# News

### Work on quantum simulations in Nature Physics

Work on cold atomic quantum simulators probing "Gaussification dynamics" is going to press in Nature Physics . Gaussian models provide an excellent effective description of a plethora of quantum many-body systems ranging from a large variety of condensed matter systems all the way to neutron stars. Gaussian states are common at equilibrium when the interactions are weak. Recently it was proposed that they can also emerge dynamically from a non-Gaussian initial state evolving under non-interacting dynamics. In this work, we present the first experimental observation of such a dynamical emergence of Gaussian correlations in a quantum many-body system. For this, we monitor the connected fourth-order correlations during non-equilibrium dynamics. These dynamics are triggered by abruptly switching off the effective interaction between the collective degrees of freedom that we observe, while leaving the interactions between the microscopic constituents unchanged. Starting from highly non-Gaussian correlations, we observe a Gaussian description becoming increasingly accurate over time. In our closed system with non-interacting effective degrees of freedom, we do not expect full thermalization. This memory of the initial state is confirmed by observing recurrences of non-Gaussian correlations. Our study points to a natural way for Gaussian models to emerge in a wide class of (microscopically interacting) quantum many-body systems.

Jan 18, 2021

### Two QIP talks

Two group contributions to QIP 2021 , the largest conference on quantum information processing, one on random quantum circuits and one on quantum metrology, have been accepted as talks. Congratulations.

Jan 04, 2021

### Work on many-body localization in Communications Physics

Understanding the conditions under which physical systems thermalize is one of the long-standing questions in many-body physics. While it has been observed that generic quantum systems do thermalize, rather little is known about the precise underlying mechanism. Furthermore, instances in which thermalization is hindered for many-body systems have been uncovered, now known as many-body localization, offering promising insights into the mechanisms that underlie thermalization. In this work, we derive upper and lower bounds on the size of a heat bath required to thermalize a many-body localized system, for a broad class of collision models. To obtain these bounds, we employ a recently developed tool from quantum information theory known as the convex split lemma. We apply our results to the disordered Heisenberg chain, which we study numerically, and we characterize the robustness of the MBL phase in this system for the family of thermalization processes considered, in terms of the required bath size. Part of the significance of this work, published in Communications Physics (Nature) , stems from transferring tools from resource-theoretic quantum thermodynamics to the study of interacting quantum many-body systems.

Jan 04, 2021

### Work on quantum advantages in PRL

Demonstrating a quantum computational speedup is a crucial milestone for near-term quantum technology. Recently, quantum simulation architectures have been proposed that have the potential to show such a quantum advantage, based on commonly made assumptions. The key challenge in the theoretical analysis of this scheme - as of other comparable schemes such as boson sampling - is to lessen the assumptions and close the theoretical loopholes, replacing them by rigorous arguments. In this work, we prove two open conjectures for these architectures for Hamiltonian quantum simulators: Anticoncentration of the generated probability distributions and average-case hardness of exactly evaluating those probabilities. The latter is proven building upon recently developed techniques for random circuit sampling. For the former, we develop new techniques that exploit the insight that approximate 2-designs for the unitary group admit anticoncentration. We prove that the 2D translation-invariant, constant depth architectures of quantum simulation form approximate 2-designs in a specific sense, thus obtaining a significantly stronger result. Our work, freshly published in the Physical Review Letters , provides the strongest evidence to date that Hamiltonian quantum simulation architectures are classically intractable.

Dec 10, 2020

### Work on quantum simulators in PNAS

Quantum simulators promise to offer new insights into strongly correlated matter beyond what is accessible by means of classical computers. We propose dynamical quantum simulators (DQSs) as a method to simulate dynamical structure factors (DSFs) for system sizes considerably larger than what classical simulations can compute and provide complexity-theoretic evidence that they cannot be classically efficiently computed. Based on state-of-the-art experimental setups, we show how results from DQSs can be directly compared to experiments exploring properties of quantum materials. At the same time, we explore long-ranged spin systems: In particular, we show that the DSFs in DQSs can exhibit the signatures of excitation confinement in long-ranged models for which a comprehensive understanding is lacking. This work has been published in the Proceedings of the National Academy of Sciences (PNAS) . A press release can be found here .

Oct 02, 2020

### Complexity of the sign problem in Science Advances

New work on the complexity of the sign problem in Quantum Monte Carlo (QMC) has been published in the Science Advances . QMC methods are the gold standard for studying equilibrium properties of quantum many-body systems - their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods are faced with a sign problem, causing the severe limitation of an exponential increase in the sampling complexity and hence the run-time of the QMC algorithm. In this work, we develop a systematic, generally applicable, and practically feasible methodology for easing the sign problem by efficiently computable basis changes and use it to rigorously assess the sign problem. Our framework introduces measures of non-stoquasticity that - as we demonstrate analytically and numerically - at the same time provide a practically relevant and efficiently computable figure of merit for the severity of the sign problem. We show that those measures can practically be brought to a good use to ease the sign problem. To do so, we use geometric algorithms for optimization over the orthogonal group and ease the sign problem of frustrated Heisenberg ladders. Complementing this pragmatic mindset, we prove that easing the sign problem in terms of those measures is in general an NP-complete task for nearest-neighbour Hamiltonians and simple basis choices by a polynomial reduction to the MAXCUT-problem. Intriguingly, easing remains hard even in cases in which we can efficiently assert that no exact solution exists. A press release can be found here.

Aug 02, 2020

### Work on multi-partite entanglement transformations in PRL

The theory of the asymptotic manipulation of pure bipartite quantum systems can be considered completely understood: The rates at which bipartite entangled states can be asymptotically transformed into each other are fully determined by a single number each, the respective entanglement entropy. In the multi-partite setting, similar questions of the optimally achievable rates of transforming one pure state into another are notoriously open. This seems particularly unfortunate in the light of the revived interest in such questions due to the perspective of experimentally realizing multi-partite quantum networks.In fact, the question of what rates are achievable in multi-partite entanglement transformations emerged in the early 2000 years as one of the key questions in quantum information theory. It has not found a comprehensive answer to date. In this work, we report substantial progress on this long-standing question by deriving surprisingly simple upper and lower bounds on the rates that can be achieved in asymptotic multi-partite entanglement transformations. These bounds are based on ideas of entanglement combing and state merging. We identify cases where the bounds coincide and hence provide the exact rates. As an example, we bound rates at which resource states for the cryptographic scheme of quantum secret sharing can be distilled from arbitrary pure tripartite quantum states, providing further scope for quantum internet applications beyond point-to-point.This work has been published in the Physical Review Letters .

Jul 26, 2020

### Review on certification and benchmarking in Nature Reviews Physics

With the rapid development of quantum technologies a pressing need has emerged for a wide array of tools for the certification and characterization of quantum devices. Such tools are critical since the powerful applications of quantum information science will only be realised if stringent levels of precision of components can be reached and their functioning guaranteed. This review in press in Nature Physics Reviews provides a brief overview of the known characterization methods for certification, benchmarking, and tomographic reconstruction of quantum states and processes, and outlines their applications in quantum computing, simulation, and communication. A press release can be found here .

Jun 01, 2020

### Work on non-equilibrium topological systems in PRL

New work that brings together ideas of topological order, many-body localization and Floquet-type non-equilibrium quantum dynamics goes is published in the Physical Review Letters . Specifically, we show how second-order Floquet engineering can be employed to realize systems in which many-body localization coexists with topological properties in a driven system. This allows one to implement and dynamically control a topologically-protected qubit even at high energies. Floquet engineering - the idea that a periodically driven non-equilibrium system can effectively emulate the physics of a different Hamiltonian - is used to simulate an ffective three-body interaction among spins in one dimension, using time-dependent two-body interactions only. In the effective system emulated topology and disorder coexist which provides an intriguing inroad into the interplay of many-body localization, defying our standard understanding of thermodynamics, and topological phases of matter, which are of fundamental and technological importance. We demonstrate explicitly how combining Floquet engineering, topology and many-body localization allows one to harvest the advantages (time-dependent control, topological protection and reduction of heating, respectively) of each of these sub-fields while protecting from their disadvantages (heating, static control parameters and strong disorder).

Apr 14, 2020

### Work on quantum readout in Communications Physics - Nature

Work on quantum readout for quantum simulators goes to press in the Communications Physics - Nature , reporting joint theoretical and experimental work done at the FU Berlin and the TU Vienna . Quantum simulators allow to explore static and dynamical properties of otherwise intractable quantum many-body systems. In many instances, however, it is the read-out that limits such quantum simulations. In this work, we introduce a new paradigm of experimental read-out exploiting coherent non-interacting dynamics in order to extract otherwise inaccessible observables. Specifically, we present a novel tomographic recovery method allowing to indirectly measure second moments of relative density fluctuations in one-dimensional superfluids which until now eluded direct measurements. We achieve this by relating second moments of relative phase fluctuations which are measured at different evolution times through known dynamical equations arising from unitary non-interacting multi-mode dynamics. Applying methods from signal processing we reconstruct the full matrix of second moments, including the relative density fluctuations. We employ the method to investigate equilibrium states, the dynamics of phonon occupation numbers and even to predict recurrences. The method opens a new window for quantum simulations with one-dimensional superfluids, enabling a deeper analysis of their equilibration and thermalization dynamics.

Jan 10, 2020

### Google AI NISQ Award

Jens Eisert wins a Google AI NISQ award, as part of a most fun and fruitful collaboration with the Google AI team.

Jan 08, 2020

### Work on equilibration in entanglement ergodic systems in PRL

One of the outstanding problems in non-equilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results show that equilibration is generic provided that the initial state has overlap with sufficiently many energy levels. But results not referring to typicality which show that natural initial states actually fulfill this condition are lacking. In this work, published in the Physical Review Letters , we present stringent results for equilibration for systems in which Renyi entanglement entropies in energy eigenstates with finite energy density are extensive for at least some, not necessarily connected, sub-system. Our results reverse the logic of common arguments, in that we derive equilibration from a weak condition akin to the eigenstate thermalization hypothesis, which is usually attributed to thermalization in systems that are assumed to equilibrate in the first place. We put the findings into the context of studies of many-body localization and many-body scars. This work has received significant attention, see, e.g., the Viewpoint in Physics 12, 123 or the article in pro-physik .

Nov 20, 2019

### Henrik Wilming wins prestigious Ernst Reuter Award

Henrik Wilming wins the prestigious Ernst Reuter Award of the FU Berlin , the highest distinction within the university for a PhD thesis in all subjects. Congratulations. This prize will be awarded during the Ernst Reuter Day , Dec 3, 2019, 3:30 pm, in conjunction with festivities celebrating the foundation of the FU Berlin.

Nov 11, 2019

### New group members

Philippe Faist (CalTech and ETH Zurich), Jonathan Conrad (QuTech Delft), Marios Ioannou QuTech Delft), and Marcel Hinsche (Cambridge and FU Berlin) join the group as a postdoc, PhD students and master student. Warm welcome.

Oct 08, 2019

### New work on tensor networks and holography in Science Advances

The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand such bulk-boundary correspondences, shedding light on connections between geometry and entanglement. We introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1+1 dimensions. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk lattices, obtaining highly accurate critical data. Within our framework, we also produce translation-invariant critical states by an efficiently contractible tensor network with the geometry of the multi-scale entanglement renormalization ansatz. Furthermore, we establish a link between holographic quantum error correcting codes and tensor networks. This work , published in the Science Advances , is expected to stimulate a more comprehensive study of tensor-network models capturing bulk-boundary correspondences. A press release can be found here .

Aug 12, 2019

### The 75th group PRL is on randomized benchmarking

Any technology requires precise benchmarking of its components, and the quantum technologies are no exception. Randomized benchmarking allows for the relatively resource economical estimation of the average gate fidelity of quantum gates from the Clifford group, assuming identical noise levels for all gates, making use of suitable sequences of randomly chosen Clifford gates. In new work in the Physical Review Letters , we report significant progress on randomized benchmarking, by showing that it can be done for individual quantum gates outside the Clifford group, even for varying noise levels per quantum gate. This is possible at little overhead of quantum resources, but at the expense of a significant classical computational cost. At the heart of our analysis is a representation-theoretic framework that we develop here which is brought into contact with classical estimation techniques based on bootstrapping and matrix pencils. We demonstrate the functioning of the scheme at hand of benchmarking tensor powers of T-gates. Apart from its practical relevance, we expect this insight to be relevant as it highlights the role of assumptions made on unknown noise processes when characterizing quantum gates at high precision.

Aug 08, 2019

### Work on routing in quantum networks in npjqi

Quantum communication between distant parties is based on suitable instances of shared entanglement. For efficiency reasons, in an anticipated quantum network beyond point-to-point communication, it is preferable that many parties can communicate simultaneously over the underlying infrastructure; however, bottlenecks in the network may cause delays. Sharing of multi-partite entangled states between parties offers a solution, allowing for parallel quantum communication. Specifically for the two-pair problem, the butterfly network provides the first instance of such an advantage in a bottleneck scenario. The underlying method differs from standard repeater network approaches in that it uses a graph state instead of maximally entangled pairs to achieve long-distance simultaneous communication. We will demonstrate how graph theoretic tools, and specifically local complementation, help decrease the number of required measurements compared to usual methods applied in repeater schemes. We will examine other examples of network architectures, where deploying local complementation techniques provides an advantage. We will finally consider the problem of extracting graph states for quantum communication via local Clifford operations and Pauli measurements, and discuss that while the general problem is known to be NP-complete, interestingly, for specific classes of structured resources, polynomial time algorithms can be identified. This work has just been published in the Nature Partner Journal Quantum Information .

Aug 07, 2019

### Emilio Onorati defends his PhD with summa cum laude

Emilio Onorati, coming from ETH Zurich and now a postdoc at UCL in London, defends his PhD thesis entitled "Random processes over the unitary group: Mixing properties and applications in quantum information" with a summa cum laude distinction. Congratulations! He is the 9th PhD student from this group who has been awarded this rare and special distinction.

Jul 24, 2019

### New work on quantum advantages in PRL

Results on the hardness of approximate sampling are seen as important stepping stones towards a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include boson sampling, IQP circuit sampling, and universal random circuit sampling. A key challenge for any such demonstration is to certify the correct implementation. For all these examples, and in fact for all sufficiently flat distributions, we show in new work in press in the Physical Review Letters that any non-interactive certification from classical samples and a description of the target distribution requires exponentially many uses of the device. Our proofs rely on the same property that is a central ingredient for the approximate hardness results: namely, that the sampling distributions, as random variables depending on the random unitaries defining the problem instances, have small second moments.

May 24, 2019

### New work on the entanglement of purification in PRL

The entanglement of purification (EoP) is a measure of total correlation between two subsystems. New work, published in the Physical Review Letters , studies this quantity for free scalar field theory on a lattice and the transverse-field Ising model by numerical methods. In both of these models, we find that the EoP becomes a non-monotonic function of the distance between subsystems when the total number of lattice sites is small. When it is large, the EoP becomes monotonic and shows a plateau-like behavior. Moreover, we show that the original reflection symmetry which exchanges of subsystems can get broken in optimally purified systems. In the Ising model, we find this symmetry breaking in the ferromagnetic phase. We provide an interpretation of our results in terms of the interplay between classical and quantum correlations.

May 22, 2019