A detailed portrait of many-body dynamics on a quantum computer

• Derek S. Wang (IBM Quantum)

Interacting many-body quantum systems and their dynamics, while fundamental to modern science and technology, are formidable to simulate and understand. However, by discovering their symmetries, conservation laws, and integrability one can unravel their intricacies. Here, using up to 124 qubits of a fully programmable quantum computer, we uncover local conservation laws and integrability in one- and two-dimensional periodically-driven spin lattices in a regime previously inaccessible to such detailed analysis. We focus on the paradigmatic example of disorder-induced ergodicity breaking, where we first benchmark the system crossover into a localized regime through anomalies in the one-particle-density-matrix spectrum and other hallmark signatures. We then demonstrate that this regime stems from hidden local integrals of motion by faithfully reconstructing their quantum operators, thus providing a detailed portrait of the system's integrable dynamics. Our results demonstrate a versatile strategy for extracting hidden dynamical structure from noisy experiments on large-scale quantum computers.

What is thermal equilibrium and how do we get there?

• Hal Tasaki (Gakushuin University)

We present a simple, rigorous example (which is essentially a free fermion chain) of an isolated macroscopic (but finite) quantum system that exhibits thermalization (in a phenomenological sense) from any pure initial state in the microcanonical energy shell. The essential ingredients of the proof are the large-deviation type strong ETH (energy eigenstate thermalization hypothesis) bound and the absence of degeneracy in the energy spectrum. As far as we know, this is the first concrete realization of the philosophy on the foundation of equilibrium statistical mechanics proposed by von Neumann in 1929.

Fermionic Bricks in the Wall

• Kareljan Schoutens (University of Amsterdam)

We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2- particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary $U_F$ and its, non-trivial, hamiltonian limit $H_\gamma$ in closed form. We find that the fermionic symmetry pins $H_\gamma$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We explore quench dynamics for this class of circuits.

Aspect of Floquet physics in closed quantum systems

• Krishnendu Sengupta (Indian Association for the Cultivation of Science)

In this talk, we shall discuss two aspects of a periodically driven closed quantum system. First, we shall discuss the existence of signatures of Hilbert space fragmentation (HSF) in a driven interacting fermi chain in its prethermal regime at special drive frequencies. We provide analytical expression for these drive frequencies, show that such prethermal regime can be exponentially long in the large drive amplitude regime, and discuss feasibility of realization of such systems in experiments. Second, we shall discuss a class of two-rate periodic drive protocol for closed quantum systems where the drive frequencies have integer ratio. We show that for protocols obeying certain conditions, there is a large class of non-integrable models where one obtains an exact Floquet flat band. Near these flat bands, heating in these driven systems is significantly reduced which may be useful, for example, in application to qubit manipulation and quantum state preparation.

Controlling ultrafast Rydberg dynamics with ultracold atoms in optical tweezers

• Takafumi Tomita (Institute for Molecular Science)

Rydberg atoms, with their giant electronic orbitals, exhibit dipole-dipole interaction reaching the GHz range at a distance of a micron, making them a prominent contender for realizing ultrafast quantum operations. However, such strong interactions have never been harnessed so far because of the stringent requirements on the atom position fluctuation and the necessary excitation strength. Here, we introduce novel techniques to enter this regime and explore it with two strongly-interacting single atoms. This interaction is the key to the realization of an ultrafast two-qubit gate for cold-atom quantum computers. The techniques demonstrated here open the path for ultrafast quantum simulation and computation

Exploring Non-Hermitian Phenomena in Ultracold Fermions

• Gyu-Boong Jo (The Hong Kong University of Science and Technology (HKUST),)

Ultracold fermions, traditionally prepared in well-isolated environments with minimal dissipation, have recently emerged as a novel platform for investigating non-Hermitian physics and broader open quantum systems. This exploration is facilitated through precise control of dissipation mechanisms. In this presentation, I will elucidate the methods for realizing such non-Hermitian systems using atomic ensembles, and discuss our recent experimental observations. These include the demonstration of the non-Hermitian skin effect in two dimensions and chiral spin transfer near exceptional points. Furthermore, I will outline our ongoing research into novel quantum dynamics that extend beyond conventional non-Hermitian frameworks within these open quantum systems.

Anyons and Edge Transport in Quantum Hall Systems

• Masayuki Hashisaka (Institute for Solid State Physics (ISSP), University of Tokyo)

Recent experiments verified abelian anyonic statistics of quasiparticles in Laughlin's fractional quantum Hall state of Landau level filling $\nu = 1/3$, about 40 years after the theoretical proposal in the 1980s. The experiments were achieved due to the progress in the long-standing theoretical and experimental research on edge transport in quantum Hall systems. In this talk, I will introduce some of our experiments and discuss recent developments in anyons and edge-transport research.

Gong Show

Poster Session 1

Exact correlation functions of quantum integrable circuits from algebraic geometry

• Yunfeng Jiang (Shing-Tung Yau Center and School of Physics, Southeast University)

In this talk, I will discuss some exact results on correlation functions of strings of spin operators for an integrable quantum circuits. These observables can be used for error calibration and mitigation of quantum simulation platforms. In the first part, I will discuss the method for the computation which includes algebraic Bethe ansatz and computational algebraic geometry. In the second part, I will present the exact results in both real space and Fourier space and discuss their physical implications.

Novel quantum dynamics with superconducting qubits

• Pedram Roushan (Google Quantum AI)

In recent years, superconducting qubits have emerged as one of the leading platforms for quantum computation and simulation. We utilize these Noisy Intermediate Scale Quantum (NISQ) processors to study quantum dynamics. I will present some of our recent works in studying robustness of bound states of photons [1], universality classes of dynamics in the 1D Heisenberg chain [2], and braiding of non-Abelian excitations [3]. These works point to the subtleties of non-equilibrium dynamics of highly entangled states in many-body systems; they provide evidence that in the absence of full-fledged quantum processors, the NISQ processors have challenged and guided our conventional wisdom. [1] Morvan et al., Nature 612, 240–245 (2022) [2] Rosenberg et al., Science 384, 48-53 (2024) [3] Andersen et al., Nature 618, 264–269 (2023)

Entanglement and tensor networks in the generalised Landau paradigm

• Frank Verstraete

Understanding Phases and Transitions in Mixed States

• Jong Yeon Lee (University of Illinois at Urbana-Champaign)

With the rapid development of quantum simulator platforms, understanding the stability of quantum phases in the presence of environmental coupling has become increasingly important. As a pure quantum state evolves into a mixed state due to decoherence, traditional notions of quantum phases need to be reconsidered. In this talk, I will present recent progress on mixed-state phases from an information-theoretic perspective, which contrasts sharply with conventional descriptions that rely on order parameters and fail to capture mixed-state phases. The presentation will be divided into three parts: (i) spontaneous symmetry breaking in mixed states, (ii) symmetry-protected topological states under decoherence and the extraction of long-range entangled states, and (iii) decohered topological orders and intrinsic error thresholds. If time permits, I will discuss how fault tolerance can be incorporated into this framework using a newly developed spacetime SPT (symmetry-protected topological) picture, highlighting the deep connection between fault tolerance and phase stability in open quantum systems.

A variety of partially solvable models: From closed spin chains to open spin chains

• Chihiro Matsui (University of Tokyo)

Non-thermal energy eigenstates of thermalizing isolated quantum systems have been intensively studied these days, as counter examples for the strong eigenstate thermalization hypothesis. These states are called “quantum many-body scars (QMBS)”, which exhibit specific properties such as low entanglement entropies and persistent oscillations. Surprisingly, many of QMBS are exactly solvable states of non-integrable Hamiltonians. This fact strongly motivates us to study partially solvable quantum systems. We show that partial solvability of a quantum many-body system can be maintained even when the system is coupled to boundary dissipators under certain conditions. We propose two mechanisms that support partially solvable structures in boundary dissipative systems: The first one is based on the restricted spectrum generating algebra, while the second one is based on the Hilbert space fragmentation. From these structures, we derive exact eigenmodes of the Gorini-Kossakowski-Sudarshan-Lindblad equation for a family of quantum spin chain models with boundary dissipators, where we find various intriguing phenomena arising from the partial solvability of the open quantum systems, including persistent oscillations (quantum synchronization) and the existence of the matrix product operator symmetry. We discuss how the presence of solvable eigenmodes affects long-time behaviors of observables in boundary dissipative spin chains based on numerical simulations using the quantum trajectory method. This talk is based on the collaboration work arXiv:2409.03208.

Non-Hermitian Topology in Hermitian Topological Matter: Wannier Localizability and Detachable Topological Boundary States

• Kohei Kawabata (Institute for Solid State Physics (ISSP), University of Tokyo)

Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk and boundary as an environment and system, we demonstrate that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology [1, 2]. We study the self-energy capturing the particle exchange between the bulk and boundary, and show that it detects Hermitian topology in the bulk and induces non-Hermitian topology at the boundary. As an illustrative example, we reveal the non-Hermitian topology and concomitant skin effect inherently embedded within chiral edge states of Chern insulators. We also identify the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators. Furthermore, we comprehensively classify our correspondence across all the tenfold symmetry classes of topological insulators and superconductors. Based on this correspondence and K-theory, we complete the tenfold classification of Wannier localizability and detachable topological boundary states [3, 4]. While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological boundary states that are detachable from the bulk bands. Here, we elucidate a close connection between these detachable topological boundary states and non-Hermitian topology. Identifying topological boundary states as non-Hermitian topology, we demonstrate that intrinsic non- Hermitian topology leads to the inevitable spectral flow. By contrast, we show that extrinsic non-Hermitian topology underlies the detachment of topological boundary states and clarify anti-Hermitian topology of the detached boundary states. References: [1] F. Schindler, K. Gu, B. Lian, and K. Kawabata, PRX Quantum \textbf{4}, 030315 (2023). [2] S. Hamanaka, T. Yoshida, and K. Kawabata, arXiv:2405.10015. [3] D. Nakamura, K. Shiozaki, K. Shimomura, M. Sato, and K. Kawabata, arXiv:2407.09458. [4] K. Shiozaki, D. Nakamura, K. Shimomura, M. Sato, and K. Kawabata, arXiv:2407.18273.

Poster Session 2

Driven Dirac systems and novel quantum anomalous states

• Takashi Oka (Institute for Solid State Physics (ISSP), University of Tokyo)

Floquet engineering, which involves controlling systems through time-periodic driving, provides a powerful method for coherently manipulating quantum materials and realizing dynamical states with novel functionalities. This presentation reports our recent experimental and theoretical findings on the dynamical states realized in Dirac electrons under various fields. Circularly Polarized Laser [1]: Nonlinear optical response experiments suggest the generation of chiral gauge fields and the creation of emergent Weyl points. AC-Magnetic Fields [2]: We demonstrate the emergence of π-Landau levels and the chiral anomaly-induced homodyne effect when Dirac electrons are subjected to a time-oscillating magnetic field B cos(Ωt). Propagating Fields [3]: Dirac electrons in a propagating wave V cos(Qx−Ωt) exhibit sensitivity to the field speed v = Ω/Q. We classify these states and explore the associated topological phase transitions. References: [1] N. Yoshikawa et al., arXiv:2209.11932; Y. Hirai et al., arXiv:2301.06072 [2] S. Kitamura and T. Oka, arXiv:2407.08115 [3] T. Oka, arXiv:2407.21458

Physics of tridiagonal matrices

• Pratik Nandy (Riken & Kyoto University)

Eigenvalues of Hermitian matrices encapsulate the core statistical and dynamical characteristics of quantum systems. Typically, this involves diagonalizing the Hamiltonian, where the diagonal elements represent the eigenvalues of the Hamiltonian. In this talk, I introduce an alternative approach: tridiagonalizing the Hamiltonian. I will discuss the properties of the tridiagonal matrix elements, highlighting that both chaotic and integrable systems share certain features, yet exhibit distinct statistical behaviors in these elements. If time permits, I will also show how these properties can be extended to non-Hermitian systems through singular value decomposition.