2023 Winter Semester

During the 2023 winter semester, the seminar generally took place on Mondays at 11:30 in the Kurt Gödel lecture room (Strudlhofgasse 4, ground floor, room 3E63). For details, please take a look at the schedule and abstracts below.  

Lilith Zschetzsche (Johannes Kepler University, Linz)

Self-Localization of an Impurity in a Bose-Einstein Condensate in One Dimension
Abstract: Mean-field calculations investigating an impurity atom immersed in a Bose-Einstein condensate of ultracold atoms in 1D [M. Bruderer et al., EPL 82, 30004 (2008)] find a “self-localized” impurity, characterized by a localized impurity density that breaks translational symmetry. Since the mean-field ansatz does not include particle correlations, this self-localization effect might well be an artefact of the ansatz. To investigate, I derive Euler-Lagrange equations based on an improved variational ansatz, which includes impurity-boson correlations, and devise an iterative solver to compute the new ground state wave function. I then study the impurity density, which is either constant for a delocalized impurity, or peaks around at a random location for a localized impurity. I also discuss the importance of impurity-boson correlations and compare the new impurity chemical potential to the mean-field results. To investigate the energy scale of the self-localization effect, I calculate the energy gained by the formation of a localized state.

(date/time: 10.10.2023, 11:30)

Jordi Tura i Brugués (Leiden University)

Quantum eigenstate broadcasting assisted by a coherent link
Abstract: Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum algorithms exist which can prepare the ground state with high precision and provable guarantees from an initial approximation, current devices are limited to shallow circuits. Here we consider the setting where Alice and Bob, in a distributed quantum computing architecture, want to prepare the same Hamiltonian eigenstate. We demonstrate that the circuit depth of the eigenstate preparation algorithm can be reduced when the devices can share limited entanglement. Especially so in the case where one of them has a near-perfect eigenstate, which is more efficiently broadcast to the other device. Our approach requires only a single auxiliary qubit per device to be entangled with the outside. We show that, in the near-convergent regime, the average relative suppression of unwanted amplitudes is improved to 1/(2\sqrt(e))≈0.30 per run of the protocol, outperforming the average relative suppression of 1/e≈0.37 achieved with a single device alone.

(date/time/location: 12.20.2023, 14:30, Erwin Schrödinger International Institute for Mathematics and Physics (ESI), Boltzmanngasse 9, 2nd floor, Schrödinger lecture hall)

Shuhei Ohyama (Yukawa Institute for Theoretical Physics, Kyoto University):

Higher structures in matrix product states
Abstract: The Berry phase, introduced by Michael V. Berry in 1984, has been widely applied in the definition of topological invariants, inspired by the trend of topological phases originating from quantum Hall systems. However, when naively calculating the Berry phase for high-dimensional many-body Hamiltonians, a divergence problem arises in the thermodynamic limit, necessitating an appropriate generalization of the definition of the Berry phase. In this seminar, I will discuss the formulation of higher Berry phases in one-dimensional systems, based on [1-3]. Specifically, by employing the matrix product state, we define the inner product for three states and demonstrate how this quantity provides a natural definition of the higher Berry phase. Please refer to similar studies from other groups as well [4,5].

[1] Shuhei Ohyama, Yuji Terashima, Ken Shiozaki arXiv:2303.04252.
[2] Shuhei Ohyama, Shinsei Ryu arXiv:2304.05356.
[3] Ken Shiozaki, Niclas Heinsdorf, Shuhei Ohyama, arXiv:2305.08109.
[4] Marvin Qi, David T. Stephen, Xueda Wen, Daniel Spiegel, Markus J. Pflaum, Agnès Beaudry, Michael Hermele arxiv:2305.07700.
[5] Daniel Spiegel, arXiv:2305.07951.

(date/time/location: 16.10.2023, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Christian Reinmoser (LMU Munich)

Optimized Gutzwiller Projected Wave Functions for Quantum Magnets
Abstract: In 1973, Anderson proposed the resonating valence bond state state as a potential alternative to the antiferromagnetic Néel state for spin-1/2 systems [1]. Subsequently, the RVB state has been used to understand aspects of the Fermi-Hubbard model with large interaction U/t on the square lattice, for example the d-wave symmetry of the superconducting phase. Yet, some aspects of the phase diagram lack full understanding and when looking at frustrated systems, for example a system on the triangular lattice, the theoretical picture is still incomplete. In recent years, quantum simulation platforms such as optical lattices with ultracold atoms have emerged as a powerful tool to probe quantum many-body behavior. The Fermi-Hubbard model has been simulated on the square lattice and, recently, on the triangular lattice using such optical lattices [2,3].
In this project our goal is to combine concepts established in the context of the RVB state with the experimental observations from these two experiments. Therefore, we employ Metropolis sampling of Gutzwiller projected wave functions to calculated estimates for two-point correlation functions in the t-J model and minimize the sum of squared deviations between those estimates and the experimental data. The type of wave function we are using is the staggered flux state, possibly including an antiferromagnetic Néel field for small temperatures. We look at the performance of the wave function for different doping ranges for both the square and triangular lattice. We find that, generally, the estimates are in qualitative agreement with the experimental data, yet some characteristics, such as sign changes of the correlation functions for certain doping ranges or the particle-hole asymmetry in the triangular lattice, are not fully captured by the staggered flux state. This implies that while this relatively simple wave function can not capture all aspects of the Fermi-Hubbard model accurately, it provides a basis for further research.

[1] Anderson et al., Materials Research Bulletin, 8(2):153–160, 1973. doi:10.1016/0025_5408(73)90167-0
[2] Chiu et al., Science, 365(6450):251–256, 2019, doi:10.1126/science.aav3587
[3] Xu et al., Nature, 620(7976):971–976, 2023, doi:10.1038/s41586-023-06280-5

(date/time: 18.10.2023, 11:30)

Pietro Brighi (University of Vienna)

Many-body localization proximity effect in a two-species bosonic Hubbard model
Abstract: The many-body localization (MBL) proximity effect is an intriguing phenomenon where a thermal bath localizes due to the interaction with a disordered system. The interplay of thermal and nonergodic behavior in these systems gives rise to a rich phase diagram, whose exploration is an active field of research. In this work, we study a bosonic Hubbard model featuring two particle species representing the bath and the disordered system. Using state of the art numerical techniques, we investigate the dynamics of the model in different regimes, based on which we obtain a tentative phase diagram as a function of coupling strength and bath size. When the bath is composed of a single particle, we observe clear signatures of a transition from an MBL proximity effect to a delocalized phase. Increasing the bath size, however, its thermalizing effect becomes stronger and eventually the whole system delocalizes in the range of moderate interaction strengths studied. In this regime, we characterize particle transport, revealing diffusive behavior of the originally localized bosons.

(date/time/location: 23.10.2023, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Paula García Molina (Institute of Fundamental Physics (IFF-CSIC), Madrid)

Global optimization of MPS in quantum-inspired numerical analysis
Abstract: This work discusses the solution of partial differential equations (PDEs) using matrix product states (MPS). The study focuses on the search for the lowest eigenstates of a Hamiltonian equation, for which five algorithms are introduced: imaginary-time evolution, steepest gradient descent, an improved gradient descent, an implicitly restarted Arnoldi method, and density matrix renormalization group (DMRG) optimization. The first four methods are engineered using a framework of limited-precision linear algebra, where operations between MPS and matrix product operators (MPOs) are implemented with finite resources. All methods are benchmarked using the PDE for a quantum harmonic oscillator in up to two dimensions, over a regular grid with up to 2^(28) points. Our study reveals that all MPS-based techniques outperform exact diagonalization techniques based on vectors, with respect to memory usage. Imaginary-time algorithms are shown to underperform any type of gradient descent, both in terms of calibration needs and costs. Finally, Arnoldi like methods and DMRG asymptotically outperform all other methods, including exact diagonalization, as problem size increases, with an exponential advantage in memory and time usage.
The arXiv link is https://arxiv.org/abs/2303.09430.

(date/time/location: 30.10.2023, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Anna Francuz (University of Vienna)

Stable and Efficient Differentiation of CTM
Abstract: Gradient based optimization methods for Projected Entangled Pair States were established to be the state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions. However, the key ingredient, the gradient itself, has proven challenging to calculate accurately and reliably in the case of a CTM-based approach. Automatic differentiation (AD), which is the best known tool for calculating the gradient, still suffers some crucial shortcomings. Some of these are known, like the problem of exploding memory and the divergences that may arise when differentiating a singular value decomposition (SVD). Importantly, there is also a fundamental inaccuracy with the back propagation of SVD that had not been noted before. In this talk, we describe all these problems and provide them with compact and easy to implement solutions. We analyse the impact of these changes and find that the last problem is by far the dominant one and should be considered a crucial patch to any AD PEPS code.

(date/time/location: 06.11.2023, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

David Blanik (University of Vienna)

Ogata's construction of an SPT index
Abstract: Ogata's construction uses C^*-algebraic methods to generalize the SPT index, originally introduced for Matrix Product States, to all (1+1)-dimensional quantum spin systems. I will give a pedagogical introduction to both the construction and the required C^*-algebra formalism.

(date/time/location: 13.11.2023, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Faruk Salihbegovic (TU Vienna)

Ab Initio Modeling of Microscopic Systems: Coupled Cluster Theory Applied to Zero-Dimensional Systems
Abstract: In this presentation, I will provide a broad overview of the intricacies associated with ab initio modeling of microscopic systems. This will be highlighted by two examples: a model Hamiltonian quantum dot and the silicon self-interstitial point defects. Specifically, we employ EOM-CCSD theory to calculate the excitation energies of quantum dots with varying numbers of electrons and within different regimes of correlation strength. Additionally, we compute the formation energies of the silicon self-interstitials using CCSD(T), often considered the gold standard in quantum chemistry. I will highlight every step that is needed to achieve converged results, while also giving an overview of the numerical methods and their reliability.

(date/time/location: 20.11.2023, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Dmytro Kolisnyk & Julian Maisriml (University of Vienna)

Efficient approximation of the dynamics of one-dimensional systems
The talk will be based on the paper arxiv.org/abs/quant-ph/0508031.

(date/time/location: 27.11.2023, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Andrea Caprotti & Tim Ehret (University of Vienna)

Isometric tensor network states in two dimensions
Abstract: Isometric tensor network states have desirable properties with regard to contraction, but moving the orthogonality centre by using a variational approach is generally inefficient. The talk focuses on the Moses Move as proposed in the seminal work by Zaletel and Pollmann [1] that allows for the efficient shifting of the orthogonality centre. Following the structure of [1], we also touch upon the comparison to the variational solution and the reduction of entanglement.

[1] M. P. Zaletel and F. Pollmann, Phys. Rev. Lett. 124, 037201 (2020)

(date/time/location: 04.12.2023, 11.30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Laszlo Jiresch & Maximilian Raderer (University of Vienna)

Exponential quantum speedup in simulating coupled classical oscillators
Abstract: Quantum computing offers an opportunity of efficiently simulating classical problems. This talk will give insight about an algorithm designed to efficiently simulate a system of 2^n classical oscillators in time poly(n). We will especially focus on mapping the equations of motion to the Schrödinger equation as well as the algorithm to achieve an exponential speedup.

This talk is based on a paper with the same name by R.Babbush et al: arxiv.org/abs/2303.13012

(date/time/location: 11.12.2023, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Simon Morelli (Basque Center for Applied Mathematics, Bilbao)

Correlation constraints - a simpler version of the quantum marginal problem
Abstract: The quantum marginal problem investigates the compatibility of the eigenvalues of the local and global states of a multipartite quantum system. It is a fundamental problem in quantum information for which the solution is only known for simple cases. We investigate a simpler question of the same flavour: Given the purities of the two local states of a bipartite system, what is the maximum purity the global state can achieve? We derive a new inequality that holds in arbitrary dimensions and gives a complete solution for two qubits. Together with previous findings, this result gives rise for a new representation of the quantum state space – the Bloch ball – of two qubits. We show that this 3-dimensional visualization has various interesting properties regarding geometry and argue why it indeed captures many relevant properties of the full, high-dimensional, state space.

(date/time/location: 08.01.2024, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Riccardo Valencia Tortora (Universität Mainz)

Non-ergodicity in Noisy Intermediate Scale Quantum devices
Abstract: Strongly interacting systems are generally expected to thermalize, making local information of the initial state scattered into highly non-local degrees of freedom that are challenging to access. However, various mechanisms exist, e.g. localization, that could prevent thermalization and, therefore, aid in passively protecting coherence and quantum information.
In this talk, I will discuss how different ergodicity-breaking mechanisms manifest in a single class of models, known as kinetically constrained models, which can be realized in current platforms based on Rydberg arrays and superconducting circuits. Moreover, I will discuss a novel kind of dynamical phase transition these models display between an ergodic phase and a non-ergodic one, which can be diagnosed through the complexity of simulating the dynamics using tensor networks.

(date/time/location: 15.01.2024, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Jose Garre Rubio (University of Vienna)

Anomalous domain wall statistics in matrix product unitary symmetry broken states
Abstract: In this talk we will study the statistics of domain wall excitations in quantum spin chains. We will focus on symmetry broken ground states permuted by matrix product unitaries (MPUs), i.e. finite depth circuits. We show that the anomaly of the symmetry restricts the statistics of the domain walls; obtaining that for anomalous MPUs those are neither bosons nor fermions. We use matrix product states (MPSs) representing the ground states and MPU-based truncated operators on top of those MPSs as ansatz for the domain walls. Within this framework we derive gauge invariant quantities, defined locally, that characterizes the domain wall statistics. The defined quantities relate to the invariants that classify MPU symmetric quantum phases. We will focus on the Z_2 case for the sake of simplicity. This is a joint work with Norbert Schuch.

(date/time/location: 22.01.2024, 11:30, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)

Andreas Klingler (Universität Innsbruck)

Exploring Positive Tensor Decompositions: Approximations and a Relation to Recurrence Sequences
Abstract: Tensor (network) decompositions are a way to parametrize multipartite tensors efficiently, finding applications in quantum many-body physics, machine learning, and probability theory. However, challenges arise when dealing with elements that satisfy positivity constraints, such as density matrices or probability distributions. These challenges include separations between ranks or the undecidability of the description validity. In this talk, we focus on positive tensor decompositions in the context of approximations. Initially, we show that fixed approximation errors eliminate certain separations between positive ranks. Additionally, we prove that there are instabilities in positive ranks for tensor networks containing a loop, a known issue for unconstrained tensor decompositions. If time permits, we establish a connection between the positivity problem for Matrix Product Operators and a modified version of Skolem's problem. This open problem involves determining whether there exists an algorithm that can decide if a linear recurrence sequence attains specific values.

(date/time/location: 29.01.2024, 12:00, Kurt Gödel lecture room, Strudlhofgasse 4, ground floor, room 3E63)