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Speakers and Abstracts

**Workshop on Quantum Information and Spacetime****December 6-8, 2021**

**ChunJun (Charles) Cao**, *University of Maryland
Title: *Tensor Network and Approximate Holographic Codes

*Abstract:*Although it is known that AdS/CFT as a quantum erasure correction code is only approximate, there is still much to learn about the precise bulk physical consequences of deviating from exact erasure correction codes. In this talk, I will take initial steps in addressing this gap of knowledge and discuss an intuitive tensor network model that corresponds to a tunable class of approximate holographic codes. We find that features analogous to gravity can emerge when "quantum noise" is injected into such holographic stabilizer codes.

**Jordan Cotler**, *Harvard University
Title: *Quantum Complexity of Experiments

*Abstract:*We introduce a theoretical framework to study experimental physics using quantum complexity theory. This allows us to address: what is the computational complexity of an experiment? For several 'model' experiments, we prove that there is an exponential savings in resources if the experimentalist can entangle apparatuses with experimental samples. A novel example is the experimental task of determining the symmetry class of a time evolution operator for a quantum many-body system. Some of our complexity advantages have been realized on Google's Sycamore processor, demonstrating a real-world advantage for learning algorithms with a quantum memory.

**Andru Gheorghiu***,

*ETH Zurich*

Title:On Estimating the Entropy of Shallow Circuit Outputs

Title:

*Abstract:*Computing the entropy of probability distributions and quantum states is a fundamental task in information processing. In this talk I'll discuss recent work with Matty Hoban (arXiv:2002.12814) in which we show that estimating the entropy of quantum states (or probability distributions) produced by shallow quantum circuits is at least as hard as the Learning-With-Errors problem, and thus believed to be intractable for efficient quantum computation. This shows that circuits do not need to be complex to render the computation of entropy a difficult task. We also give complexity-theoretic evidence that the problem is not as hard as its counterpart with general polynomial-size circuits, seemingly occupying an intermediate hardness regime. As a potential application to quantum gravity research, we relate these results to the complexity of the bulk-to-boundary dictionary of AdS/CFT.

**Felix M. Haehl**, *Institute for Advanced Study
Title: *Spin Glasses and Holography

*Abstract:*The connections between disordered quantum systems (specifically the SYK model), ensemble averaging, and two-dimensional dilaton gravity underlie much of the recent progress on holography and quantum gravity. I will discuss simple disordered systems, which exhibit spin glass order and allow for an analytical treatment in certain limits. I will focus on some of their properties that are of interest from a gravitational point of view (such as thermodynamics and quantum chaos) and propose a holographic interpretation.

**Thomas Hertog**, *Katholieke Universiteit, Leuven
Title: *A Page-like Transition in Quantum Cosmology

*Abstract:*

**Ling-Yan (Janet) Hung***, *Fudan University
Title: *Bending the Padic Tensor Network and Emergent Einstein Equation

*Abstract:*We take the tensor network describing explicit p-adic CFT partition functions proposed in 1902.01411, and consider boundary conditions of the network describing a deformed Bruhat-Tits (BT) tree geometry. We demonstrate that this geometry satisfies an emergent graph Einstein equation in a unique way that is consistent with the bulk effective matter action encoding the same correlation function as the tensor network, at least in the perturbative limit order by order away from the pure BT tree. Moreover, the (perturbative) definition of the graph curvature in the Mathematics literature naturally emerges from the consistency requirements of the emergent Einstein equation. The emergent "metric" in the tenor network can be interpreted as a Fisher information between states.

**Luca Iliesiu**, *Stanford University
Title: *The Volume of the Black Hole Interior at Late Times

*Abstract:*Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this paper, we provide a path integral definition of the volume of the black hole interior and study it at arbitrarily late times for black holes in various models of two-dimensional gravity. Because of a novel universal cancellation between the contributions of the semi-classical black hole spectrum and some of its non-perturbative corrections, we find that, after a linear growth at early times, the length of the interior saturates at a time, and towards a value, that is exponentially large in the entropy of the black hole. I will additionally discuss why the volume is a self-averaging quantity and the consequences for gravitational theories in which the factorization puzzle is resolved. This provides non-perturbative evidence for the complexity equals volume proposal since complexity is also expected to plateau at the same value and at the same time.

**Shaokai Jian**, *Brandeis University
Title: *Late Time von Neumann Entropy and Measurement-induced Phase Transition

*Abstract:*We present our studies on the late-time von Neumann entropy and its transition in Brownian SYK models. Without measurement, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the calculation. In the presence of measurements, we show that a continuous von Neumann entropy transition from volume-law to area-law occurs at the point of replica symmetry breaking.

**Jorrit Kruthoff**, *Stanford University
Title: *Gravity Factorized

*Abstract:*In this talk I will discuss models of two-dimensional gravity that resolve the factorization puzzle and have a discrete spectrum, whilst retaining a semiclassical description. A novelty of these models is that they contain non-trivially correlated spacetime branes or, equivalently, nonlocal interactions in their action. Demanding factorization fixes almost all brane correlators, and the exact geometric expansion of the partition function collapses to only two terms: the black hole saddle and a subleading "half-wormhole" geometry, whose sum yields the desired discrete spectrum. Non-perturbatively, the correlated branes are a certain multitrace interaction and I will show how it results in a factorizing theory with discrete spectrum. I will end with a few comments on the relevance of wormholes and higher dimensions.

**Adam Levine**, *Institute for Advanced Study
Title: *Scattering Strings Off Quantum Extremal Surfaces

*Abstract:*I will discuss recent work on a Hayden & Preskill like setup for both maximally chaotic and sub- maximally chaotic quantum field theories. I will discuss computations of various quantum information measures on the boundary that tell us when a particle has left the entanglement wedge of a given region. In a maximally chaotic theory, these measures indicate a sharp transition where the particle enters the wedge exactly when the insertion is null separated from the quantum extremal surface for r. For sub-maximally chaotic theories, we find a smoothed crossover at a delayed time given in terms of the smaller Lyapunov exponent and dependent on the time-smearing scale of the probe excitation. I will speculate on the extent to which our results reveal properties of the target of the probe excitation as a “stringy quantum extremal surface” or simply quantify the probe itself thus giving a new approach to studying the notion of longitudinal string spreading.

**Alexey Milekhin**, *University of California, Santa Barbara
Title: *Charge Fluctuation Entropy of Hawking Radiation: A Replica-free Way to Find Large Entropy

*Abstract:*We study the fluctuation entropy for two-dimensional matter systems with an internal symmetry coupled to Jackiw--Teitelboim(JT) gravity joined to a Minkowski region. The fluctuation entropy is the Shannon entropy associated with probabilities of finding a particular charge in a region. We first consider a case where the matter has a global symmetry. We find that the fluctuation entropy of Hawking radiation shows an unbounded growth and exceeds the entanglement entropy in the presence of islands. This indicates that the global symmetry is violated. We then discuss the fluctuation entropy for matter coupled to a two-dimensional gauge field. We find a lower bound on the gauge coupling g_0 in order to avoid a similar issue. Also, we point out a few puzzles related to the island prescription in presence of a gauge symmetry.

Based on: https://arxiv.org/abs/2109.03841 in collaboration with Amirhossein Tajdini

**Tatsuma Nishioka***, *Yukawa Institute for Theoretical Physics, Kyoto University
Title: *Topological Pseudo Entropy

*Abstract:*Recently, a new quantum information measure called pseudo entropy was introduced as a generalization of entanglement entropy to quantify quantum correlation between initial and final states in a time-dependent system. In this talk, I will examine some aspects of pseudo entropy in topological field theory and conformal field theory (CFT). In three-dimensional Chern-Simons theory, pseudo entropy can be given by a partition function on a three-sphere with Wilson loops in a similar manner to topological entanglement entropy. I will also show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional CFTs, and leverage the equivalence to calculate the pseudo entropies in particular examples. Furthermore, I will define a pseudo entropy extension of the left-right entanglement entropy in two-dimensional boundary CFTs and derive a universal formula for a pair of arbitrary boundary states.

**Juan Pedraza***, *University of Barcelona
Title: *Lorentzian Threads and Holographic Complexity

*Abstract:*The continuous min flow-max cut principle is used to reformulate the 'complexity=volume' conjecture using Lorentzian flows. Conceptually, discretized flows are interpreted in terms of `gatelines', one-dimensional time-like curves that connect layers of a tensor network grid in the bulk spacetime. We imagine each gateline represents a unitary operation such that the bulk calculation for complexity matches its information-theoretic definition. The bulk symplectic potential provides a 'canonical' flow configuration characterizing perturbations around arbitrary CFT states. Its consistency requires the bulk to obey linearized Einstein's equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating a notion of 'spacetime complexity'. Finally, we explain the need for a more general measure of complexity that captures the role of suboptimal flows or tensor network configurations. Based on 2105.12735 and 2106.12585.

**Geoffrey Penington**, *University of California, Berkeley & Institute for Advanced Study
Title: *One-Shot Holography

*Abstract:*

**Suvrat Raju***, * International Centre for Theoretical Sciences, Bengaluru
Title: *Failure of the Split Property in Gravity and the Information Paradox

*Abstract:*In an ordinary quantum field theory, the "split property" implies that the state of a system can be specified independently on a bounded subregion of a Cauchy slice and its complement. This property does not hold for theories of gravity. It can be shown in specific examples that observables near the boundary of a Cauchy slice uniquely fix the state on the entire slice. The original formulation of the information paradox explicitly assumed the split property and we follow this assumption to isolate the precise error in Hawking's argument. A similar assumption also underpins the monogamy paradox of Mathur and AMPS. Finally the same assumption is used to support the common idea that the entanglement entropy of the region outside a black hole should follow a Page curve. It is for this reason that recent computations of the Page curve have been performed only in nonstandard theories of gravity, which include a nongravitational bath and massive gravitons. We discuss possibilities for coarse graining that might lead to a Page curve in standard theories of gravity.

**Phil Saad**, * Institute for Advanced Study
Title: *Comments on Wormholes and Factorization

*Abstract:*

**Arvin Shahbazi-Moghaddam**, *Stanford University
Title: * Island Finder and Singularity Theorem

*Abstract:*Identifying an entanglement island requires exquisite control over the entropy of quantum fields, which is available only in toy models. I will present a set of sufficient conditions that guarantee the existence of an island and place an upper bound on the entropy computed by the island rule. I will then discuss a new quantum singularity theorem.

**Nicole Yunger Halpern**, *NIST & University of Maryland
Title: *Proofs of Two Brown-and-Susskind Complexity Conjectures

*Abstract:*In 2017, Adam Brown and Lenny Susskind posed two conjectures about

quantum complexity, the difficulty of preparing a desired many-body state

from a simple tensor product: (1) Under chaotic evolutions, complexity

grows linearly for a time exponential in the system size. (2) A resource

theory for uncomplexity can be defined. (Resource theories are simple

models, developed in quantum information theory, for situations in which

constraints restrict the operations one can perform. Uncomplexity is a lack

of complexity, useful in inputs to quantum computations.) We prove both

conjectures correct, using tools from quantum information theory, algebraic

geometry, and differential topology.

References:

1) Haferkamp, Faist, Kothakonda, Eisert, and NYH, arXiv:2106.05305 (2021).

2) NYH, Kothakonda, Haferkamp, Munson, Faist, and Eisert, arXiv:2110.11371 (2021).

**Pengfei Zhang***, *Caltech
Title: *Branching Time in SYK-like Models

*Abstract:*The branching time in SYK-like models is defined as the average time separation of rungs when computing the out-of-time-order correlator. We argue that a parametrically large branching time is necessary to obtain holographic models with non-trivial bulk dynamics. In this work, we establish a bound on the branching time for SYK-like models. Thus, such models are unlikely candidates for sub-AdS holography. We also derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime in the weak coupling limit.

**Ying Zhao**, *University of California, Santa Barbara
Title: *Quantum Circuit and Collisions in the Black Hole Interior

*Abstract:*

** Zoom talk *