### 2022 Summer Semester

During the 2022 summer semester, the seminar generally took place Wednesdays at 14:15 in the Kurt Gödel lecture room (Strudlhofgasse 4, Room 3E63) in person if the situation reg. the COVID pandemic allowed this.

#### Seminar calendar for the 2022 Summer Semester

##### Alberto Ruiz De Alarcón Torregrosa (ICMAT - Instituto de Ciencias Matemáticas, Madrid)

##### Phases of Matter of 1D Mixed States

16.03.2022, 14:15,Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: One of the main projects that quantum science is undertaking is the classification of exotic topological phases of quantum matter. Here, we will take the first steps towards the classification of open quantum systems in 1D. In our framework, the definition of phase will rely on the existence of a short-depth circuit of bounded-range quantum channels mapping one mixed state into the other. We will restrict our attention to the classification of simple states, known as Renormalization Fixed Point MPDOs, show how to construct them from C*-quantum groupoids and prove that some belong to the trivial phase.

##### Ilya Kull (University of Vienna)

##### Lower bounding ground state energies of local Hamiltonians: tractable relaxations of the quantum marginal problem

23.03.2022, 14:15, online

Abstract: Applying variational methods to the problem of finding the lowest energy of a many-body system can only produce upper bounds on the true value. We propose a method that produces lower bounds on ground energies of local Hamiltonians and is thus capable of certifying variational solutions. This is achieved by formulating the problem as a semidefinite program in terms of the reduced density matrices corresponding to the local Hamiltonian terms, and systematically relaxing the condition requiring all of them to be compatible with a global quantum state. The relaxation involves an iterative coarse-graining procedure that reduces the memory scaling of the program to polynomial in the system size and the coarse-graining dimension. We demonstrate the method on 1D spin chains.

##### David Blanik (University of Vienna)

##### Topological Codes from Homology

30.03.2022, 14:15, online

Abstract: I will discuss how certain types of stabilizer codes can be defined entirely in terms of (co-)homology. The motivating example will be the toric code. If time permits I will also dicuss elements of fault-tolerant quantum computation with planar surface codes in this formalism.

##### Ofek Bengyat (University of Vienna)

##### Recent approaches to the QM-GR interface and gravity-induced entanglement

06.04.2022, 14:15, online

Abstract: In recent years it has been attempted to provide a theoretical description for and come up with a feasible experimental realization of the idea of gravity-induced entanglement, which dates back to Feynman in 1957. Observing gravity-induced entanglement could prove that a theory of gravity must permit a superposition of spacetimes. The talk will review some of those theoretical considerations.

##### Bryan Renard (Université de Namur)

##### Construction of MPS and PEPS using Recovery Maps for Approximate Markov Chains

27.04.2022, 14:15 CEST, Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: Recovery maps have been developed in quantum information theory, where they are used to reverse the action of a quantum channel on a system. For Markov chains, they allow to retrieve a state from its marginals, giving a solution of the quantum marginal problem. In the situation of a 1D spin chain, we used recovery maps to reconstruct the state of the chain. The process, under some assumptions, gives an MPS with polynomial scaling of the bond dimension.

##### András Molnár (University of Vienna)

##### Adiabatic theorems for quantum many-body systems

04.05.2022, 14:15 CEST, Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: The adiabatic theorem guarantees that a state evolved by a time-dependent Hamiltonian H follows the ground state of H provided that H is changing slowly (and the evolution is started from the ground state). This idea then can be used to prepare the ground state of a complex Hamiltonian by slowly interpolating between the Hamiltonian and a trivial system. For practical applications, it is crucial to understand how slow the adiabatic evolution has to be. Conventional adiabatic theorems give a bound on the required speed in terms of the norm of the Hamiltonian and the gap. This bound, however, scales poorly with the system size, as the proofs do not make use of the locality of the system. In this talk we try to exploit locality to obtain versions of the adiabatic theorem that scale better with the system size.

##### David Perez-Garcia (Universidad Complutense Madrid)

##### Physics solutions for machine learning privacy leaks

11.05.2022, 14:15 CEST, Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: Machine learning systems are becoming more and more ubiquitous in increasingly complex areas, including cutting-edge scientific research. The opposite is also true: the interest in better understanding the inner workings of machine learning systems motivates their analysis under the lens of different scientific disciplines. Physics is particularly successful in this, due to its ability to describe complex dynamical systems. While explanations of phenomena in machine learning based on physics are increasingly present, examples of direct application of notions akin to physics in order to improve machine learning systems are more scarce. Here we provide one such application in the problem of developing algorithms that preserve the privacy of the manipulated data, which is especially important in tasks such as the processing of medical records. We develop well-defined conditions to guarantee robustness to specific types of privacy leaks, and rigorously prove that such conditions are satisfied by tensor-network architectures. These are inspired by the efficient representation of quantum many-body systems, and have shown to compete and even surpass traditional machine learning architectures in certain cases. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.

See also arxiv.org/abs/2202.12319

##### Yang Yang (Universität Hamburg)

##### String-net models, conformal field theories with defects and double categories

18.05.2022, 14:15 CEST, online

Abstract: In this talk, I will present a generalized version of string-net models that have pivotal bicategories as input data and showcase their application to 2-dimensional (rational) conformal field theories.

When the input datum is chosen to be a modular fusion category C viewed as a single-object pivotal bicategory, the construction recovers the string-net model formalized by Kirillov Jr. as a 2-dimensional skein theory and provides an open-closed modular functor that assigns the Drinfeld center Z(C) to a circle, which serves as an concrete model for the spaces of conformal blocks for an RCFT with fixed chiral data.

On the other hand, if we choose the bicategory to be that of frobenius algebras, bimodules and bimodule morphisms internal to C, we get a modular functor that classifies the worldsheets with defects for the said RCFT, where the equivalence relation on the worldsheets is generated by the local graphical calculus of the defects.

The crucial observation is that the two modular functors provided by the string-net construction extend to two symmetric monoidal double functors between double categories of bordisms and profunctors, and that the a consistent system of correlators for all worldsheets corresponds to a monoidal vertical transformation between the double functors.

The talk is based on joint work with Jürgen Fuchs (Karlstad) and Christoph Schweigert (Hamburg).

##### Andrea Pizzi (Cambridge)

##### Bridging the gap between classical and quantum many-body information dynamics

25.05.2022, 14:15 CEST, Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens of the bipartite entanglement entropy, a quantity that describes correlations in a comprehensive (nonlocal) way. Among the most striking features of the entanglement entropy are its unbounded linear growth in the thermodynamic limit, its asymptotic extensivity in finite-size systems, and the possibility of measurement-induced phase transitions, all of which have no obvious classical counterpart. Here, we show how these key qualitative features emerge naturally also in classical information spreading, as long as one treats the classical many-body problem on par with the quantum one, that is, by explicitly accounting for the exponentially large classical probability distribution. Our analysis is supported by extensive numerics on prototypical cellular automata and Hamiltonian systems, for which we focus on the classical mutual information and also introduce a `classical entanglement entropy'. Our study sheds light on the nature of information spreading in classical and quantum systems, and opens new avenues for quantum-inspired classical approaches across physics, information theory, and statistics.

Reference: arxiv.org/abs/2204.03016

##### Mingru Yang (University of Vienna)

##### Detecting emergent continuous symmetries at quantum criticality

01.06.2022, 14:15 CEST, Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: New symmetries which the Hamiltonian does not possess can emerge at low energy in quantum many-body systems. Such a phenomenon generally occurs when the symmetry-breaking terms in the Hamiltonian are irrelevant under the renormalization group (RG) flows. To determine the signal of and confirm the existence of the emergent symmetries, involved field theory analysis and calculations of correlation functions are usually required. Here, we provide an alternative way to directly detect emergent continuous symmetries at the quantum critical points, based on the variational uniform matrix product states. I will also discuss some issues that remain to be solved and welcome any comments.

##### Clemens Karner (University of Vienna)

##### A variational optimization algorithm for uniform matrix product states

08.06.2022, 14:15 CEST, Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: One of the fundamental questions in quantum mechanics is how to numerically calculate the ground state of a one dimensional quantum lattice in the thermodynamic limit. We present a novel algorithm, variational uniform Matrix Product State (VUMPS), for numerically calculating ground states of Hamiltonians based on a variational approach. To begin with, we introduce basic notations and the notion of tangent-spaces of uniform matrix product states. Afterwards, we explain the VUMPS algorithm in detail. Finally, we demonstrate by numerical experiments that VUMPS surpasses well-known algorithms, such as infinite Density Matrix Renormalization Group (IDMRG) and infinite Time Evolving Block Decimation (ITEBD), in terms of convergence speed as well as precision.

##### Iason Douveas & Markus Miethlinger (University of Vienna)

##### What limits the simulation of quantum computers

15.06.2022, 14:15 CEST, Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: Simulation of perfect quantum computers is exponentially hard. However NISQ-era quantum computers are characterized by their non-perfect implementation of gates. Taking the noise into account, the simulation of such QC may become accessible to current classical computers. In this talk we examine a simple approach using well known techniques implement an algorithm that simulates a noisy quantum computer and how these results compare to real quantum computing fidelities.

##### Leander Thiessen & Erim Cakmak (University of Vienna)

##### Provably efficient machine learning for quantum many-body problems

22.06.2022, 14:15 CEST, Kurt Gödel lecture hall (Strudlhofgasse 4, Room 3E63)

Abstract: Machine learning algorithms (ML) may provide an advantage over traditional methods when solving quantum many-body problems. However, there is a lack of rigorous theory characterizing this advantage. In this work, rigorous performance guarantees are derived in two settings: Predicting ground states of gapped Hamiltonians and classifying quantum states of matter. It is shown that classical ML algorithms can accurately and efficiently predict ground states of gapped Hamiltonians in finite spatial dimension, in particular there is a genuine advantage over algorithms that don’t learn from data. The theoretical results are accompanied by numerical simulations, applying ML algorithms to Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases and topologically ordered phases.