2024 Summer Semester

During the 2024 summer semester, the seminar generally tookoplace on Tuesdays at 11:30 in the seminar room on the 5th floor (Strudlhofgasse 4, room nr. 3510). For details, please take a look at the schedule and abstracts below.

Adrián Franco Rubio (Max Planck Institute for Quantum Optics, Garching)

Gaussian tensor networks, conformal field theories, and analogue quantum simulation - An overview of my recent research
Abstract: I will introduce three research projects I have been working on. The first one involves the study of the expressive power of Gaussian fermionic tensor networks, and leads to the proof that, in 1d, they cannot approximate Gaussian critical systems with polynomial bond dimension. The second project revolves around families of ansatz wavefunctions for spin chains defined by virtual conformal field theories on a torus, which can be interpreted as matrix product states of infinite bond dimension. The last project involves the study of the impact of extensive errors in analogue quantum simulation for thermodynamic limit problems, and the search for a rigorous framework to define quantum advantage in this setting.
Based on arXiv:2204.02478, arXiv:2212.04924 and ongoing research.

(date/time/location: 05.03.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Jose Garre Rubio (University of Vienna)

Emergent (2+1)D topological orders from iterative (1+1)D gauging
Abstract: Gauging involves introducing new degrees of freedom, known as gauge fields, to localize an existing global symmetry. It is known that, following this process, the gauge fields exhibit a dual global symmetry. Subsequently, one can gauge this emergent global symmetry by creating new gauge fields that once again exhibit a global symmetry. We investigate this iterative process, wherein new degrees of freedom are created and entangled with the previous ones through local symmetries. We focus on gauging spin chains with Abelian group symmetries and arranging the new spins on a 2D lattice. The local symmetries of the emergent 2D state, which are modified by the concatenation of the following gauging maps surprisingly correspond to the stabilizer terms of the $XZZX$-code generalized to any Abelian group. We encode our construction in the family of tensor network states that we dub "projected entangled pair emergent states" (PEPES). Utilizing this representation and considering the local symmetries as stabilizer Hamiltonian terms, we establish a connection between the condensable anyons at the boundary and the quantum phase of the initial symmetric state before the gauging process.

(date/time/location: 12.03.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

David Blanik (University of Vienna)

SPT and SSB Phases under Gauging
Abstract: It has been well established that gauging maps implement a duality between VecG and RepG symmetric (1+1)D systems. For abelian G, both cases correspond to global group symmetries and ground states can be classified into SPT (symmetry protected topological/trivial) phases and/or SSB (spontaneous symmetry breaking) phases. In ongoing work with Norbert Schuch and José Garre Rubio we use MPS (matrix product states) to investigate how these phases behave under gauging. I will give an introduction to our method and discuss preliminary results.

(date/time/location: 19.03.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Ilya Kull (University of Vienna)

Certified algorithms for equilibrium states of local quantum Hamiltonians
Abstract: I will talk about this recent paper [1] by Fawzi, Fawzi & Scalet. The paper describes a complete hierarchy of convex optimization problems that gives both upper and lower bounds on expectation values of local observables in thermal states of local Hamiltonians.

[1] arxiv.org/abs/2311.18706

(date/time/location: 09.04.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Lilith Zschetzsche (University of Vienna)

Simulating coupled classical oscillators using Hamiltonian simulation - proof of BQP-completeness
Abstract: I will give an introduction to the simulation of exponentially large networks of classical oscillators using Hamiltonian simulation, based on the paper [1] by Babbush et al.. When the displacements and momenta of the oscillators are encoded in a wave function, the time evolution simulating the classical dynamics of a sparse network can be efficiently computed on a quantum computer. The kinetic energy of a subset of harmonic oscillators can be obtained by measurement on the wave function. Based on that, a BQP-complete problem can be constructed.

[1] R. Babbush et al., "Exponential quantum speedup in simulating coupled classical oscillators", Phys. Rev. X (2023), https://doi.org/10.1103/PhysRevX.13.041041

(date/time/location: 23.04.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Milán Rozmán (University of Vienna)

Methods to bound the spectral gap in spin chains
Abstract: The spectral gap of a given many-body Hamiltonian provides important insights about the low-temperature physics and the phase of the quantum system. In this talk I am going to introduce and contrast two main constructions for lower bounding and proving the existence of the spectral gap: Knabe’s method [1] which relates the gap of a restricted finite system to the gap in the thermodynamic limit, and the martingale method introduced by Nachtergaele [2] that proves the existence of the spectral gap for a large class of models by exploiting certain restrictions on the ground space.

[1] Knabe, S. Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets. J Stat Phys 52, 627–638 (1988).
doi.org/10.1007/BF01019721
[2] Nachtergaele, B. The spectral gap for some spin chains with discrete symmetry breaking. Commun.Math. Phys. 175, 565–606 (1996).
doi.org/10.1007/BF02099509

(date/time/location: 30.04.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Paul Brehmer (University of Vienna)

PEPS optimization based on automatic differentiation
Abstract: Recent years have seen methodological advances in the optimization of tensor networks based on techniques from differentiable programming [1]. I will explore these concepts as applied to two-dimensional PEPSs in two parts: First, I will give a pedagogical overview of automatic differentiation (AD) to differentiate computer programs, and of the corner transfer matrix renormalization group (CTMRG) that is used to approximate contractions of infinite PEPSs. In the second part, I combine these two notions and discuss state-of-the-art PEPS optimization based on last year's pre-print by Anna, Norbert and Bram [2]. Finally, I will discuss the ongoing work that extends the recent developments.

[1] H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang. Differentiable programming tensor networks. Phys. Rev. X 9, 031041 (2019 
[2] A. Francuz, N. Schuch, and B. Vanhecke. Stable and efficient differentiation of tensor network algorithms. arXiv:2311.11894 (2023) 

(date/time/location: 07.05.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Kevin Tam (University of Vienna)

Topological dualities via tensor networks
Abstract: Dualities in physics allow us to map between superficially distinct theories. In this seminar, I will discuss a recent publication by Wille, Eisert and Altland [1], clarifying a concrete example in the correspondence between the partition function of the classical Ising model, the topologically ordered ground state of the toric code and a free fermion Hamiltonian of a class D topological superconductors. The translation between these paradigmatic systems is mediated through a matchgate tensor network, which I will introduce along with its Gaussian fermionic counterpart. I will then explain how this provides intuitive insights into analogous phase transitions, as well as how the physics of inhomogeneous defects is intertwined with the study of correlation functions.

[1] C. Wille, J. Eisert, and A. Altland. Topological dualities via tensor networks. Physical Review Research 6, 013302 (2024)

(date/time/location: 14.05.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Yoshiko Ogata (University of Tokyo)

Boundary states of a bulk gapped ground state in 2-D quantum spin systems
Abstract: We introduce a natural mathematical definition of boundary states of a bulk gapped ground state in the operator algebraic framework of 2-D quantum spin systems. With the approximate Haag duality at the boundary, we derive a C*-tensor category M out of such boundary state. Under a non-triviality condition of the braiding in the bulk, we show that the Drinfeld center (with an asymptotic constraint) of M is equivalent to the bulk braided C*-tensor category.

(date/time/location: 22.05.2024, 11:30; Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture room (room 3500))

Andras Molnar (University of Vienna)

State-sum constructions for topological quantum field theories
Abstract: A D+1-dimensional topological quantum field theory -- according to the definition of Atiyah -- assigns a vector space to every D-dimensional manifold, and to every cobordism between two such manifolds a linear map between the corresponding vector spaces. These vector spaces and linear maps are required to be topological invariants. One way to create examples is the state-sum construction. I will review the connection between this construction and tensor networks.

(date/time/location: 28.05.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Bram Vanhecke (University of Vienna)

Active inference with Matrix Product States
Abstract: I discuss the role that MPS can play in machine learning and active inference. Specifically I will focus on recent progress made on utilising infinite MPS, the necessary adjustments for this and how the active inference planning looks in tensor network language.

(date/time/location: 04.06.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Christian Reinmoser (University of Vienna)

Reduced density matrix theory for lattice systems
Abstract: Reduced density matrices can be used to obtain estimates for ground state properties of quantum systems such as the energy. In the recently published paper by Ilya, Norbert and coworkers [1] a method to reduce computational complexity via coarse graining has been introduced to obtain better estimates. So far this method is mainly based on the formulation of the problem in terms of reduced density matrices of subsystems. For other problems, such as non-translationally invariant systems, a different formulation using moment matrices may be better suited. In this talk I will review this alternative formulation, often referred to as reduced density matrix theory (RDMT), and give a short overview of our ongoing research regarding its application on lower bounding the ground state energy and the spectral gap.

[1] Kull, I., Schuch, N., Dive, B., & Navascués, M. (2024). Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group. Phys. Rev. X, 14(2), 021008.

(date/time/location: 11.06.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)

Bram Vancraeynest-De Cuiper (Ghent University)

Gauging Higher-Form Symmetries on the Lattice
Abstract: I will provide a broad introduction to the topic of (invertible) higher-form symmetries on the lattice, with a particular focus on those that originate from gauging global 0-form symmetries. I will also discuss the process of gauging higher-form symmetries, using the (2+1)d Ising model as illustrative example. If time permits, I will briefly touch upon non-invertible higher-form symmetries and connect these concepts to projects with José Garre Rubio.

(date/time/location: 18.06.2024, 11:30, Strudlhofgasse 4, 5th floor, seminar room/Kleiner Seminarraum, room no. 3510)