Seminar Abstracts

Alexander Altland (University of Cologne, Germany)

Field Theory in Circuit Dynamics

Abstract:

Recent years have witnessed major advances in the understanding of quantum circuit dynamics—progress essential as quantum hardware increasingly moves beyond the reach of classical simulation. The emerging theory of quantum devices is largely discrete in character, with prevalent concepts drawn from statistical mechanics, tensor networks, or the combinatorics of random matrices. At the same time, quantum field theory—physics’ established lingua franca for the understanding of complex many-body systems—remains strangely underrepresented, raising the question of why this is so.

In this talk we discuss two paradigmatic aspects of circuit dynamics, thermalization and late-time ergodic dynamics, and entanglement generation, to suggest some answers. We identify use cases where quantum field theory can provide access to physical regimes or system classes that may be difficult to approach by other means, and substantiate this perspective through comparison with exact diagonalization.

Aranya Bhattacharya (University of Bristol, UK)

Quantum complexity in random and time-periodic unitary circuits

Abstract:

I will discuss the notion of complexity in Krylov basis and its characteristics in random quantum circuits. In Haar-random unitary evolution, for large system sizes, this notion of complexity grows linearly before saturating at a late-time value of d/2, where d is the Hilbert space dimension, at timescales $\sim$ d. Our analysis encompasses two classes of random circuits: brick-work and Floquet random circuits. In brick-work case, complexity exhibits dynamics consistent with Haar-random unitary evolution, while the inclusion of measurements significantly slows its growth down. For Floquet random circuits, we show that localized phases lead to reduced late-time saturation values of the complexity enabling us to probe the transition between thermal and many-body localized phases. While this extends the usual notion of complexity to quantum dynamics generated by unitaries, the characteristic behaviour in the diverse set of models we study, agrees with other probes of quantum chaos, such as level spacing ratio, and spectral form factor. Based on arXiv:2409.03656

John Chalker (University of Oxford, UK)

Chaotic many-body quantum dynamics, spectral correlations, and energy diffusion

Abstract:

I will describe a study of chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions. It has a time-independent Hamiltonian, in contrast to quantum circuits and Brownian models, and is simple at the single-site level, in contrast to Sachdev-Ye-Kitaev chains. It is analytically tractable for large local Hilbert space dimension and weak intersite coupling. In this limit we show that energy dynamics is described by a classical master equation and is diffusive. We also show that the spectral form factor can be expressed exactly in terms of the solution to this master equation.

Joint work with Dominik Hahn, arXiv2510.02198

Jordan Cotler (Harvard University, USA)

Quantum chaos and quantum optimal transport

Abstract:

The wavelike nature of quantum states and the non-commutative geometry of quantum phase space obstruct a straightforward generalization of classical chaos theory. We develop a new approach to quantum chaos by leveraging a quantum version of optimal transport theory, which provides a natural and useful geometry for the distance between quantum states. We suggest that quantum optimal transport may be used to build a unifying mathematical foundation for quantum chaos theory, giving new tools to characterize quantum dynamics.

Lennart Dabelow (Queen Mary University of London, UK)

Basis dependence of eigenstate thermalization

Abstract:

Eigenstate thermalization refers to the property that an energy eigenstate of a many-body system is indistinguishable from a thermal equilibrium ensemble at the same energy as far as expectation values of local observables are concerned. The eigenstate thermalization hypothesis (ETH) conjectures that all (strong ETH) or almost all (weak ETH) basis states in the energy eigenbasis of generic systems exhibit eigenstate thermalization in the thermodynamic limit. In systems with degeneracies, however, the choice of an energy eigenbasis is not unique. We demonstrate and provide explicit examples that this can lead to unsettling ambiguities where the (strong or weak) ETH is satisfied in one basis, but violated in another basis. This finding challenges the widely perceived fundamental role of the ETH as the microscopic mechanism for thermalization in many-body quantum systems. It furthermore reveals that numerical ETH studies which exploit noncommuting symmetries for diagonalization may falsely conclude thermalization. Common examples are systems with simultaneous spatial translation and reflection symmetries.

Aydin Deger (University of Oxford, UK)

Efficient simulation of quantum circuits with large entanglement, magic and non-Gaussianity

Abstract:

We introduce a family of quantum circuits that exhibit standard indicators of classical simulation hardness, including large entanglement entropy, significant magic, and non-Gaussian features. Despite this, they can still be simulated efficiently using matrix product states.

These circuits arise from quantum error correcting codes, where logical complexity can differ substantially from the structure seen at the physical level. This places them outside the usual classes of efficiently simulable circuits, such as Clifford or matchgate circuits, and allows for a broad range of initial states, including entangled and non-stabiliser inputs. We show that the dynamics of these circuits appear strongly scrambling, with growing entanglement and increasingly complex correlations as indicated by quantum mutual information.

Our results demonstrate that, for these circuit families, commonly used resource measures are not sufficient on their own to indicate classical hardness. Instead, the relevant notion of complexity is shaped by the underlying structure of the circuit, rather than by gate taxonomy alone. This offers a different perspective on quantum circuit complexity at the interface of quantum information and scrambling.

Luca Delacretaz (University of Chicago, USA)

Superdiffusion in chaotic spin chains with quantum group symmetry

Abstract:

The interplay between symmetry and thermalization governs the late-time dynamics of local quantum and classical many-body systems at nonzero temperature. Recently, two parallel frontiers have emerged: the search for robust anomalous hydrodynamics---such as superdiffusion---in generic, non-integrable models, and the formal effort to generalize the fundamental concept of global symmetry. This talk will bridge these frontiers by demonstrating that quantum group symmetry provides a novel mechanism for anomalous hydrodynamics in chaotic systems. I will present dynamics of local operators carrying U(1) charge in non-integrable lattice models that also have quantum group symmetry. One example is transverse spin in the XXZ model with integrability breaking deformations. While such excitations are expected to decay very quickly at high temperature because their charge forbids overlap with conventional hydrodynamic densities, I will show that protection by the quantum group symmetry makes these modes long-lived, despite the absence of local quantum group charge density or current. Furthermore, the dynamics is superdiffusive across Hamiltonian, Floquet, and classical realizations, and exhibits unusual finite size effects at very late times. I will also revisit transverse spin dynamics in the integrable XXZ model.

Yan Fyodorov (King’s College London, UK)

Parametric correlations in Dissipative Quantum Chaos: non-Hermitian random matrix approach

Abstract:

Using non-Hermitian random matrices as a framework for description of universal characteristics of dissipative chaotic quantum many-body systems, we address the problem of characterizing the parametric correlations of their spectral densities. Considering parameter-dependent family of complex Ginibre matrices, we employ the method of exact replica integrability (Kanzieper, 2002) to derive an explicit, closed-form expression for the parametric number variance in the systems of symmetry class A for eigenvalues in a circular domain containing on average a finite number of eigenvalues in the spectral bulk. We also discuss a relation between parametric correlations of spectral densities and the distribution of the so-called eigenvector non-orthogonality factor, which attracted considerable interest in recent years. The talk will be based on a joint work-in-progress with Bertrand Lacroix-A-Chez-Toine.

Felix Haehl (University of Southampton, UK)

Modular-invariant random matrix theory and AdS3 wormholes

Abstract:

I will discuss a non-perturbative definition of RMT2: a generalization of random matrix theory that is compatible with the symmetries of 2d CFT. Given any random matrix ensemble, its spectral correlations admit a modular-invariant lift to RMT2, which reduce to the original random matrix correlators in a near-extremal limit. This also sheds a new light on the AdS3 wormhole geometries with multiple torus boundaries.

Sean Hartnoll (University of Cambridge, UK)

Towards a quantum lattice bootstrap

Abstract:

A “bootstrap” approach to physical systems starts from basic physical principles and aims to constrain the possible dynamics. For example, the S-matrix bootstrap uses analyticity and boundedness properties of the S-matrix to constrain scattering in relativistic field theories. I will explain how this methodology can be applied to quantum mechanical lattice models. The basic quantity will be the retarded Green’s function, for which I will establish strong analyticity and boundedness properties starting from Lieb-Robinson causality in local lattice models. I will explain how these properties (bounds and analyticity) can be used to place constraints on transport coefficients and on non-Fermi liquid coupling constants.

Nick Hunter-Jones (University of Texas at Austin, USA)

Complexity dynamics of subsystems

Abstract:

The circuit complexity of a quantum state is defined as the size of the shortest quantum computation that prepares that state. For generic quantum many-body systems, the complexity of a time-evolved pure state is believed to grow linearly with time for an exponentially long time. This linear complexity growth has been rigorously proven in certain models, such as random quantum circuits (RQCs). In this talk, we’ll consider the circuit complexity of subsystems of time-evolved states. We'll prove a sharp transition that occurs in the subsystem complexity for random quantum circuits and discuss a number of conjectures for subsystem complexity growth inspired by holography. We’ll also discuss the dynamics of the distinguishability of subsystems.

Tara Kalsi (University of Maryland, Baltimore County, USA)

Spectral Universality in Stochastic Quantum Scrambling Dynamics

Abstract:

Complex quantum many-body systems evolve towards ergodic states in which spectral correlations flow towards universal random-matrix-theory forms and information becomes scrambled across all degrees of freedom. Stochastic quantum dynamics provides a controlled framework for understanding this emergence of random-matrix-theory–like behaviour from a spectral perspective. We develop a single-parameter scaling theory that captures the full evolution of spectral correlations during scrambling and defines universal bounds on scrambling efficiency, yielding quantitative benchmarks for diagnosing incomplete or inefficient scrambling in more general quantum dynamics. Brownian models of quantum chaos play a privileged role by saturating these bounds. In these models, spectral form factors and out-of-time-ordered correlators obey a closed hierarchy of differential equations valid for all system sizes and across the three standard symmetry classes. Model-dependent information enters only through a single dynamical timescale, allowing one to identify which spectral correlations are universal. Numerical tests in the Brownian Sachdev–Ye–Kitaev model validate the predicted symmetry-class universality across all three classes.

Pavel Kos (University of Ljubljana, Slovenia)

Mixed state deep thermalization

Abstract: We introduce the notion of the mixed state projected ensemble (MSPE), a collection of mixed states describing a local region of a quantum many-body system, conditioned upon incomplete measurements of the complementary region. This constitutes a generalization of the pure state projected ensemble in which measurements are assumed ideal and complete, and which has been shown to tend towards limiting pure state distributions depending only on symmetries of the system, thus representing a new kind of universality in quantum equilibration dubbed deep thermalization. We study the MSPE generated by solvable (1+1)d dual-unitary quantum circuit evolution, and identify the limiting mixed state distributions which emerge at late times depending on the size of the incomplete measurement, which we assume to be lossy, finding that they correspond to certain random density matrix ensembles known in the literature. We also derive the rate of the emergence of such universality. Furthermore, we uncover a sharp transition in the ensemble's capacity to teleport quantum information: the fidelity switches from zero to maximal when the number of lost measurement outcomes matches the number of teleported degrees of freedom. These results provide a framework for observing deep thermalization and sampling random matrix ensembles in realistic, lossy quantum simulators. I will also comment on the ongoing follow-up.

Andy Lucas (University of Colorado Boulder, USA)

Error-correcting codes as counterexamples to the postulates of quantum statistical mechanics

Abstract:

I will present a rigorous construction of many-body Anderson localization. This explicitly violates the eigenstate thermalization hypothesis. The model is based on classical error-correcting expander codes, perturbed by quantum fluctuations. I will overview the elegant properties of random classical codes which lead to a provable guarantee of localization for every sufficiently low energy-density eigenstate. This localization phenomenon is (almost surely) stable to arbitrary perturbations, even when the perturbations do not respect the locality of the original code, meaning that ETH is not “generic” in this corner of the space of many-body systems.

Mark Mezei (University of Oxford, UK)

Fluctuating hydrodynamics of the SYK lattice

Abstract: To capture universality in many-body quantum chaos, it is useful to reformulate the dynamics of solvable models in the framework of effective field theory. The SYK lattice is a spatially local generalisation of the SYK model. In the low-temperature limit the pseudo-Goldstone bosons dominate its dynamics. In a further long wavelength limit, we reorganise their action as the effective field theory for fluctuating hydrodynamics. We compute the hydrodynamic effective action to high orders in the derivative expansion, determine all the corresponding transport coefficients, and discuss its symmetries. We outline how this framework extends to the computation of OTOCs and the second Renyi entropy using a fourfold contour. We also discuss moving beyond the low-temperature limit.

Xiao Mi (Google)

Beyond-classical computation with early quantum processors

Abstract:

Quantum processors based on superconducting qubits have made tremendous progress over recent years, with average two-qubit gates closing on 99.9% fidelity on the 100-qubit scale and quantum error-correction crossing the fault-tolerant threshold. In parallel with these developments, the prospect of attaining quantum advantage in simulating physical phenomena of interest has also become increasingly likely with current or near-term quantum processors. In this talk, I will introduce the basics of superconducting qubits and how to build quantum processors using these elements. The talk will then focus on recent works that demonstrate beyond-classical quantum computation of correlation functions which have applications in nuclear magnetic resonance spectroscopy, and using the quantum processor to study the critical properties of the two-dimensional XY model.

Anatoli Polkovnikov (Boston University, USA)

Defining chaos through geometry and non-adiabatic response

Abstract:

Traditionally chaos is defined through Lyapunov exponents in classical systems and through various random-matrix related measures in quantum systems. In this talk I will argue that these two definitions are generally incompatible and not directly related or measurable. Instead I will show that one can define chaos in all dynamical systems through a divergent response to adiabatic transformations, which are encoded in quantum-information geometry. Physically chaos means instability to slow variations in parameters, basically response to steering. This response is weak both when a system is close to an integrable limit with regular motion and, conversely, when a system has a very fast thermalization time. The strongest chaos is achieved in the intermediate regime with long but nonzero relaxation times. I will also briefly discuss emergence of thermalization close to integrable limits showing there are two generic mechanisms: confined and deconfined chaos.

Klaus Richter (University of Regensburg, Germany)

Quantum Chaotic Dynamics on Hyperbolic Manifolds: From OTOCs to JT gravity

Abstract:

Jackiw-Teitelboim (JT) gravity, as an exactly solvable model of two-dimensional quantum gravity, has found remarkable application in the study of holography in recent years. I will address JT gravity from a complementary perspective, namely through the lense of quantum chaos. I consider a single prototypical quantum chaotic system, a high-dimensional variant of the Hadamard-Gutzwiller model. Using semiclassical path-integral techniques for chaotic dynamics I will discuss three, intertwined topics:
(i) How, in the infinite-dimensional limit, the system's quantum Lyapunov exponent, quantifying scrambling and the growth of out-of-time-order correlators, saturates the Maldacena-Shenker-Stanford bound on chaos, supporting a possible duality with gravity.
(ii) How, in view of the factorization problem in quantum gravity, that single dynamical system can still reproduce the leading-topology one- and two-point correlation functions of JT gravity. To this end I will use a semiclassical, but exact calculation based on Selberg’s trace formula.
(iii) How subtle correlations between classical periodic orbits provide the key to the leading topology correction to the two-point function of unorientable topological gravity.

Lucas Sá (University of Cambridge, UK)

Quantum Ruelle-Pollicott resonances from weak dissipation: insights from SYK and quantum circuits

Abstract:

We discuss the theory of quantum Ruelle-Pollicott (RP) resonances and their connection to irreversible relaxation and the many timescales of quantum many-body chaos. We relate the spectral form factor to the sum of ensemble- averaged autocorrelation functions and, in generic many-body lattice systems without conservation laws, argue that all quantum RP resonances converge within the unit disk, highlighting the role of nonunitarity and the thermodynamic limit. While we conjecture this picture to be general, we analytically prove the emergence of irreversibility in the random phase model (RPM), a paradigmatic quantum circuit model. To this end, we couple it to arbitrary external local baths and compute the exact time evolution of autocorrelation functions, the dissipative form factor, out-of-time-order correlation functions, and operator size. Although the results are valid for any dissipation strength, we then focus on weak dissipation to clarify the origin of irreversibility in the unitary system. When the dissipationless limit is taken after the thermodynamic limit, the unitary quantum map develops an infinite tower of quantum RP resonances within the unit disk. Finally, we discuss the RP resonances of the Sachdev-Ye-Kitaev (SYK) model, a model of randomly interacting Majorana fermions in zero dimensions, where the large-N limit provides analytic tractability.

Lea Santos (University of Connecticut, USA)

Dissipation as a Resource: From Transient to Steady-State Chaos

Abstract:

Ginibre statistics is often taken as an indicator of dissipative chaotic dynamics. However, the Grobe–Haake–Sommers conjecture, which links Ginibre statistics to chaos and 2D Poisson statistics to integrability, can break down. This talk shows that Ginibre spectral correlations primarily reflect short-time instability and therefore signal transient chaotic dynamics rather than steady-state chaos. The quantum–classical correspondence can instead be restored through a dynamical perspective based on information scrambling, using the von Neumann entropy and out-of-time-ordered correlators, which distinguish transient from steady-state chaotic behavior. Building on this result, it is further shown that dissipation can serve as a tool to regulate the duration of chaotic dynamics and information scrambling, enabling the recovery of coherence at long times.

Ruth Shir (University of Luxembourg, Luxembourg)

From Hermitian to Non-Hermitian Quantum Chaos: Spectral Statistics in Closed and Open Systems

Abstract:

In this talk, we investigate the interplay between quantum chaos, integrability, and non-Hermiticity across closed and open quantum systems. While the spectral signatures of quantum chaos admit natural extensions to open systems, complex spectral statistics encode not only the crossover from integrability to chaos but also the degree of Hermiticity breaking. We show how Hermiticity breaking can be quantified through spectral statistics and related to the onset of quantum chaos. The resulting spectral behaviour encompasses Hermiticity breaking, integrability breaking, chaotic statistics, and a re-emergence of integrable statistics, revealing a rich structure beyond the traditional framework of Hermitian quantum chaos.

Emanuele Tirrito (EPFL, Switzerland)

Nonstabilizerness spreading in quantum many-body systems

Abstract:

Quantum computers require several distinct resources to solve computational tasks faster than classical computers. Entanglement is one such resource, but by itself it is not sufficient to guarantee a quantum advantage. Nonstabilizerness, colloquially known as magic, quantifies the departure of a quantum state from the class of stabilizer states and captures the non-Clifford resources required for universal quantum computation [1]. Understanding how magic builds up and propagates in many-body quantum systems is therefore a fundamental question, with direct implications for quantum chaos, classical simulability, and near-term quantum devices. In this talk, I will discuss the spreading of magic under genericl unitary dynamics. I will consider both Haar-random brick-wall circuits [2] and Hamiltonian dynamics, with particular emphasis on the role of conservation laws. In U(1)-symmetric systems, I will compare the growth of stabilizer Rényi entropy [3] and participation entropy across different dynamical regimes. Participation entropy becomes closely connected to symmetry-compatible notions of magic, allowing resource growth to be related to transport properties. I will show that the buildup and saturation of magic distinguish ballistic, superdiffusive, and diffusive regimes, revealing dynamical information beyond that captured by entanglement alone [4].

[1] S. Bravyi, A. Kitaev, Universal quantum computation with ideal clifford gates and noisy ancillas. Phys. Rev. A 71, 022316 (2005).
[2] X. Turkeshi, E. Tirrito, and P. Sierant, Magic spreading in random quantum circuits, Nature Comm. 16, 2575 (2025)
[3] L. Leone, S. F. E. Oliviero, and A. Hamma, Stabilizer Rényi entropy, Phys. Rev. Lett. 128, 050402 (2022).
[4] E. Tirrito, P. S. Tarabunga, D. S. Bhakuni, M. Dalmonte, P. Sierant, and X. Turkeshi, Universal spreading of nonstabilizerness and quantum transport, arXiv preprint arXiv:2506.12133

Shreya Vardhan (Caltech, USA)

Fidelity estimation from quantum many-body chaos

Abstract:

Random unitaries play a central role in recently developed shadow tomography protocols for estimating the fidelity between an experimentally prepared state and a target state. Based on similarities in the statistical properties of random unitaries and chaotic quantum many-body systems, it has recently been proposed that the latter can be used as a replacement for the former in fidelity estimation. However, physical constraints from locality and energy conservation prevent chaotic Hamiltonian dynamics from forming perfect analogs of Haar-random unitaries. We will examine the consequences of these constraints for the fidelity estimation task. We will show that conserved quantities such as energy give rise to “spoofing states” which appear to have O(1) fidelity with the target state despite being orthogonal to it, and characterize the physical conditions under which the protocol nevertheless performs well. Our analysis is based on the emergence of “Scrooge ensembles” in chaotic quantum many-body dynamics, and provides a concrete example of the physical consequences of these ensembles. Based on work in progress with Wai-Keong (Dariel) Mok and Thomas Schuster.

Lev Vidmar (Jožef Stefan Institute and University of Ljubljana, Slovenia)

Ergodicity Breaking Transitions as Quantum Phase Transitions Above Ground States

Abstract:

Beni Yoshida (Perimeter Institute for Theoretical Physics, Canada)

Aspects of tripartite Haar random states

Abstract:

We show that no EPR-like bipartite entanglement can be distilled from a tripartite Haar random state by local unitaries or local operations when each subsystem has fewer than half of the total qubits. Viewing it as a bipartite quantum error-correcting code, this implies that neither the output subsystem supports any non-trivial logical operator, exhibiting breakdown of complementary recovery. We then discuss a physical interpretation in the AdS/CFT correspondence, indicating that a connected entanglement wedge does not necessarily imply bipartite entanglement, contrary to a previous belief. This also suggests an interpretation where a closed baby universe emerges as logical degrees of freedom that cannot be accessed from either boundary alone, circumventing previous no-go arguments. Finally, we propose a general method to evaluate distillable entanglement for chaotic spin systems.