The main seminar of the theory division usually takes place on Wednesdays at 11:30am in the Herbert-Walther Lecture Hall G0.25 next to the foyer. Attendance of all group members present at MPQ is expected. Talks should be about 45 minutes in length plus up to 15 minutes of question time; 60 minutes total should not be exceeded. A projector or a blackboard and a small flip chart are available in the lecture hall.

Point of contact: Claudius Hubig

13.11.2019

*Current Topics in our Field*

Ignacio Cirac (MPQ Theory Department)

21.11.2019 – *special theory group seminar at 11:30*

*TBA*

Laurens Vanderstraeten (U Gent)

TBA

11.12.2019

*TBA*

Michal Heller (Albert Einstein Institute, Potsdam)

TBA

08.11.2019 – *special theory seminar at 11:30*

*Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing*

Davide Orsucci

In this talk, I will present the results of the paper [Subasi, Somma, Orsucci, PRL 122(6), 060504 (2019)]. Here, a new quantum algorithms is developed that allows to prepare a quantum state |x⟩ that is proportional to the solution of the linear system of equations Ax=b. The algorithm is based on evolution randomization, a simple variant of adiabatic quantum computing. The time complexity is almost linear ϰ and linear in 1/ε, where ϰ is the condition number of A and ε is the precision. The algorithms is simple: it is not obtained using equivalences between the gate model and adiabatic quantum computing, does not use phase estimation, and does not use variable-time amplitude amplification. Further recent experimental results and theoretical developments are also presented and discussed.

06.11.2019 – *in our group seminar room B2.46*

*Variational Time Evolution: A Clock-based approach*

Stavros Efthymiou (MPQ Theory Department)

I will present a variational approach for unitary time evolution of many-body systems, in which time is treated as an additional quantum degree of freedom and the problem can be viewed as a ground state optimization in a larger Hilbert space. I will start with a brief introduction of methods that motivated this idea, particularly the time-dependent Variational Principle (TDVP) and time-dependent Variational Monte Carlo (t-VMC), and I will show how time evolution can be expressed as a minimization problem. This minimization will turn out to be related to the ground state of the "Clock Hamiltonian", a construction first introduced by Feynman. I will then describe our attempts to implement the method numerically and show some preliminary results on simple (and small!) systems.

30.10.2019 – *in the intermediate lecture hall B0.32*

*Criteria for approximation of mixed states by MPDO*

Jiri Guth Jarkovsky (MPQ Theory Department)

It was shown by F. Verstraete and I. Cirac in 2006 that there is the following sufficient condition for a pure 1D state to be efficiently approximable by an MPS: The α-Renyi entropy (for some α<1) of a reduced subsystem scales at most logarithmically with the subsystem's size. In this talk I will briefly summarize this result and describe our attempts at generalizing it for 1D mixed states. That includes introducing various measures of correlation and overcoming a few mathematical obstacles that pop up along the way.

12.09.2019 –* special theory group seminar at 11:30*

*Subradiant States of a 1D Qubit Chain*

Yuxiang Zhang (U Aarhus)

Subradiance is the phenomenon that the spontaneous emission from an atomic ensemble is inhibited cooperatively. Excitations in subradiant states have lifetime longer than an individual atom coupled to the same light fields. For a finite chain of two-level atoms coupled to a 1D waveguide, and being based on a non-Hermitian Hamiltonian formalism, we analytically revealed the wave functions of the one-excitation subradiant states and their lifetimes. For atom chains with multiple excitations, we identified two families of subradiant states. One has fermionic behaviours that can be explained through Lieb-Liniger model at the Tonks-Girardeau limit. The other is the bound state of two atomic excitations, where one excited atom effectively constitutes a defect (a site blocking further excitation) and establishes a localised mode for the other excitation. The results can be extended to atom chains coupled to 3D free space.

11.09.2019

*Witnessing quantum gravity in a lab*

Anupam Mazumdar (Gröningen)

Is gravity classical or quantum? I will be discussing a protocol to precisely test the quantum aspect of gravity in a lab. The proposal utilises the overarching physical property that local operations (supported by classical communication) cannot create entanglement between non-interacting systems. In the proposed experimental setting, two masses, each endowed with a spin-like degree of freedom, are made to gravitationally interact as they traverse adjacent interferometers. By ensuring that gravity is the sole agent acting between the masses, the observation of entanglement between the probes, would certify the quantum nature of gravity.Quite remarkably, the proposed scheme would provide a signature of quantumness of gravity that is within the grasp of state-of-the-art experiments, despite the purported weakness of the gravitational coupling. The manuscript shows that the challenges of avoiding non-Gravitational interactions (namely electromagnetic interactions of various forms) can be met, so that the quantum nature of gravity can be concluded without ambiguity, and through the sole, experimentally friendly test of entanglement between two spins.

04.09.2019

*Quantum chaos in the Brownian SYK model with large finite N: OTOCs and tripartite information*

Christoph Sünderhauf (MPQ Theory Department)

The Brownian SYK model features all-to-all interactions of Majorana fermions with time-dependent disordered couplings. Quantum chaos and scrambling can be diagnosed with out-of-time ordered correlators (OTOCs) and the tripartite information. After introducing these concepts, I will focus on their computation in the Brownian SYK model. Exploiting permutational symmetry of averaged quantities leads to a description as an imaginary-time quench problem in terms of bosonic collective modes. Thus, we devise a method to calculate the diagnostics of scrambling within an effective Hilbert space growing merely linearly or quadratically with N. Since this enables us to study large systems up to a million particles numerically exactly, we can explicitly uncover a scrambling time logarithmic in N. Further, we demonstrate the decay to Haar-scrambling values at late times.

The talk is based on our recent work arXiv:1908.00775.

27.08.2019 – *special theory group seminar at 11:30*

*Simulating thermalizing spin chains with matrix product density operators*

Christopher White (Caltech)

I will describe a method for approximating density operators of 1D systems called "DMT". When combined with a standard framework for time evolution (TEBD), DMT makes possible simulation of the dynamics of large thermalizing systems to long times (with computation time linear in system size and time). As a benchmark, I will apply DMT to the dynamics of the ETH random-field Heisenberg model. Time permitting, I will also discuss its application to the prethermal regime of a spin system with a high-frequency drive, where we see not only the expected slow Floquet heating but also clear diffusive hydrodynamics.

31.07.2019

*Certified Quantum Measurement of Majorana Fermions and New Entangled Quantum Probes*

Gerardo Ortiz (Indiana University)

In the quantum information literature, self-testing refers to the action of uniquely determining a quantum state based solely on the statistics of measurement outcomes and minimal assumptions. These quantum self-testing protocols are more stringent than well-known Bell tests. While violation of a Bell inequality for a bipartite system establishes that its quantum state is entangled, it cannot certify, for instance, that its quantum state is maximally entangled. We extend self-testing techniques to certification of quantum measurements in various physical settings. In particular, and because of its importance for realizing the topological qubit, we present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana modes, a smoking gun for Majorana fermion detection. Another application is in the realm of new quantum probes of matter. I will present a fundamentally new quantum probe, an entangled neutron beam, where individual neutrons can be entangled in spin, trajectory and energy. Its tunable entanglement length from nanometers to microns and energy differences from peV to neV opens a pathway to a future era of entangled neutron scattering in matter. We developed an interferometer to prove entanglement of these distinguishable properties of the neutron beam by observing clear violations of both Clauser-Horne-Shimony-Holt and Mermin contextuality inequalities in the same experimental setup.

30.07.2019 – *special theory group seminar at 11:30 in our group seminar room B2.46*

*Scattering theory in quantum optics & Scaling up and understanding the limits of photonic inverse design*

Rahul Trivedi

Part 1: Scattering theory in quantum opticsQuantum optical systems can often be modelled as a low-dimensional quantum system (such a two-level system, Jaynes-Cummings system etc.) coupling to an electromagnetic bath. Within the Markovian approximation, calculating the propagator for this system is a computation that is equivalent to calculating the propagator corresponding to an effective non-hermitian hamiltonian. I will briefly sketch a proof of this result using the input-output formalism [1] along with its applications to understanding the dynamics of some paradigmatic systems [1, 2]. I will then go onto discuss the application of this technique in understanding photon transport through the multi-emitter cavity QED system [3]. In particular, I will focus on photon blockade induced by this system, and its dependence on the number of emitters interacting with the cavity mode.

Part 2: Scaling up and understanding the limits of photonic inverse designPhotonic inverse design has been immensely successful in producing compact, highly efficient and robust devices for applications in silicon photonics, metasurface optics, quantum optics etc. A typical photonic inverse design run requires a few hundred to thousands of electromagnetic simulations – performing these simulations is the limiting factor in scaling photonic inverse design to larger devices. In this part of my talk, I will present two approaches to accelerate electromagnetic simulations – (a) data-driven approach to augment iterative solutions of frequency-domain Maxwell’s equations [4], and (b) GPU accelerated implementation of the transfer-matrix algorithm for simulating a collection of electromagnetic scatterers. Finally, I will present some attempts at characterizing the fundamental performance limits on photonic devices by calculating the Lagrangian dual of the electromagnetic design problem.

- Rahul Trivedi, Kevin Fischer, Shanshan Xu, Shanhui Fan, and Jelena Vuckovic. "Few-photon scattering and emission from low-dimensional quantum systems." Physical Review B98, no. 14 (2018): 144112.
- Rahul Trivedi, Kevin Fischer, Sattwik Deb Mishra, and Jelena Vuckovic. "Point-coupling Hamiltonian for broadband linear optical devices." arXiv preprint arXiv:1907.02259 (2019).
- Rahul Trivedi, Marina Radulaski, Kevin A. Fischer, Shanhui Fan, and Jelena Vučković. "Photon Blockade in Weakly Driven Cavity Quantum Electrodynamics Systems with Many Emitters." Physical Review Letters 122, no. 24 (2019): 243602.
- Rahul Trivedi, Logan Su, Jesse Lu, Martin F. Schubert, and Jelena Vuckovic. "Data-driven acceleration of Photonic Simulations." arXiv preprint arXiv:1902.00090 (2019).

17.07.2019

*Partial bosonization of the extended Hubbard model.*

Evgeny Stepanov

Mean-field theory is a simple and transparent method that is suitable for a description of collective fermionic excitations in a broad range of physical problems. The underlying idea of the method is based on the partial bosonization of collective fermionic fluctuations in leading (charge, spin, and etc.) channels of instability. This allows to solve the initial problem diagrammatically in terms of original fermionic and effective bosonic propagators in the GW fashion.

Theoretical description of electronic effects in the regime of strong electron-electron interaction requires more advanced approaches than the mean-field solution of the problem. One of them is the (extended) dynamical mean-field theory (EDMFT), which is found to be a good approximation for single-particle quantities, especially when properties of the system are dominated by local correlations. Description of collective electronic fluctuations in correlated materials requires more efforts, since they are essentially nonlocal. Their accurate description is possible only within a certain extension of (E)DMFT.

In the case when accurate quantum mechanical calculations are challenging, the initial quantum problem can be replaced by an appropriate classical one. Indeed, some collective phenomena, such as magnetism, can be sufficiently described by simple Heisenberg-like models that are formulated in terms of bosonic variables. This fact suggests that other many-body excitations can also be described by simple bosonic models in the spirit of Heisenberg theory. Following the mean-field idea, a partially bosonized description of collective electronic effects in strongly interacting systems can also be performed on the basis of the dynamical mean-field theory. This allows to account for nonlocal fluctuations in a simplified GW way, and resulted in the development of GW+(E)DMFT, TRILEX, and Dual Boson methods.

Although the GW extension of the dynamical mean-field theory is an efficient and inexpensive numerical approach, it has a significant drawback, which is common for every partially bosonized theory. This severe problem is known as the Fierz ambiguity in decomposition of the local Coulomb interaction into different bosonic channels, which drastically affects the result of the method. Surprisingly, this issue is yet unsolved even for a simple mean-field theory, let alone the GW+DMFT method that became a standard approach for calculation of physical properties of realistic multiband systems and for the solution of interacting time-dependent problems.

Here, I will show how the partial bosonization of the extended Hubbard model can be performed avoiding the Fierz ambiguity. The resulting theory is formulated in terms of fermionic degrees of freedom and new bosonic fields that describe the interaction in a certain channel. I will also define a physical regime where the obtained model action reduces to an effective Ising and Heisenberg models for charge and spin variables, respectively. This method accounts for nonlocal fluctuations diagrammatically beyond the EDMFT level and allows to include the effect of magnetic fluctuations in the GW scheme. As the result, the proposed method improves already existing GW, GW+(E)DMFT, and TRILEX approaches that are used for description of wide range of physical problems. Although the method is discussed here in the context of the extended Hubbard model, it is not restricted only to this particular model and can be applied to other fermionic problems broadly defined.

16.07.2019 *– special theory group seminar at 11:30*

*What parts of a quantum state tell about the whole*

Nikolai Wyderka (Uni Siegen)

Correlations in quantum states have to obey restrictions from the underlying quantum theory, such as positivity or purity. These restrictions give rise to an abundance of interesting quantum features, like monogamy of entanglement or the existence of absolutely maximally entangled states. On the other hand, they allow to infer many properties of the whole state from knowledge of subsets of the correlations only. For example, whether or not a state is uniquely determined by its low-body correlations is directly connected to the question of whether or not it is the unique ground state of a local Hamiltonian.

In this talk I will discuss some instances of this uniqueness problem, more formally known as the marginal problem, in the case of multi-qubit systems. Furthermore, I will formulate positivity constraints for a certain type of LU-invariants, known as sector lengths, and will discuss their relation to entanglement and entropic strong subadditivity.

15.07.2019 *– special theory group seminar at 11:30*

*Tensor-network methods for topological error correction*

Andrew Darmawan

A universal quantum computer will require error correction to protect logical qubits from noise. However, practical implementation of quantum error correcting codes remains a challenge due to the large amount of physical resources (qubits, operations) required. I will discuss how some of these challenge may be met using tensor-network methods. I will focus on surface-code error correction, which, due to its simplicity, may be implementable in near-term devices. I will describe two ways in which tensor networks may be applied to surface-code error correction. One is for simulation: to understand how the surface code performs under different types of realistic noise. Another is as part of the classical control software of the error-correcting code, namely the decoder, which determines how to correct errors based on information provided by measurements. I will describe various scenarios in which tensor-network based decoders can achieve substantially improved logical error rates over other decoders.

11.07.2019 *– special theory group seminar at 11:30 in the theory group seminar room B2.46*

*Multi-Time formalism in a Quantum Field Theory Model*

Sascha Lill

In order to describe a Quantum-N -body system in the Schrödinger picture in a manifestly covariant way, one needs to introduce a separate time coordinate t k for each of the particles k∈{1, …, N}. The wave function therefore depends on N time coordinates (“Multi-Time wave function”) and the Schrödinger equation becomes a system of N Partial Differential Equations (PDEs). Multi-Time wave functions were already introduced in the 1930’s and have become a topic of active research again throughout the past years.

So far, a series of papers has been published, which investigate the existence and uniqueness of solutions to the Multi-Time Schrödinger equation systems appearing in various quantum mechanical models. However, most of the considerations in these papers were done on a non-rigorous level, for example by checking a certain consistency condition. In my master thesis, I could establish a rigorous proof of existence and uniqueness of a solution to the equations of motion for a Quantum Field Theory (QFT) toy model. This talk will concern about Multi-Time formal- ism in general, how to construct a solution to the equations of motion and how to show that this PDE system is actually solved.

19.06.2019

*Automatic Differentiation of Tensor Expressions*

Sören Laue (Uni Jena)

Automatic differentiation is a powerful tool that allows to compute derivatives not only of mathematical expressions but also of functions that are given as a computer program. While it has been used successfully in many areas it has recently gained considerable attention in the area of machine learning, especially in deep learning. In this talk, I will provide an introduction into the concept of automatic differentiation, explain the different algorithms for computing derivatives of computer programs, and provide examples. I will then focus on computing derivatives of problems involving not only scalars, but also vectors, matrices, and higher-order tensors. Finally, I will highlight the application of automatic differentiation to tensor networks.

12.06.2019

*Identifying the trap loss mechanism in ultracold diatomic gases*

Arthur Christianen (Radboud University, Nijmegen)

Ultracold dipolar gases have many applications such as quantum computation/simulation, controlled chemistry, and high precision measurements to challenge the standard model. The experimentally realized coherence time in these gases is approaching the second (for NaK) and is now limited by the trapping time of the molecules. The loss mechanism limiting this trapping time is not yet understood and the loss rate is unexpectedly high, since nonreactive molecules disappear from the trap with a rate as if they were reactive. The hypothesis in the field is that the loss is caused by "sticky collisions", i.e., that molecules stick together when they collide for times in the order of milliseconds to seconds. In this time, the collision complexes themselves may leave the trap or a third molecule may collide with the complex, resulting in the loss of both collision partners.

In our work we show that the actual sticking times of the molecules are three orders of magnitude smaller than previously estimated and that the previously suggested loss mechanisms can therefore not explain the experimental observations. We construct a realistic potential energy surface for NaK-NaK collisions and we study the dynamics of the complexes quasiclassically and statistically. We find that trapping laser excitation of the collision complexes is the most likely cause of the experimental losses. We propose that the losses may be strongly suppressed by changing the wavelength of the trapping lasers from 1064 nm to 10 micron.

Reference: arXiv:1905.06846

06.06.2019 *– in the theory group seminar room B2.46*

*Large deviations and cMPS in open quantum dynamics*

Juan Garrahan (University of Nottingham)

In this talk I will describe a perspective on the dynamics of Markovian open quantum systems based on the study of the statistical properties of ensembles of quantum trajectories. This "thermodynamics of quantum trajectories" approach is to dynamics what the standard equilibrium configuration ensemble method is for statics. Just like in the static case in the thermodynamic limit, for long-time dynamics this is based on the formalism of large deviations. I will also describe how many useful results can be derived by considering a formal connection between trajectory ensembles and continuous matrix product states (cMPS). I will go through the main ideas, and discuss applications to problems such as trajectory phase transitions, how to optimally realise rare events, prediction-retrodiction, fluctuation bounds, and catching and reversing quantum jumps.

05.06.2019

*Combining Tensor Networks and Monte Carlo for Lattice Gauge Theories*

Patrick Emonts (MPQ Theory Department)

By combining Monte Carlo sampling and Tensor Networks, specifically Gauged Gaussian Projected Entangled Pair States (GGPEPS), we show an efficient way to compute expectation values for lattice gauge theories in two and three spatial dimensions. The method can be applied to arbitrary gauge groups, in the talk, however, we will focus on the U(1) gauge group. In the first part of the talk, we will explore the difference between a path integral approach to lattice gauge theories and the Hamiltonian approach that we are using. The second part details the interplay between Monte Carlo sampling and the tensor network construction of a locally gauge invariant state. Further details can be found in arXiv:1710.11013.

22.05.2019 – *please note the poster distribution session starting at 10:45*

*Typical entropy of a subsystem: Page curve and its variance*

Eugenio Bianchi (Institute for Gravitation and the Cosmos (IGC), Pennsylvania State University)

In a quantum system in a pure state, a subsystem generally has a non-zero entropy because of entanglement with the rest of the system. Is the average entanglement entropy of pure states also the typical entropy of the subsystem? In this seminar, I address the question of typicality of the entanglement entropy in energy eigenspaces and present the Page curve for two model systems: (i) non-interacting spins in a magnetic field and (ii) black body radiation.

17.05.2019 – *Special Theory Seminar at 13:45*

*Irreducible projective representations and their physical applications*

Zheng-Xin Liu (Renmin University of China)

In the first part of the talk, we apply the eigenfunction method to obtain all irreducible projective representations (Reps) of finite groups, especially anti-unitary groups. To this end, we first solve the cocycle equations to obtain the factor system of each class of projective Rep, from which we construct the regular projective Rep. Then we use the eig-values of class operators to label the bases of each irreducible Rep. In the second part, we discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as the Dirac semimetals in Magnetically ordered systems.

15.05.2019

*Quantum reference frames and quantum general covariance*

Philipp Höhn (Institute for Quantum Optics and Quantum Information (IQOQI) Wien)

Reference frames (or, more generally, systems) provide the vantage points from which to describe the remaining physics. Treating them fundamentally as quantum systems is inevitable in quantum gravity, where coordinates are a priori unavailable, but also in quantum foundations once accepting that all frames are physical systems. Both fields thus face the question of how to describe physics from the perspective of quantum reference systems and how the descriptions relative to different such choices are related. I will summarize a recent systematic method for such switches, which works in analogy to coordinate changes on a manifold, except that these `quantum coordinate changes' proceed between different Hilbert spaces. This method employs a symmetry principle, sets the stage for a quantum version of general covariance and applies to both temporal and spatial reference systems. Strikingly, it shows that quantum correlations and superposition become quantum frame dependent.

08.05.2019

*Dynamical Quantum Phases: New routes to ergodicity breaking in interacting many-body systems*

Michael Knap

It has been the believe that generic quantum many-body systems necessarily approach thermal equilibrium after a long time evolution. As a consequence any quantum information encoded in the initial state is lost in the course of the dynamics and the late time dynamics is described by simple hydrodynamics. However, recently exceptions have been found to the rule. For example, disordered and interacting many-body systems realize the non-ergodic, many-body localized phase. In this talk, we show how constraints can significantly alter the quantum dynamics of interacting many-body system. To this end, we will first discuss the far-from-equilibrium dynamics of a two-dimensional quantum dimer model, which leads to a rich dynamical phase diagram with some almost ergodicity breaking regimes [1]. As a second example we show that the combination of charge and dipole conservation, characteristic of fractonic quantum matter, leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization [2].

- Dynamical Phase Transitions in the Quantum Dimer Model on a Square Lattice. Johannes Feldmeier, Frank Pollmann, Michael Knap [arXiv:1901.07597]
- Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians. Pablo Sala, Tibor Rakovszky, Ruben Verresen, Michael Knap, Frank Pollmann [arXiv:1904.04266]

24.04.2019 *– in the theory group seminar room B2.46*

*Variational approaches to Hamiltonian lattice gauge theory*

Julian Bender (MPQ Theory Department)

Non-perturbative phenomena play a crucial role in the study of quantum field theories, since they appear e.g. in the low-energy sector of QCD (quantum chromodynamics), e.g. in the mechanism of confinement. As perturabtive series are not valid in these regimes, non-perturbative methods have been developed. One of the most prominent methods is lattice gauge theory, since the lattice allows a non-perturbative regularization of quantum field theories. Calculations are then usually carried out in the euclidean path-integral formalism, where expectation values can be evaluated by Monte-Carlo simulations. Although this technique has been extremely successful over the past decades, certain aspects are hard to capture in this framework, like real-time evolutions or finite chemical potentials. I will review the path-integral method to motivate and introduce the Hamiltonian formalism of lattice gauge theory. Afterwards, I will give an overview over the methods which can be used to study this Hamiltonian, with a particular focus on variational techniques.

10.04.2019

*Maximizing Rényi Entropy to approximate thermal states*

Giacomo Giudice (MPQ Theory Department)

Tensor networks have been incredibly efficient at describing many-body physics at low-energy, particularly in one dimension.

A key ingredient of this success, from a numerical perspective, is the stability and accuracy of variational approximations of pure states. However, success for mixed states has been more moderate. In particular, there are currently no variational methods to approximate thermal states. Yet describing thermal states of many-body system is of interest, not only from a fundamental standpoint, but also to describe experiments. In the first part of this talk, I will introduce an alternative family of mixed states, namely those that maximize the Rényi entropy under certain constraints. Under the hypothesis of local Hamiltonians, I hope to convince you that local observables become indistinguishable from their thermal counterparts. Therefore, this class of states introduces novel perspectives for numerical methods. The second part of the talk will be dedicated to introducing algorithms to approximate such states with tensor networks.

03.04.2019

*Computational speedups using small quantum devices*

Yimin Ge (MPQ Theory Department)

While fully scalable quantum computers may be far off, small quantum computers may be achievable in the foreseeable future. It remained unclear however, how they could be utilised for speeding up relevant computations of much larger problem instances. The reason is that quantum and classical algorithms typically exploit global structures of problems, and restricting superpositions to smaller block sizes will break that structure. Thus, for structured problems where arbitrarily sized quantum computers offer large speedups, small quantum computers may be expected to be of no significant help given large inputs. In this talk, I will show that this is in general not true: given a small quantum computer with only M qubits, it is possible to significantly speed up certain important classical algorithms, even when the problem size is much larger than M. Based on the famous 3SAT algorithm of Schöning, I will present a quantum-enhanced version for solving 3SAT problems involving n>>M variables that significantly speeds up its fully classical counterpart. I will also show similar results for the cubic Hamiltonian cycle problem, and moreover hightlight general criteria for when such speedups may be possible in other algorithms. Joint work with Vedran Dunjko and Ignacio Cirac.

27.03.2019

*Tensor network state methods for systems in confined potentials*

Örs Legeza (Hungarian Academy of Sciences)

Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin and fermionic models. In this contribution, we overview tensor network states techniques that can be used for the treatment of high-dimensional optimization tasks used in many-body quantum physics with long range interactions, ab initio quantum chemistry and in nuclear structure theory. We will also discuss the controlled manipulation of the entanglement, which is in fact the key ingredient of such methods, and which provides relevant information about correlations. We will present recent developments on fermionic orbital optimization, tree-tensor network states, multipartite entanglement, externally corrected coupled cluster density matrix renormalization group (TCCSD-DMRG). Finally, new results will be shown for systems of continuously confined fermions and for Wigner crystals.

References:

- Tensor product methods and entanglement optimization for ab initio quantum chemistry, Szalay Sz , Pfeffer M , Murg V , Barcza G , Verstraete F , Schneider R , Legeza O, INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 115:(19) pp. 1342-1391. (2015)
- Fermionic orbital optimisation in tensor network states, C. Krumnow, L. Veis, O. Legeza, J. Eisert, Phys. Rev. Lett. 117, 210402 (2016)
- Role of the pair potential for the saturation of generalized Pauli constraints, Ors Legeza, Christian Schilling, Phys. Rev. A 97, 052105 (2018)
- Imaging the Wigner Crystal of Electrons in One Dimension, Ilanit Shapir, Assaf Hamo, Sharon Pecker, Catalin Pascu Moca, Ors Legeza, Gergely Zarand, Shahal Ilani, arXiv:1803.08523

13.03.2019

*TBA*

Henrik Dreyer (MPQ Theory Department)

TBA

06.03.2019

*TBA*

David Sauerwein (MPQ Theory Department)

TBA

20.02.2019 – *in the theory seminar room*

*Characterization and detection of subsystem symmetry-protected topological order. *

David Stephen (MPQ Theory Department)

Subsystem symmetry-protected topological (SSPT) order is a new kind of quantum phase of matter that is protected by subsystem symmetries. These are symmetries that lie halfway in between global and local (gauge) symmetries, and act on lower-dimensional subsystems of the entire system, e.g. lines, planes, or even fractals. SSPT phases of matter have recently garnered interest due to their close relation to fracton topological order and also to universal measurement-based quantum computation. In this talk, I will first show how SSPT phases of matter can be characterized using tensor networks and quantum cellular automata, and also how this relates to quantum computation. In the second half of the talk, I will show that SSPT phases of matter are associated with corrections to the entanglement area law, similar to the topological entanglement entropy. These corrections are generically uniform throughout a given SSPT phase, and they may therefore be used to detect SSPT order in ground-state wave functions. To test, we use this correction to probe various SSPT phase transitions numerically, with some surprising results.

13.02.2019

*Single-shot interpretations of von Neumann entropy *

Henrik Wilming (ETH Zürich)

In quanum information theory, the von Neumann entropy usually arises in i.i.d settings, while single-shot settings are commonly characterized by (smoothed) Renyi entropies. I discuss new results that give single-shot interpretations to the von Neumann entropy under appropriate conditions. First, I present results that give a single-shot interpretation to the Area Law of entanglement entropy in many-body physics in terms of compression of quantum information on the boundary of a region of space. Then I show that the von Neumann entropy governs single-shot transitions whenever one has access to arbitrary auxiliary systems, which have to remain invariant in a state-transition ("catalysts"), as well as a decohering environment. Getting rid of the decohering environment yields the "catalytic entropy conjecture", for which I present some supporting evidence. I also discuss applications to thermodynamics.

06.02.2019

*Quantum Glasses: a biased overview (with some results) *

Nicola Pancotti (MPQ Theory Department)

I will give a general biased perspective of spin glasses. After introducing classical constrained models, I will try to convince you that we can use them to model glassy behavior and, in particular, slow relaxation to equilibrium. I will then generalize this framework to quantum systems where slow dynamics has been elusive for many years. Finally I will show how numerical techniques ranging from tensor networks to exact diagonalization may be employed in order to understand dynamical properties of such systems.

30.01.2019

*Dissipative engineering of cold atomic systems *

Jolge Yago (University of Strathclyde)

Cold atom systems in optical lattices provide a promising platform for a wide variety of applications, ranging from quantum simulation to quantum metrology, due to their extremely high tunability and the ability to derive microscopic models under well-controlled approximations that give access to accurate descriptions. The proper characterization of those systems requires, in many scenarios, taking into account that they are subject to some dissipation sources, as dissipation can drastically modify the behaviour of the known phases of matter or even generate new ones. However, the description of open systems can quickly become numerically unaffordable. In this talk, we investigate several important examples of dissipative many-body dynamics combining matrix product states and matrix product operator approaches. First, we focus on the study of one-dimensional spinless fermions and hard-core bosons. We observe how dissipation induces differences in local observables that are identical in the closed system. secondly, we focus on characterizing the role of dissipation, specifically particle loss and dephasing, in the long-time behaviour of many-body localized systems. We analyze under which conditions dissipation leads to thermalization in the localized phase. The last part of the talk presents an example of the use of engineered coupling to the environment, both coherent and dissipative, to robustly create spin-symmetric fermionic states. This scheme, which combines a Raman transfer between Bloch bands and sympathetic cooling with a reservoir gas, prepares entangled states that exhibit quantum enhanced precision for metrology.

23.01.2019

*Experimental tests of quantum non-locality beyond EPR-steering and beyond Bell *

Howard Wiseman (Griffith University)

In this talk I will present unpublished theory and experiment for two quantum nonlocality scenarios which generalise EPR-steering and Bell, respectively, in the sense of having weaker assumptions and thus more stringent experimental conditions. The first is to allow a finite amount of FTL communication of classical information in an EPR-steering scenario. The second relates to the recent theorem of Bruckner using "Wigner friends" in place of the determinism assumption in some formulations of Bell's theorem.

09.01.2019

*Many-body physics with quantum impurities in cold atoms and beyond *

Richard Schmidt (MPQ Theory Department)

Understanding the role of interactions between an impurity and its environment is a paradigm problem of quantum many-body physics. A central concept for the description of such systems is the formation of quasiparticle excitations called polarons. Depending on the character of the environment and the form of interactions, different types of polarons are created. In this talk, I will review recent experimental and theoretical progress on studying the many-body physics of polarons in ultracold atomic systems [1], and discuss related polaronic phenomena encountered in two-dimensional semiconductors [2] and the study of rotating molecules in superfluid Helium [3]. I will then put particular focus on impurities interacting with bosonic quantum gases and discuss the recent progress on the theoretical description of Rydberg excitations coupled to Bose-Einstein condensates. In such systems the interaction between the Rydberg atom and the Bose gas is mediated by the Rydberg electron. This gives rise to a new polaronic dressing mechanisms, where instead of collective excitations, molecules of gigantic size dress the Rydberg impurity. We develop a functional determinant approach [4] to describe the dynamics of such Rydberg systems which incorporates atomic and many-body theory. Using this approach we predict the appearance of a superpolaronic state which has recently been observed in experiments [5,6].

References: [1] R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, Rep. Prog. Phys. 81, 024401 (2018). [2] M. Sidler et al., Nature Physics 13, 255 (2017) [3] R. Schmidt, and M. Lemeshko, Phys. Rev. Lett. 114, 203001 (2015); [4] R. Schmidt, H. Sadeghpour, and E. Demler, Phys. Rev. Lett. 116, 105302 (2016). [5] F. Camargo et al., Phys. Rev. Lett. 120, 083401 (2018). [6] R. Schmidt et al., Phys. Rev. A 97, 022707 (2018).

Earlier seminars: 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005