning the existence of a measurement-induced entanglement transition: While there is such a transition when both the Hamiltonian and the measurements break particle number conservation, an apparent Kosterlitz-Thouless transition in systems with a conserved number of particles has recently been argued to be unstable in the thermodynamic limit. In my talk, I will further clarify the role of particle number conservation in the entanglement dynamics of free fermions on a one-dimensional lattice and subjected to continuous measurements. I will show that a model with a particle number conserving Hamiltonian but nonconserving measurements is described by the same long-wavelength effective field theory as a fully conserving model, and present analytical and numerical evidence for the absence of a measurement-induced phase transition in the thermodynamic limit. However, within a well-defined range of length scales, there is a critical phase with logarithmic growth of the entanglement entropy and emergent conformal invariance. I will further address the question, how the finite-size phase diagram is affected by the breaking of energy conservation through Floquet driving in the form of a Trotterization of the hopping across even and odd bonds. While overall features of the phase diagram remain robust for generic driving parameters, we observe a change in the scaling of the phase boundaries with the measurement rate for the driving period corresponding to a dual-unitary circuit. This change can be traced back to the dispersion relation wrapping linearly around the Floquet-Brillouin zone.

When subjected to quasiperiodic driving protocols, superconducting systems have been found to harbor robust time-quasiperiodic Majorana modes, extending the concept beyond static and Floquet systems. However, the presence of incommensurate driving frequencies results in dense energy spectra, rendering conventional methods of defining topological invariants based on band structure inadequate. In this work, we introduce a real-space topological invariant capable of identifying time-quasiperiodic Majoranas by leveraging the system's spectral localizer, which integrates information from both Hamiltonian and position operators. Drawing insights from non-Hermitian physics, we establish criteria for constructing the localizer and elucidate the robustness of this invariant in the presence of dense spectra. Our numerical simulations, focusing on a Kitaev chain driven by two incommensurate frequencies, validate the efficacy of our approach.

The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern insulators in condensed matter, to protected states in complex photonic lattices in optics, and the structure of the QCD vacuum. Here, we introduce another playground for topology: the dissipative dynamics of the Sachdev-Ye-Kitaev (SYK) model, $N$ fermions in zero dimensions with strong $q$-body interactions coupled to a Markovian bath. For $q=4,8,\dots$ and certain choices of $N$ and bath details, involving pseudo-Hermiticity, we find a rectangular block representation of the vectorized Liouvillian that is directly related to the existence of an anomalous trace of the unitary operator implementing fermionic exchange. As a consequence of this rectangularization, the Liouvillian has purely real modes for any coupling to the bath. Some of them are demonstrated to be topological by an explicit calculation of the spectral flow, leading to a symmetry-dependent topological index $\nu$. Topological properties have universal features: they are robust to changes in the Liouvillian provided that the symmetries are respected and they are also observed if the SYK model is replaced by a quantum chaotic dephasing spin chain in the same symmetry class. Moreover, the topological symmetry class can be robustly characterized by the level statistics of the corresponding random matrix ensemble. In the limit of weak coupling to the bath, topological modes govern the approach to equilibrium, which may enable a direct path for experimental confirmation of topology in dissipative many-body quantum chaotic systems. Based on arXiv:2311.14640, with A. M. García-García, J. J. M. Verbaarschot, and C. Yin

In this talk, I will discuss theory aimed at understanding recent experimental data on driven YBa2Cu3O6.48 presented recently in the reference arXiv:2405.00848. Experiments on optically pumped YBa2Cu3O6.48 in the pseudogap phase far above Tc have shown evidence of dynamical Meissner effect. In our effort to understand the new experimental signatures, we have uncovered a universal instability triggered in Josephson junctions in a magnetic field that are strongly driven with an AC field. The instability leads to the generation of giant paramagnetic current loops at the edges of Josephson plasmons. For strong enough drive such instabilities ultimately lead to a soliton ratchet after driving. I will focus on why this instability of a generic Josephson junction is applicable to the pseudogap YBa2Cu3O6.48 far above Tc and how it matches the experimental observations. Finally, I will discuss implications of driven giant paramagnetism for amplifying magnetic fields in other systems and in cold atoms.

We discuss a new model for quantum computation with Rydberg atom arrays, which only relies on programmable positioning of atoms, global driving and the Rydberg blockade mechanism. Importantly this model eliminates the requirement of local addressing of individual atoms. Instead, in this model a quantum circuit is imprinted in the temporal phase dependence of two laser that globally drive an array of atoms (static) trap positions in a dual-species setup. We discuss all the ingredients for universal quantum computation in this setup, including initialization, execution of single and two-qubit gates, and readout, as well as the overhead in atom numbers with respect to standard quantum processor designs.

Most of our techniques to design driving protocols are based on perturbative approximations, because of the exponentially large effort of numerically exact techniques. Inspired by the framework of quantum invariants I will discuss how specific systems admit a way around this exponential scaling, and I will give examples for state preparation and the realisation on synthetic interactions in driven spin chains.

I will discuss two recent works that leverage ideas from quantum information dynamics to understand the impact of noise in many-body quantum systems. First, I will introduce a framework based on information spreading to understand how noise impacts the fidelity of ergodic many-body dynamics experiments. I will show that noisy quantum dynamics exhibit universal classes of information spreading that fundamentally differ from their unitary counterparts. This universal behavior provides a potential explanation for recent NMR experiments on 100s-1000s of interacting quantum spins. Second, in a more theoretical context, I will show how the same fundamental ideas enable a rigorous polynomial-time classical algorithm to simulate noisy quantum circuits. Our algorithm formalizes a simple intuition---that one can approximately simulate dynamics by keeping track of the local components of time-evolved operators---and provides the most extensive evidence yet that noisy quantum circuits without error correction can be simulated classically.

A great variety of topological phases have been classified as a consequence of discovery of the quantum Hall effect, but this work has recently led to discovery of some topologically non-trivial phases of matter, which contradict key assumptions of established classification schemes. These phases, which are the topological skyrmion phases of matter, multiplicative topological phases of matter, and finite-size topological phases of matter, necessitate a paradigm shift from the quantum Hall effect framework to that of the quantum skyrmion Hall effect, in which the point charges of the quantum Hall effect are generalised to compactified p-branes. For compactification via fuzzification, these compactified p-branes carrying charge are necessarily expressed in terms of angular momentum as quantum skyrmions.