SEMINARS

Our group seminar features talks on current research topics from the field of Quantum Information and Quantum Many-Body Physics, and in particular Tensor Networks, given both by group members and by external guest speakers.

If you are interested in receiving seminar announcements, please send an informal e-mail to schuch-office.quantum[at]univie.ac.at to be added to our mailing list.

For info on past seminars click here.

2024 Winter Semester

During the 2024 winter semester, the seminar generally takes place on Mondays at 11:30 in the Erwin Schrödinger lecture room (Boltzmanngasse 5, 5th floor). Occasionally, there might be additional seminars out of schedule, or seminars given online, as announced here.

Ilya Kull (University of Vienna)

Methods for certifying the presence of a spectral gap in frustration-free spin systems
Abstract: I will first give a pedagogical overview of the existing methods to certify spectral gaps of frustration-free spin systems (Knabe and co., Martingale), and will then proceed to present our recently developed method.

(date/time/location: 14.10.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Adrian Franco Rubio (University of Vienna)

Defects and gauging for matrix product states with matrix product unitary symmetries
Abstract: Gauging, or the promotion of a global symmetry to a local symmetry, plays a fundamental role in many areas of physics, from high energy theory to topological phases of matter. Tensor network states, and in particular 1d matrix product states, provide a nice framework where the gauging of global symmetries has been developed for unitary onsite symmetries and certain matrix product operator groups. In this talk, we review this formalism and present a potential extension to states with matrix product unitary group symmetries, based on a defect construction that mimics the onsite formalism and can be of interest on its own.

(date/time/location: 21.10.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Shuhei Oyama (University of Vienna)

1+1d SPT phases with fusion category symmetry: interface modes and non-abelian Thouless pump
Abstract: Fusion category symmetry is the most general finite symmetry in 1+1 dimensional systems. We investigated gapped phases defined on a lattice with fusion category symmetry using the technique of matrix product states, focusing on the following aspects:
1. SPT invariants
2. Bulk-boundary correspondence/Thouless pump
3. Classification of a parametrized family of general gapped phases
In my talk, I will first review the basics of topological phases, and then I would like to mainly explain topic 1.
This talk is based on a joint work arXiv:2408.15960 with Kansei Inamura.

(date/time/location: 28.10.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Refik Mansuroglu (University of Vienna)

Preparation of matrix-product states with quantum circuits
Abstract: I discuss several ways of preparing matrix-product states (MPS) on a quantum computer with local gates. MPS provide an efficient classical representation of ground states of gapped local Hamiltonians and are of versatile use in studying quantum many-body physics. As a resource for quantum computation, they define a class of promising initial states, in particular for the simulation of non-equilibrium dynamics. I compare natural circuit implementations that are apparent from the MPS structure with more elaborate techniques enabling state preparation with circuits of logarithmic and in some cases even constant depth. I close with an outlook to hardware-oriented state preparation methods that strive to find optimal circuits tailored to a given MPS and the available gate set.

(date/time/location: 04.11.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

David Blanik (University of Vienna)

Dualities from Gauging
Abstract: Dualities are a powerful tool in statistical mechanics and quantum phase transitions, often simplifying complex models by relating them to more tractable ones, thus revealing deep insights into low-energy dynamics, phase transitions, and critical behavior. A prominent example is the Kennedy-Tasaki (KT) transformation, which connects the Z2xZ2 symmetry-protected topological (SPT) phase in spin-1 chains to its symmetry-broken (SSB) counterpart. Recent research has explored generalized approaches to such transformations using the concept of gauging and in this talk I will discuss how our recent classification of SPT and SSB phase behaviors under gauging facilitates the construction of novel dualities across diverse phases and symmetry groups. These new dualities offer a systematic framework to understand and classify phases, enriching our understanding of quantum phase transitions and critical phenomena.

(date/time/location: 11.11.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Paul Brehmer (University of Vienna)

Topology Protects Chiral Edge Currents in Stochastic Systems
Abstract: I present a recent publication by Tang et al. [1] which finds interesting connections between topology, non-Hermitian physics and stochastic systems. Based on two-dimensional stochastic networks, both numerical and analytical approaches are used to show the emergence of chiral edge currents in the configuration space as well as non-Hermitian features driven by out-of-equilibrium cycles at the microscopic scale. As an application, we focus on a biochemical oscillator where a global clock arises from macroscopic time scales of the underlying edge currents.

[1] E. Tang, J. Agudo-Canalejo, and R. Golestanian, Phys. Rev. X 11, 031015 (2021).

(date/time/location: 18.11.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Andreas Klingler (University of Vienna)

(Un)decidability of Positivity in Tensor Networks
Abstract: Determining whether a Matrix Product Operator (MPO) gives rise to a positive semidefinite matrix is a computationally challenging problem, known to be undecidable for general system sizes. In this talk, we explore the problem under two specific restrictions: (1) MPOs with physical dimension 1, and (2) MPOs where the local tensors are derived from unitary matrices. For physical dimension 1, we establish a correspondence between the positivity problem and Skolem’s problem, an open question in the field of linear recurrence sequences. Using this connection, we demonstrate the undecidability of a generalized version of Skolem’s Problem. In contrast, when the local tensors correspond to unitary matrices, we show that the positivity problem becomes decidable.

This talk is based on the following preprint: arXiv:2404.15053

(date/time/location: 25.11.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Lilith Zschetzsche (University of Vienna)

Equivalence of Quantum Walk Hamiltonian Simulation and Simulating Coupled Classical Oscillators
Abstract: Informally speaking, the complexity class BQP (bounded-error quantum polynomial time) contains all problems that can be solved efficiently and with high probability on a quantum computer. The hardest problems amongst those are called BQP-complete, and as such, they encompass the power of quantum computing. In general, a complete problem is a member of a complexity class that all other members can be reduced to, i.e., they can be efficiently rephrased as an instance of the complete problem. Recently, two problems have been shown to be BQP-complete, one based on the time evolution under a quantum walk Hamiltonian on a sparse graph [1, 2], the other based on the simulation of sparsely coupled classical oscillators [3]. The proof of BQP-completeness is via reduction of a known BQP-complete problem. I want to show that both problems can also be reduced directly to one another, in the hope of highlighting parallels between the two problems.

[1] A. M. Childs et al., "Exponential algorithmic speedup by quantum walk" (2002),
arxiv.org/abs/quant-ph/0209131
[2] A. M. Childs, "Universal computation by quantum walk", Phys. Rev. Lett. 102, 180501 (2009),
arxiv.org/abs/0806.1972
[3] R. Babbush et al., "Exponential quantum speedup in simulating coupled classical oscillators", Phys. Rev. X (2023),
journals.aps.org/prx/abstract/10.1103/PhysRevX.13.041041

(date/time/location: 02.12.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Milán Rozmán (University of Vienna)

Transfer Matrices and their applicability
Abstract: Transfer matrices have a wide range of applicability in quantum physics, reaching from the characterization of (quantum) Markov processes and the motivation for the Finitely Correlated State construction to the calculation of physically relevant quantities, such as normalization and two-point correlation functions for systems exhibiting a matrix product state as a ground state. In this talk I will introduce these important aspects and explain a strategy for lower bounding spectral gaps in translation invariant systems which utilizes the properties of transfer matrices.

(date/time/location: 09.12.2024., 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Christian Schilling (Arnold Sommerfeld Centre for Theoretical Physics, LMU Munich)

Quantum Information Perspective on the Ground State Problem: What is Electron Correlation?
Abstract: Describing strongly interacting electrons is one of the crucial challenges of modern quantum physics. A comprehensive solution to this electron correlation problem would simultaneously exploit both the pairwise interaction and its spatial decay. By taking a quantum information perspective, we explain how this structure of realistic Hamiltonians gives rise to two conceptually different notions of correlation and entanglement. The first one describes correlations between orbitals while the second one refers more to the particle picture. We illustrate those two concepts of orbital and particle correlation and present measures thereof. Our results for different molecular systems reveal that the total correlation between molecular orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Finally, we also speculate on a promising relation between orbital and particle correlation and explain why this may replace the obscure but widely used concept of static and dynamic correlation.

(date/time/location: 16.12.2024, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Christian Reinmoser (University of Vienna)

Odd Behavior of Semidefinite Programming Methods for Bosonic Ground State Computations
Abstract: Semidefinite Programming (SDP) methods have been successfully employed to bound the ground state energy of fermionic systems as well as spin systems. For bosonic systems it can be shown that the SDP hierarchy collapses after the first relaxations instead of converging to the optimal solution. In numerical simulation this convergence can be observed nevertheless. In Navascués et al. [1] this paradox is analyzed and attributed to rounding errors as part of the numerical simulation. In the talk I will discuss this odd behavior of SDP hierarchies when simulating bosonic systems.

[1] Navascués, M., García-Sáez, A., Acín, A., Pironio, S., & Plenio, M. B. (2013). A paradox in bosonic energy computations via semidefinite programming relaxations. New J. Phys., 15(2), 023026. doi: 10.1088/1367-2630/15/2/023026

(date/time/location: 13.01.2025. 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Martin Kerschbaumer (University of Vienna)

Proposal for a Noise-Robust Nonlocal Experiment in the Triangle Network
Abstract: Bell nonlocality in quantum networks, particularly the triangle network, faces challenges in demonstrating robust correlations under realistic experimental noise, such as photon loss and source imperfections. Current nonlocality proofs, often reliant on token-counting principles, have limited applicability. We propose a nearly loophole-free experiment using passive optical elements, addressing photon loss and source imperfections, in order to avoid global post-processing. This approach theoretically proves nonlocality under more realistic conditions, extending beyond token counting. By providing a noise-robust framework for testing nonlocality, our work paves the way for more reliable quantum network implementations.

(date/time/location: 20.01.2025, 11:15; Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Georg Hübner (University of Vienna)

Exact time evolution of MPS under local hamiltonians
Abstract: Matrix product states express states with the help of local building blocks (tensors). One of the reasons why they are so successful is that this local structure reflects the locality present in physical systems. Specifically, if a matrix product state is the solution of the Schrödinger equation with a local Hamiltonian, then one can re-express this equation with the help of the local building blocks of the MPS. Numerically, some surprising examples of such MPS paths can be found. In the talk I will give an introduction to the topic and discuss properties of MPS paths with exact time evolution.

(date/time/location: 20.01.2025, 11:15; Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Kevin Tam (University of Vienna)

Jordan-Wigner Transformation as Fermionic Tensor Network
Abstract: Fermionic tensor networks provide a natural extension of their highly successful bosonic counterparts, efficiently describing fermionic many-body systems with local interactions [1]. In this seminar, I outline one possible formulation in terms of Z2-graded vector spaces [2], which accounts for the anticommutation relations of the fermionic degrees of freedom without the need for swap gates at line crossings [3]. I also review the celebrated Jordan-Wigner transformation as a duality mapping between spin and fermionic operators. In particular, I focus on its construction as a matrix product productor and the interplay between charge sectors and boundary conditions. Time allowing, I will turn to the generalization to two dimensions, traditionally thought to be plagued by issues of non-locality [4].

[1] Kraus, Christina V., et al. "Fermionic projected entangled pair states." Physical Review A 81.5 (2010): 052338.
https://doi.org/10.48550/arXiv.0904.4667
[2] Mortier, Quinten, et al. "Fermionic tensor network methods." SciPost Physics 18.1 (2025): 012. 
https://doi.org/10.48550/arXiv.2404.14611
[3] Corboz, Philippe, et al. "Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states." Physical Review B 81.16 (2010): 165104.
https://doi.org/10.48550/arXiv.0912.0646
[4] O’Brien, Oliver, et al. “Local Jordan-Wigner transformations on the torus.” arXiv preprint.
https://doi.org/10.48550/arXiv.2404.07727

(date/time/location: 27.01.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, ground floor, Kurt Gödel lecture room)

Adam Artymowicz (Caltech)

Hamiltonian learning via energy-entropy inequalities
Abstract: In this talk I will describe a new algorithm for determining a local Hamiltonian from local expectations of its Gibbs state. The algorithm works by imposing a set of correlation inequalities that arise from local thermodynamic stability. I will argue that it is well-suited for use in quantum many-body theory by determining entanglement Hamiltonians, which are useful diagnostics of entanglement in quantum many-body states. A prominent example is 2+1d topological order, where it is believed that entanglement Hamiltonians can be used to measure the chiral central charge of the boundary CFT.

(date/time/location: 28.01.2025, 14:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Albert Gasull Celades (Max Planck Institute of Quantum Optics)

Field tensor network states
Abstract: Tensor networks (TNS) can provide exact representative ground-states for a wide variety of systems that possess an entanglement area law. However, states which demand an entanglement structure beyond that, such as critical states in one-dimensional systems, lack an exact analytical description in terms of matrix product states (MPS). Furthermore, there are states in two-dimensional systems that can also not be exactly expressed as projected entangled pair states (PEPS), such as chiral gapped states like the Laughlin state. In order to provide exact descriptions for these states, we construct a field theory generalization of tensor network states known as field tensor network states (fTNS). These are by construction infinite dimensional tensor networks whose virtual space is described by a conformal field theory (CFT).
To better understand this ansatz, we first aim to understand which theorems of standard TNS theory translate to fTNS. We prove an analogous relation about symmetry protected topological (SPT) order classification for the case of fMPS, by studying the interplay between symmetry representations of the physical and virtual space for a critical spin system. We use this result to distinguish the two ground states of the critical Majumdar-Ghosh point according to their critical SPT classification. In two dimensions, we use fPEPS to provide an exact and analytically contractible tensor network representation of a chiral gapped state, the Laughlin state on a plane and a recipe for the Kalmeyer-Laughlin state on a torus.

(date/time/location: 05.02.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)