Speaker:   Miles Stoudenmire
Title:   Part 1: Quantum Dynamics in 2D and 3D Using Tensor Belief Propagation
Abstract:   This mini-course will introduce new methods for quantum dynamics simulations based on tensor networks. Until recently, tensor network simulations of dynamics have been primarily limited to one-dimensional systems and short times. However, recent algorithmic developments are rapidly changing this picture.
The first family of algorithms discussed will be the belief propagation (BP) framework. BP is well-established in the classical statistical mechanics and spin glass fields, but was only recently adapted for quantum tensor network states. Building on the notion of "tree-like" structure, BP gives offers an affordable and complementary perspective for evolving 2D and even 3D wave functions in real and imaginary time. I will end by discussing recent applications to dynamics and thermal properties of spin systems.

The second family of algorithms revolves around the energy content of quantum states. Imaginary time evolution is known to be efficient for tensor networks, due to the rapid damping of high-energy states. One can leverage these benefits for real-time evolution by introducing "complex time" dynamics, which balance benefits of imaginary and real time, in particular controlling the growth of entanglement. Despite the dynamics being fictitious, there are controlled reconstruction techniques to extract real-time correlation functions. I will discuss the philosophy and promise of these methods and possible implications for the future of dynamics simulations.

Speaker:   Miles Stoudenmire
Title:   Part 2: New Approaches for Quantum Dynamics: Complex and Imaginary Time
Abstract:   This mini-course will introduce new methods for quantum dynamics simulations based on tensor networks. Until recently, tensor network simulations of dynamics have been primarily limited to one-dimensional systems and short times. However, recent algorithmic developments are rapidly changing this picture.

The first family of algorithms discussed will be the belief propagation (BP) framework. BP is well-established in the classical statistical mechanics and spin glass fields, but was only recently adapted for quantum tensor network states. Building on the notion of "tree-like" structure, BP gives offers an affordable and complementary perspective for evolving 2D and even 3D wave functions in real and imaginary time. I will end by discussing recent applications to dynamics and thermal properties of spin systems.

The second family of algorithms revolves around the energy content of quantum states. Imaginary time evolution is known to be efficient for tensor networks, due to the rapid damping of high-energy states. One can leverage these benefits for real-time evolution by introducing "complex time" dynamics, which balance benefits of imaginary and real time, in particular controlling the growth of entanglement. Despite the dynamics being fictitious, there are controlled reconstruction techniques to extract real-time correlation functions. I will discuss the philosophy and promise of these methods and possible implications for the future of dynamics simulations.

Speaker:    Anatoly Dymarsky
Title:    Title:   Holographic Krylov complexity
Abstract:   I will discuss how the Krylov space method can be formulated for holographic theories, and how it can help to define a dual holographic description for non-holographic systems.

Speaker:   Mohammad Maghrebi
Title:   Universal dynamics from dark states
Abstract:   Open quantum systems can host dark or subradiant states whose decay is highly suppressed. While these states have been extensively studied in the few-excitation regime, their impact on the many-body dynamics remains largely unexplored. In this talk, I introduce a minimal model of a spin chain with correlated dissipation on neighboring sites, featuring a single-particle dark state at zero momentum. I show that the single-particle dark state qualitatively alters the many-body dynamics at long times, and identify its distinct universal behavior. While the zero-momentum mode is dark at the single-particle level, it decays slowly as 1/ log t as it becomes dressed by other modes through a dissipation-induced nonlinearity. I end the talk with an outlook on new possibilities afforded by dark states for realizing exotic dynamics and even strongly correlated quantum states.

Speaker:   Hosho Katsura
Title:    Integrable SYK-like models
Abstract:   In this talk, we introduce two disorder-free variants of the Sachdev–Ye–Kitaev (SYK) model, both built from Majorana fermions with all-to-all interactions: (i) the clean Majorana SYK model and (ii) its N=1 supersymmetric extension. Unlike the original disordered SYK model, which is maximally chaotic, these models are integrable, in the sense that their Hamiltonians commute with a quadratic Hamiltonian.

This integrability allows us to study the static and dynamical properties of Model (i) with 4-body interactions in detail. We find that the out-of-time-order correlators (OTOCs) exhibit early-time exponential growth, resembling that of the disordered SYK model. We also discuss the effect of dissipation on this 4-body clean SYK model. Time permitting, I will briefly touch on a disorder-free version of the quantum breakdown model with all-to-all interactions.

Speaker:   Marcello Dalmonte
Title:   Complexity of the many-body problem beyond entanglement: magic and sampling
Abstract:   Entanglement has revolutionized the way we understand the quantum many-body problem. A key conceptual advance has been the relation between collective phenomena and their computational complexity, rooted in the concept of tensor network states and (lack of) separability.

Over the last few years, very remarkable experimental advances have put forward the need to better understand different facets of complexity - in reference to actual cost of quantum computations (in the context of error corrections) and of data structures (in the context of collective measurements of wave functions). In this talk, I will descrive some progress along these two directions.

Firstly, I will discuss how magic - the figure of merit of complexity in the context of quantum error correction schemes - relates to the many-body problem. I will discuss examples in the context of gauge theories, symmetry-protected topological phases, and tensor network states, and will show how understanding the magic/entanglement interplay can lead to new classes of variational states with uncharted computational capabilities.

Secondly, I will present a new theoretical paradigm to understand snapshots of many-body states, that takes inspiration from the field of classical network theory. Using these tools, I will show how it is possible to reveal universal features in wave functions with no priors, and how one can, with the help of a “snapshot” renormalization group, classify phases of matter in one spatial dimension.
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Speaker:   Max McGinley
Title:   Universality and complexity in quantum dynamics at early times
Abstract:   While many-body quantum systems can be extraordinarily complex, quantitative predictions can often be made by identifying statistical ensembles that capture the universal behaviour of a broad class of systems. For instance, the Haar ensemble is expected to capture the the late-time behaviour of isolated systems without conservation laws. Accordingly, by understanding the key properties of Haar-random states, we can understand the physics of a diverse range of many-body systems in a unified way.

In this talk, I will describe new universal statistical theories that capture the dynamics of systems in regimes beyond Haar, focusing in particular on the states generated by early-time dynamics. We argue that the behaviour of these early-time states can be captured by the so-called Scrooge ensemble [PRA 49, 668 (1994)], a more structured generalization of the Haar ensemble. I will first present evidence that the Scrooge ensemble describes the outputs of random constant-depth quantum circuits. This hypothesis has implications for the complexity of simulating shallow circuits: While noiseless simulation is thought to be exponentially hard, we prove that a vanishingly small noise rate ɣ = Ω  (log(n) / n) is enough to render these circuits efficiently simulable. I will conclude by illustrating how the Scrooge ensemble could be used to describe other kinds of dynamics with beyond-Haar-random structure, such as the volume-law phase of monitored quantum circuits, and dynamics with conservation laws. Based on work with Thomas Schuster, David Gosset, and Calvin Liu
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Speaker:   Ben Craps
Title:   Quantum Chaos, Operator Spreading, and Dynamical Compressed Sensing of Quantum States
Abstract:   I will discuss three results related to the distinction between integrable and chaotic quantum dynamics. First, I present a random matrix ensemble that correctly reproduces the level spacing distributions across the integrability-to-chaos transition in a variety of test systems. A key role is played by the statistics of the matrix elements of the nonintegrable perturbation Hamiltonian in the energy eigenbasis of the unperturbed integrable system, which turn out to be dominated by simple power laws. Second, I introduce multiseed Krylov complexity, a generalization of Krylov complexity based on the block-Lanczos algorithm applied simultaneously to all simple operators. It reliably distinguishes chaotic from integrable dynamics by assigning higher complexity saturation values to the former. Third, I propose a method for reconstructing low-rank quantum states from a small number of simple local measurements made at different times. This dynamical compressed sensing protocol succeeds for chaotic systems that sufficiently scramble simple operators.Hashtag: #workshop

Speaker:   Masaki Oshikawa
Title:   Conformal boundary conditions of Z_2 orbifolds and Stabilizer Renyi Entropy
Abstract:   I will discuss conformal boundary conditions of the Z_2 orbifold of free boson conformal field theory in 1+1 dimensions. As applications to statistical mechanics, I will discuss the boundary phase diagram of the critical Ashkin-Teller model including the double-layer critical Ising model and the critical 4-state Potts model. A conformal boundary condition of the Z_2 orbifold of multicomponent free boson conformal field theory is also related to the Stabilizer Renyi Entropy, a measure of "nonstabilizerness" also known as quantum magic which is a resource for quantum computation.
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