Conference

Neural quantum states have emerged as a powerful framework for representing classical probability distributions derived from quantum many-body systems. However, fundamental questions remain about their computational learnability, particularly for physically relevant quantum states. We identify and analyze a fundamental obstacle to the efficient learning of locally indistinguishable quantum states using neural network architectures. We introduce a restricted statistical query (SQ) learning model that captures the essential features of noisy gradient descent training in autoregressive models such as recurrent neural networks networks. Within this framework, we prove that locally indistinguishable states cannot be learned in polynomial time, establishing an inherent computational barrier. Conversely, we show that distributions with finite Markov length remain efficiently learnable in the restricted SQ model. We demonstrate the practical implications through numerical experiments on paradigmatic examples of strong-to-weak symmetry breaking, including ferromagnetic ground states and syndrome distributions of quantum error-correcting codes beyond their decoding thresholds. Our findings suggest that the hardness of neural quantum state learning could serve as a novel computational probe for identifying mixed-state phase transitions and decoding thresholds in both numerical simulations and experiments.

I will talk about effective description of quantum dynamics for systems interacting with thermal environment. I will focus on a prototypical example of Brownian Motion and show how one can leverage symmetries to build a general effective path integral description with quantum/thermal corrections using methods of Non-Equilibrium QFT.

Recent advances have argued how gravitational entropies can be computed directly from Lorentzian path integrals, avoiding the problems of Euclidean methods associated with the conformal factor problem that makes a path integral over Euclidean geometries manifestly ill defined. In particular, the de Sitter horizon entropy can be recovered from a real-time path integral that computes the dimension of the Hilbert space associated with a spatial ball. Similarly, the swap entropy of an evaporating black hole (central to the replica paradigm resolution of the black hole information paradox) can be computed in this way. Quantum Regge Calculus, a lattice-like approach to quantum gravity, enables concrete realizations of these scenarios, providing insights beyond continuum methods. This perspective clarifies aspects of gravitational path integrals and may have implications for approaches such as causal dynamical triangulations and spin foams, where Regge-like formulations play a fundamental role.

For physical problems, the well-posedness of initial-boundary-value problems is crucial. Asking this question in general relativity, is is furthermore important to understand the necessary gauge choices and constraints. As different groups and communities ask similar questions coming from different backgrounds, it is important to be able to translate between different formulations. In this talk I will explain the approach I have taken so far, based on the 3+1 Einstein system, and highlight connections to other works, hoping to spark discussions with people from other areas of research.

:We revisit the Holographic duality between SU(N)κ Chern-Simons theory and the A-model Topological String Theory. We develop a strategy to systematically compute the large N saddles for correlation functions of Wilson lines in antisymmetric powers Λ•C N of the fundamental representation. The mathematical structures which appear in the calculation match in detail the data of dual A-model D-branes. Me and Sergio would like to give more of a two-part talk

We revisit the Holographic duality between SU(N) Chern-Simons theory and the A-model Topological String Theory. We develop a strategy to systematically compute the large N saddles for correlation functions of Wilson lines in antisymmetric powers of the fundamental representation. The mathematical structures which appear in the calculation match in detail the data of dual A-model D-branes. Suriyah Rajalingam's talk is giving another perspective about the same project.

Ordered structures that tile the plane in an aperiodic fashion - thus lacking translational symmetry - have long been considered in the mathematical literature. A general method for the construction of quasicrystals is known as *cut-and-project* ($\mathsf{CNP}$ for short), where an irrational slice ''cuts'' a higher-dimensional space endowed with a lattice and suitably chosen lattice points are further ''projected'' down onto the slice to form the vertices of the quasicrystal. However, all of the known examples of $\mathsf{CNP}$ quasicrystals are Euclidean. In this talk, after presenting the main ingredients of the Euclidean prescription, we will extend it to Lorentzian spacetimes and develop Spacetime $\mathsf{CNP}$. This will allow us to discuss the first-ever examples of spacetime quasicrystals, one in (1+1)- and another in (1+3)-dimensional spacetime. Finally, we will argue why the latter construction might be relevant for *our Lorentzian spacetime*. In particular, we shall appreciate how the picture of a quasi-crystalline spacetime could provide a potentially new string-compactification scheme that can naturally accommodate for the hierarchy problem and the smallness of our cosmological constant. Lastly, we will briefly comment on its relevance to quantum gravity; first, as a conformal Lorentzian structure of no intrinsic scale, and second through the connection of quasicrystals to quantum error-correcting codes.

After a brief reminder/introduction of relevant facts about 4d N=2 SQFTs (BPS things, twisting, wall-crossing, line defects) I will try to sketch our proposal for the category of 1/2-BPS line defects in terms of certain bimodules over Cohomological Hall algebra of the BPS quiver; maybe even say a few words about why we believe it is a correct thing to do.

Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum error correction (QEC) can recover the HL in various scenarios. A notable example is estimating a Pauli-Z signal under bit-flip noise using the repetition code, which is both optimal for metrology and robust against noise. However, previous protocols often assume noise affects only the signal accumulation step, while the QEC operations---including state preparation and measurement---are noiseless. To overcome this limitation, we study fault-tolerant quantum metrology where all qubit operations are subject to noise. We focus on estimating Pauli-Z signal with single-qubit bit-flip noise and measurement noise. We propose a fault-tolerant metrological protocol where a repetition code is prepared via repeated syndrome measurements and logically measured after being merged into a thin surface code. We demonstrate the existence of an error threshold, below which errors are effectively suppressed and the HL is attained.

We consider the problem of simulating dynamics of classical nonlinear dissipative systems with N>>1 degrees of freedom. To make the problem tractable for quantum computers, we add a weak Gaussian noise to the equation of motion and the initial state. Our main result is an end-to-end quantum algorithm for simulating the noisy dynamics of nonlinear systems satisfying certain sparsity and divergence-free conditions. For any constant nonzero noise rate, the quantum runtime scales polynomially with log(N), evolution time, inverse error tolerance, and the relative strength of nonlinearity and dissipation.

In this talk, I will explore the fascinating landscape of minimal assumptions in quantum cryptography—how little we need to assume to build secure quantum protocols. We will cover key cryptographic primitives including quantum encryption, signatures, and money, and show how these primitives imply the existence of one-way puzzles, a quantum analogue of classical one-way functions. I will also highlight the utility of one-way puzzles and discuss concrete assumptions that enable their realization, revealing intriguing connections with quantum advantage.