Talk 44 - Large N von Neumann Algebras and the renormalization of Newton's constant

• Elliot Gesteau (Caltech)

Room: PI/1-100 - Theatre In holography, the quantum extremal surface formula relates the entropy of a boundary state to the sum of two terms: the area term and the entropy of bulk fields inside the entanglement wedge. As the bulk effective field theory suffers from UV divergences, the second term must be regularized. It has been conjectured since the work of Susskind and Uglum that the renormalization of Newton’s constant in the area term exactly cancels the difference between different choices of regularization for bulk entropy. In this talk, I will explain how the recent developments on von Neumann algebras appearing in the large N limit of holography allow to prove this claim within the framework of holographic quantum error correction, and to reinterpret it as an instance of the ER=EPR paradigm. This talk is based on the paper arXiv:2302.01938.

Talk 88 - Type II_1 algebras for local subregions in quantum gravity

• Antony Speranza (University of Illinois, Urbana-Champaign)

Room: PI/1-100 - Theatre We argue that generic local subregions in semiclassical quantum gravity are associated with von Neumann algebras of type II_1, extending recent work by Chandrasekaran et.al. beyond subregions bounded by Killing horizons. The subregion algebra arises as a crossed product of the type III_1 algebra of quantum fields in the subregion by the flow generated by a gravitational constraint operator. We conjecture that this flow agrees with the vacuum modular flow sufficiently well to conclude that the resulting algebra is type II_\infty, which projects to a type II_1 algebra after imposing a positive energy condition. The entropy of semiclassical states on this algebra can be computed and shown to agree with the generalized entropy by appealing to a first law of local subregions. The existence of a maximal entropy state for the type II_1 algebra is further shown to imply a version of Jacobson’s entanglement equilibrium hypothesis. We discuss other applications of this construction to quantum gravity and holography, including the quantum extremal surface prescription and the quantum focusing conjecture.

Talk 124 - von Neumann algebras in JT gravity with matter

• David Kolchmeyer (Massachusetts Institute of Technology)

Room: PI/1-100 - Theatre We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II infinity factors. These algebras provide a precise notion of the entanglement wedge away from the semiclassical limit.

Talk 61 - Horizons are Watching You

• Gautam Satishchandran (Princeton University)

Room: PI/1-100 - Theatre We show that if a massive (or charged) body is put in a quantum superposition of spatially separated states in the vicinity of any (Killing) horizon, the mere presence of the horizon will eventually destroy the coherence of the superposition in a finite time. This occurs because, in effect, the long-range fields sourced by the superposition register on the black hole horizon which forces the emission of entangling “soft gravitons/photons” through the horizon. This enables the horizon to harvest “which path” information about the superposition. We provide estimates of the decoherence time for such quantum superpositions in the presence of a black hole and cosmological horizon. Finally, we further sharpen and generalize this mechanism by recasting the gedankenexperiment in the language of (approximate) quantum error correction. This yields a complementary picture where the decoherence is due to an “eavesdropper” (Eve) in the black hole attempting to obtain "which path" information by measuring the long-range fields of the superposed body. We explicitly compute the quantum fidelity to determine the amount of information such an Eve can obtain and show, by the information-disturbance tradeoff, a direct relationship between the information gained by Eve and the decoherence of the superposition in the exterior. In particular, we show that the decoherence of the superposition corresponds to the "optimal" measurement made by Eve in the black hole interior.

An SYK model with a scaling similarity.

• Juan Maldacena (Institute for Advanced Study)

Room: PI/1-100 - Theatre We describe supersymmetric SYK models which display a scaling similarity at low temperatures, rather than the usual conformal behavior. We discuss the large N equations, which were studied previously as uncontrolled approximations to other models. We also present a picture for the physics of the model which suggest that the relevant low energy degrees of freedom are almost free. We also searched for a spin glass phase but we found no replica symmetry breaking solutions.

Petz recovery from subsystems in conformal field theory

• Shreya Vardhan (Stanford University)

Room: PI/1-100 - Theatre We probe the multipartite entanglement structure of the vacuum state of a CFT in 1+1 dimensions, using recovery operations that attempt to reconstruct the density matrix in some region from its reduced density matrices on smaller subregions. We use an explicit recovery channel known as the twirled Petz map, and study distance measures such as the fidelity, relative entropy, and trace distance between the original state and the recovered state. One setup we study in detail involves three contiguous intervals A, B and C on a spatial slice, where we can view these quantities as measuring correlations between A and C that are not mediated by the region B that lies between them. We show that each of the distance measures is both UV finite and independent of the operator content of the CFT, and hence depends only on the central charge and the cross-ratio of the intervals. We evaluate these universal quantities numerically using lattice simulations in critical spin chain models, and derive their analytic forms in the limit where A and C are close using the OPE expansion. We also compare the mutual information between various subsystems in the original and recovered states, which leads to a more qualitative understanding of the differences between them. Further, we introduce generalizations of the recovery operation to more than three adjacent intervals, for which the fidelity is again universal with respect to the operator content.

Talk 67 - Irreversibility, QNEC, and defects

• Gonzalo Torroba (Centro Atomico Bariloche, Argentina)

Room: PI/1-100 - Theatre In this talk, we will first present an analysis of infinitesimal null deformations for the entanglement entropy, which leads to a major simplification of the proof of the C, F and A-theorems in quantum field theory. Next, we will discuss the quantum null energy condition (QNEC) on the light-cone. Finally, we combine these tools in order to establish the irreversibility of renormalization group flows on planar d-dimensional defects, embedded in D-dimensional conformal field theories. This proof completes and unifies all known defect irreversibility theorems for defect dimensions below d=5. The F-theorem on defects (d=3) is a new result using information-theoretic methods. The geometric construction connects the proof of irreversibility with and without defects through the QNEC inequality in the bulk, and makes contact with the proof of strong subadditivity of holographic entropy taking into account quantum corrections.

Talk 41 - Mutual Information of Holographic Generalized Free Fields

• Pedro Jorge Martinez (Instituto Balseiro)

Room: PI/1-100 - Theatre We study Generalized Free Fields (GFF) from the point of view of information measures. We begin by reviewing conformal GFF, their holographic representation, and the multiple possible assignations of algebras to a single spacetime region that arise in these theories. We will focus on manifestations of these features present in the Mutual Information (MI) of holographic GFF. First, we show that the MI can be expected to be finite even if the AdS dual space is of infinite volume. Then, we present the long-distance limit of the MI for regions with arbitrary boundaries in the light cone for the causal and entanglement wedge algebras. The pinching limit of these surfaces shows the GFF behaves as an interacting model from the MI point of view. The entanglement wedge algebra choice allows these models to ``fake'' causality, giving results consistent with their role in the description of large N models. Finally, we explore the short distance limit of the MI. Interestingly, we find that the GFF has a leading volume term rather than an area term and a logarithmic term in any dimension rather than only for even dimensions as in ordinary CFTs. We also find the dependence of some subleading terms on the conformal dimension of the GFF.

Talk 110 - NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians

• Valérie Bettaque (Brandeis University)

Room: PI/1-100 - Theatre Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a generalization of MERA, DMERA, and branching MERA networks with the constraints of spatial locality removed. We argue that the architecture is potentially expressive enough to capture the entanglement and complexity of the ground space of the SYK model, thus making it a suitable variational ansatz, but we leave a detailed study of SYK to future work. We further explore the architecture in the special case in which the tensors are random Clifford gates. Here the architecture can be viewed as the encoding map of a random stabilizer code. We introduce a family of codes inspired by the SYK model which can be chosen to have constant rate and linear distance at the cost of some high weight stabilizers. We also comment on potential similarities between this code family and the approximate code formed from the SYK ground space.

Talk 106 - Holographic Codes from Hyperinvariant Tensor Networks

• Alexander Jahn (Free University of Berlin)

Room: PI/1-100 - Theatre Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.

Talk 71 - Topological Toy Models for the Emergence of Spacetime.

• Annie Wei (Massachusetts Institute of Technology)

Room: PI/1-100 - Theatre We study entanglement entropy in (2+1)-dimensional gravity as a window into larger open questions regarding entanglement entropy in gravity. (2+1)-dimensional gravity can be rewritten as a topological field theory, which makes it a more tractable model to study. In these topological theories, there remain key questions which we seek to answer in this work, such as the questions 1) What is the entropy of the physical algebra of observables in a subregion, 2) How do we define a factorization map such that the entropy of the resulting factors agrees with this algebraic entropy, and 3) Can we use these insights to build a tensor network that exhibits non-commuting areas? We investigate non-Abelian toric codes / Levin-Wen models as a toy model for black hole entropy in Chern Simons theory. These differ from the usual model in that the stabilizers are implemented as constraints. By enforcing constraints for both Gauss' Law and the flatness of the gauge field, we obtain a choice of algebra that contains only topological operators. The desirable properties of this model are twofold: first, we produce the finiteness of black hole entropy described in previous literature while providing a natural algebraic motivation for this result. Secondly, we obtain non-commuting area operators on a toy model with the topology of a torus.

Talk 16 - Toward random tensor networks and holographic codes in CFT

• Jeevan Chandra Namburi (Cornell University)

Room: PI/1-100 - Theatre In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a random tensor network. The geometry of the tensor network corresponds to a spatial slice in the holographic dual, with the tensors discretizing the radial direction. In spherically symmetric states in any dimension and more general states in 2d CFT, this leads to a holographic error-correcting code, defined in terms of OPE data, that can be systematically corrected beyond the random tensor approximation. The code is shown to be isometric for light operators outside the horizon, and non-isometric inside, as expected from general arguments about bulk reconstruction. The transition at the horizon occurs due to a subtle breakdown of the Virasoro identity block approximation in states with a complex interior.

Holographic Quantum Simulation with Atoms and Photons

• Monika Schleier-Smith (Stanford University)

Room: PI/1-100 - Theatre

Complexity = (almost) anything

• Robert Myers (Perimeter Institute)

Room: PI/1-100 - Theatre

Talk 120 - Security of position-based cryptography limits Hamiltonian simulation via holography

• Harriet Apel (University College London)

Room: PI/1-100 - Theatre We investigate the link between position-based quantum cryptography (PBQC) and holography established in [May19] using holographic quantum error correcting codes as toy models. If the "temporal" scaling of the AdS metric is inserted by hand into the toy model via the bulk Hamiltonian interaction strength we recover a toy model with consistent causality structure. This leads to an interesting implication between two topics in quantum information: if position-based cryptography is secure against attacks with small entanglement then there are new fundamental lower bounds for resources required for one Hamiltonian to simulate another.

Talk 10 - Constraints on physical computers in holographic spacetimes

• Alex May (Perimeter Institute)

Room: PI/1-100 - Theatre Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than $O(2^n)$. To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as the inputs and description of the unitary to be run are not too large. We then prove a bound on quantum processors which shows many unitaries cannot be implemented inside the black hole, and further show some of these have short descriptions and act on small systems. These unitaries with short descriptions must be computationally forbidden from happening inside the black hole.

talk 30 - Measurement-based quantum simulation of Abelian lattice gauge theories

• Hiroki Sukeno (Stony Brook University)

Room: PI/1-100 - Theatre Quantum simulation of lattice gauge theory is expected to become a major application of near-term quantum devices. In this presentation, I will talk about a quantum simulation scheme for lattice gauge theories motivated by Measurement-Based Quantum Computation [1], which we call Measurement-Based Quantum Simulation (MBQS). In MBQS, we consider preparing a resource state whose entanglement structure reflects the spacetime structure of the simulated gauge theory. We then consider sequentially measuring qubits in the resource state in a certain adaptive manner, which drives the time evolution in the Hamiltonian lattice gauge theory. It turns out that the resource states we use for MBQS of Wegner’s models possess topological order protected by higher-form symmetries. These higher-form symmetries are also practically useful for error correction to suppress contributions that violate gauge symmetries. We also discuss the relation between the resource state and the partition function of Wegner’s model. This presentation is based on my work with Takuya Okuda [2]. [1] R. Raussendorf and H. J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86, 5188 (2001) [2] H. Sukeno and T. Okuda, Measurement-based quantum simulation of Abelian lattice gauge theories, arXiv:2210.10908

(VIRTUAL) Talk 63 - Measurement-induced phase transition in teleportation and wormholes

• Alexey Milekhin (University of California, Santa Barbara)

Room: PI/1-100 - Theatre We demonstrate that some quantum teleportation protocols exhibit measurement induced phase transitions in Sachdev-Ye-Kitaev model. Namely, Kitaev-Yoshida and Gao-Jafferis-Wall protocols have a phase transition if we apply them at a large projection rate or at a large coupling rate respectively. It is well-known that at small rates they allow teleportation to happen only within a small time-window. We show that at large rates, the system goes into a new steady state, where the teleportation can be performed at any moment. In dual Jackiw-Teitelboim gravity these phase transitions correspond to the formation of an eternal traversable wormhole. In the Kitaev-Yoshida case this novel type of wormhole is supported by continuous projections. Based on https://arxiv.org/abs/2210.03083

Talk 79 - Measurements in holographic systems: current status and future directions

• Grado-White Brianna (Brandeis University)

Room: PI/1-100 - Theatre Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual boundary theory. At the same time, we know that local projective measurements tend to destroy entanglement. This leads to a natural question: what happens to the holographic bulk spacetime if we perform strong local projective measurements on a subsystem $A$ of the boundary? In particular, I will explain the effect of measurements performed both on subsystems of a single CFT in its vacuum state, which is dual to pure AdS spacetime, and on various subsystems of two copies of a CFT in the thermofield double state, which is dual to a double-sided AdS black hole. The post-measurement bulk is cut off by end-of-the-world branes and is dual to the complementary unmeasured subsystem $A^c$. The measurement triggers an entangling/disentangling phase transition in the boundary theory, corresponding to a connected/disconnected phase transition in the bulk dual geometry. Interestingly, the post-measurement bulk includes regions that were part of the entanglement wedge of $A$ before the measurement, signaling a transfer of information from the measured to the unmeasured subsystem analogous to quantum teleportation. Finally, I will discuss open questions and future directions related to our work, with a particular focus on its consequences for the complexity of bulk reconstruction.

Talk 17 - Channeling quantum criticality

• Yijian Zou (Stanford University)

Room: PI/1-100 - Theatre We analyze the effect of decoherence, modelled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a "g-function" in conformal field theory (CFT), allowing us to define a notion of renormalization group (RG) flow (or "phase transitions") between quantum channels. We also find that the entropy of a subsystem in the decohered state has a subleading logarithmic scaling with subsystem size, and we relate it to correlation functions of boundary condition changing operators in the CFT. Finally, we find that the subsystem entanglement negativity, a measure of quantum correlations within mixed states, can exhibit log scaling or area law based on the RG flow. When the channel corresponds to a marginal perturbation, the coefficient of the log scaling can change continuously with decoherence strength. We illustrate all these possibilities for the critical ground state of the transverse-field Ising model, in which we identify four RG fixed points of dephasing channels and verify the RG flow numerically. Our results are relevant to quantum critical states realized on noisy quantum simulators, in which our predicted entanglement scaling can be probed via shadow tomography methods.

Euclidean Wormholes and Gravity as an Average

• Alexander Maloney (McGill University)

Room: PI/1-100 - Theatre

Sparse random Hamiltonians are quantumly easy

• Chi-Fang (Anthony) Chen (Caltech)

Room: PI/1-100 - Theatre

Talk 29 - Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible

• Flaminia Giacomini (ETH Zurich)

Room: PI/1-100 - Theatre When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which is inherently classical. Fundamentally, this tension should result in breaking one of the fundamental principles of quantum theory or general relativity, but it is usually hard to assess which one without resorting to a specific model. Here, we answer this question in a theory-independent way using General Probabilistic Theories (GPTs). We consider the interactions of the gravitational field with a single matter system, and derive a no-go theorem showing that when gravity is classical at least one of the following assumptions needs to be violated: (i) Matter degrees of freedom are described by fully non-classical degrees of freedom; (ii) Interactions between matter degrees of freedom and the gravitational field are reversible; (iii) Matter degrees of freedom back-react on the gravitational field. We argue that this implies that theories of classical gravity and quantum matter must be fundamentally irreversible, as is the case in the recent model of Oppenheim et al. Conversely if we require that the interaction between quantum matter and the gravitational field are reversible, then the gravitational field must be non-classical.

Talk 81 - Testing the quantumness of gravity without entanglement

• Ludovico Lami (University of Amsterdam)

Room: PI/1-100 - Theatre We propose a conceptually new class of dynamical experiments whose goal is to falsify the hypothesis that an interaction between quantum systems is mediated by a purely local classical field. The systems we study implement a dynamics that cannot be simulated by means of local operations and classical communication (LOCC), even when no entanglement is ever generated at any point in the process. Using tools from quantum information theory, we estimate the maximal fidelity of simulation that a local classical interaction could attain while employing only LOCC. Under our assumptions, if an experiment detects a fidelity larger than that calculated threshold, then a local classical description of the interaction is no longer possible. As a prominent application of this scheme, we study a general system of quantum harmonic oscillators initialised in normally distributed coherent states and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the calculation of the above bound on the maximal LOCC simulation fidelity for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalised states of motion nor the detection of entanglement.

Type I Von Neumann algebras from bulk path integrals: RT as entropy without AdS/CFT

• Donald Marolf (University of California, Santa Barbara)

Talk 22 - Microstates of a 2d Black Hole in string theory

• Panos Betzios (University of British Columbia)

Room: PI/1-100 - Theatre We analyse models of Matrix Quantum Mechanics in the double scaling limit that contain non-singlet states. The finite temperature partition function of such systems contains non-trivial winding modes (vortices) and is expressed in terms of a group theoretic sum over representations. We then focus on the model of Kazakov-Kostov-Kutasov when the first winding mode is dominant. In the limit of large representations (continuous Young diagrams), and depending on the values of the parameters of the model such as the compactification radius and the string coupling, the dual geometric background corresponds either to that of a long string (winding mode) condensate or a 2d (non-supersymmetric) semi-classical Black Hole competing with the thermal linear dilaton background. In the matrix model we are free to tune these parameters and explore various regimes of this phase diagram. Our construction allows us to identify the origin of the microstates of the long string condensate/2d Black Hole arising from the non trivial representations.

Talk 33 - Microscopic origin of the entropy of black holes

• Javier Magan (Instituto Balseiro)

Room: PI/1-100 - Theatre We present a construction in which the origin of black hole entropy gets clarified. We start by building an infinite family of geometric microstates for black holes in general relativity. This construction naively overcounts the Bekenstein-Hawking entropy. We then describe how wormholes in the Euclidean path integral for gravity cause these states to have exponentially small, but universal, overlaps. These overlaps recontextualize the Gibbons-Hawking thermal partition function. We finally show how these results imply that the microstates span a Hilbert space of log dimension equal to the Bekenstein-Hawking entropy, and how they clarify the nature of the volumes of Eisntein-Rosen bridges.

Talk 125 - Partition function of a volume of space

• Manus Visser (University of Cambridge)

Room: PI/1-100 - Theatre We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The result is the exponential of the Bekenstein-Hawking entropy associated with the area of the saddle ball boundary, and is reliable within effective field theory provided the mild curvature singularity at the ball boundary is regulated by higher curvature terms. This generalizes the classic Gibbons-Hawking computation of the de Sitter entropy for the case of positive cosmological constant and unconstrained volume, and hence exhibits the holographic nature of nonperturbative quantum gravity in generic finite volumes of space.

Talk 74 - The Riemann Zeta Function, Poincare Recurrence, and the Spectral Form Factor

• Michael Winer (University of Maryland)

Room: PI/1-100 - Theatre The Spectral Form Factor is an important diagnostic of level repulsion Random Matrix Theory (RMT) and quantum chaos. The short-time behavior of the SFF as it approaches the RMT result acts as a diagnostic of the ergodicity of the system as it approaches the thermal state. In this work we observe that for systems without time-reversal symmetry, there is a second break from the RMT result at late times: specifically at the Heisenberg Time $T_H=2\pi \rho$. That is to say that after agreeing with the RMT result to exponential precision for an amount of time exponential in the system size, the spectral form factor of a large system will very briefly deviate in a way exactly determined by its early time thermalization properties. The conceptual reason for this is the Riemann-Siegel Lookalike formula, a resummed expression for the spectral determinant relating late time behavior to early time spectral statistics. We use the lookalike formula to derive a precise expression for the late time SFF for semiclassical systems, and then confirm our results numerically. We find that at late times, the various modes act on the SFF via repeated, which may give hints as to the analogous behavior for systems with time-reversal symmetry.

A symmetry algebra in double-scaled SYK

• Douglas Stanford (Stanford University)

Room: PI/1-100 - Theatre

Merged talks - An effective field theory for non-maximal quantum chaos; 66- Effective description of sub-maximal chaos: stringy effects for SYK scrambling

• Felix Haehl (University of Southampton)
• Ping Gao (Massachusetts Institute of Technology)

Room: PI/1-100 - Theatre 66 - It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective 'scramblon' modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with sub-maximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.

Talk 135 - Spectral properties of the sparse SYK model, with analysis of recent experimental simulation of holography

• Patrick Orman (Caltech)

Room: PI/1-100 - Theatre The Sachdev-Ye-Kitaev (SYK) model is a simple toy model of holography that has seen widespread study in the area of quantum gravity. It is particularly notable for its feasibility of simulation on near-term quantum devices. Recently, Swingle et al. introduced a sparsified version of the SYK model and analyzed its holographic properties, which are remarkably robust to deletion of Majorana interaction terms. Here we analyze its spectral and quantum chaotic properties as they pertain to holography as well as how they scale with sparsity and system size through large scale numerics. We identify at least two transition points at which features of chaos and holography are lost as the model is sparsified, and above which all important features are preserved, which may serve as guidelines for future experiments to simulate quantum gravity. Additionally, we apply these analyses to the SYK model that was recently experimentally simulated on the Google Sycamore quantum processor, which itself was a highly sparsified SYK model obtained through a machine learning algorithm incorporating mutual information signatures of a traversable wormhole.

Talk 2 - Large N Matrix Quantum Mechanics as a Quantum Memory

• Gong Cheng (University of Maryland)

Room: PI/1-100 - Theatre In this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large N matrix quantum mechanics models. First, we investigate the gauged SU(N) matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the mutual information between the system and a reference which purifies the encoded information, we identify a transition temperature, Tc, below which the encoded quantum information is protected from thermal noise for a memory time scaling as N^2. Conversely, for temperatures higher than T_c, the information is quickly destroyed by thermal noise. Second, we relax the requirement of gauge invariance and study a matrix harmonic oscillator model with only global symmetry. Finally, we further relax even the symmetry requirement and propose a model that consists of a large number N^2 of qubits, with interactions derived from an approximate SU(N) symmetry. In both ungauged models, we find that the effects of gauging can be mimicked using an energy penalty to give a similar result for the memory time. The final qubit model also has the potential to be realized in the laboratory.

Talk 118 - Overlapping qubits from non-isometric maps and de Sitter tensor networks

• Alexander Jahn (Free University of Berlin)

Room: PI/1-100 - Theatre We construct approximately local observables, or "overlapping qubits", using non-isometric maps and show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom, similar to our expectation in holography. Furthermore, the spoofed system naturally deviates from an actual local theory in ways that can be identified with features in quantum gravity. For a concrete example, we construct two MERA toy models of de Sitter space-time and explain how the exponential expansion in global de Sitter can be spoofed with many fewer quantum degrees of freedom and that local physics may be approximately preserved for an exceedingly long time before breaking down. Conceptually, we comment on how approximate overlapping qubits connect Hilbert space dimension verification, degree-of-freedom counting in black holes and holography, approximate locality in quantum gravity, non-isometric codes, and circuit complexity.

Talk 95 - A Large Holographic Code and its Geometric Flows

• Xi Dong (University of California, Santa Barbara)

Room: PI/1-100 - Theatre The JLMS formula is a cornerstone in our understanding of bulk reconstruction in holographic theories of quantum gravity, best interpreted as a quantum error-correcting code. Moreover, recent work has highlighted the importance of understanding holography as an approximate and perhaps non-isometric code. In this work, we construct an enlarged code subspace for the bulk theory that contains multiple non-perturbatively different background geometries. In such a large holographic code, we carefully derive an approximate version of the JLMS formula from an approximate FLM formula for a class of nice states. We do not assume that the code is isometric, but interestingly find that approximate FLM forces the code to be approximately isometric. Furthermore, we show that the bulk modular Hamiltonian of the entanglement wedge makes important contributions to the JLMS formula and cannot in general be neglected even when the bulk state is semiclassical. Nevertheless, when acting on states with the same background geometry, we find that the modular flow is well approximated by the area flow which takes the geometric form of a boundary-condition-preserving kink transform. We also generalize the results to higher derivative gravity, where area is replaced by the geometric entropy. We conjecture that a Lorentzian definition of the geometric entropy is equivalent to its original, Euclidean definition, and we verify this conjecture in a dilaton theory with higher derivative couplings. Thus we find that the flow generated by the geometric entropy takes the universal form of a boundary-condition-preserving kink transform.

Talk 84 - Complementarity and the unitarity of the black hole S-matrix

• Isaac Kim (University of California, Davis)

Room: PI/1-100 - Theatre Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S-matrix of an evaporating black hole has polynomial computational complexity.

Supersymmetry in quantum complexity: clique homology is QMA_1-hard

• Tamara Kohler (Instituto de Ciencias Matemáticas)

Room: PI/1-100 - Theatre In this talk I will present recent results about the computational complexity of determining homology groups of simplicial complexes, a fundamental task in computational topology. In arXiv:2209.11793 we showed that this decision problem is QMA1-hard. Moreover, we showed that a version of the problem satisfying a suitable promise is contained in QMA. This suggests that the seemingly classical problem may in fact be quantum mechanical. In fact, we were able to significantly strengthen this by showing that the problem remains QMA1-hard in the case of clique complexes, a family of simplicial complexes specified by a graph which is relevant to the problem of topological data analysis. The proof combines a number of techniques from Hamiltonian complexity and homological algebra, and is inspired by a link with supersymmetric quantum mechanics. In this talk I will focus on how the link with supersymmetry inspired the result, and explain the intuition behind the proof.

It from Qubit: The Game Show

• Patrick Hayden (Stanford University)

Room: PI/1-100 - Theatre