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Complexity of the sign problem in Science Advances

New work on the complexity of the sign problem in Quantum Monte Carlo (QMC) goes to press 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.

Jun 02, 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

New work on a single-shot interpretation of the von-Neumann entropy in PRL

The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent i.i.d. copies of the state are available, in a regime that is often referred to as being asymptotic. In this work, we provide a new operational characterization of the von Neumann entropy which neither requires an i.i.d. limit nor any explicit randomness. We do so by showing that the von Neumann entropy fully characterizes single-shot state transitions in unitary quantum mechanics, as long as one has access to a catalyst - an ancillary system that can be re-used after the transition - and an environment which has the effect of dephasing in a preferred basis. Building upon these insights, we formulate and provide evidence for the catalytic entropy conjecture, which states that the above result holds true even in the absence of decoherence. If true, this would prove an intimate connection between single-shot state transitions in unitary quantum mechanics and the von Neumann entropy. Our results add significant support to recent insights that, contrary to common wisdom, the standard von Neumann entropy also characterizes single-shot situations and opens up the possibility for operational single-shot interpretations of other standard entropic quantities. In new work in press in the Physical Review Letters we discuss implications of these insights to readings of the third law of quantum thermodynamics and hint at potentially profound implications to holography.

May 20, 2019

New work on holographic area laws in PRL

The area law conjecture states that the entanglement entropy of a region of space in the ground state of a gapped, local Hamiltonian only grows like the surface area of the region. In new work going to press in the Physical Review Letters show that, for any quantum state that fulfills an area law, the reduced quantum state of a region of space can be unitarily compressed into a thickened surface of the region. If the interior of the region is lost after this compression, the full quantum state can be recovered to high precision by a quantum channel only acting on the thickened surface. The thickness of the boundary scales inversely proportional to the error for arbitrary spin systems and logarithmically with the error for quasi-free bosonic systems. Our results can be interpreted as a single-shot operational interpretation of the area law. The result for spin systems follows from a simple inequality showing that probability distributions with low entropy can be approximated by distributions with small support, which we believe to be of independent interest. We also discuss an emergent approximate correspondence between bulk and boundary operators and the relation of our results to tensor network states.

May 16, 2019

New work on topological quantum simulators

New work that shows how to quantum simulate topological Levin-Wen models has been published , work that brings together ideas of tensor networks with ones of mesoscopic physics and quantum simulations. The realization of topological quantum phases of matter remains a key challenge to condensed matter physics and quantum information science. In this work, we demonstrate that progress in this direction can be made by combining concepts of tensor network theory with Majorana device technology. Considering the topological double semion string-net phase as an example, we exploit the fact that the representation of topological phases by tensor networks can be significantly simpler than their description by lattice Hamiltonians. The building blocks defining the tensor network are tailored to realization via simple units of capacitively coupled Majorana bound states. In the case under consideration, this defines a remarkably simple blueprint of a synthetic double semion string-net, and one may be optimistic that the required device technology will be available soon. Our results indicate that the implementation of tensor network structures via mesoscopic quantum devices may define a powerful novel avenue to the realization of synthetic topological quantum matter in general.

Mar 13, 2019

New work on tensor networks in PRL

New work that shows how one can simulate strongly correlated two-dimensional systems in thermal states has been published in the Physical Review Letters . Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark we study the finite-temperature phase transition of the Ising model on an infinite square lattice, for which we obtain remarkable agreement with the exact solution. We then turn to study the finite-temperature Bose-Hubbard model in the limits of two (hard-core) and three bosonic modes per site. Our technique can be used to support the experimental study of actual effectively two-dimensional materials in the laboratory, as well as to benchmark optical lattice quantum simulators with ultra-cold atoms.

Feb 25, 2019

Quantum simulation in the Flagship

A brief article on the web page of the Flagship on Quantum Technologies written by Jens Eisert summarizes what quantum simulation is all about, and what perspectives the field has.

Jan 10, 2019

Work on topological quantum error correction in Quantum

Work on topological quantum error correction is published in Quantum , the open journal for quantum science. The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls.

Oct 26, 2018