# Simons Collaboration on It From Qubit Annual Meeting 2018

• Organized by
• Patrick Hayden, Ph.D.Stanford University
Date & Time

The interface of quantum information theory and high-energy theory has seen rapid progress over the last few years, with significant advances on topics such as scrambling and chaos in quantum systems; complexity and black holes; holography and quantum error correction; entropy and energy bounds in quantum field theories; and traversable wormholes and quantum teleportation in semiclassical quantum gravity. This progress has shifted the landscape of physics, changing our perspectives on the deepest problems in the two fields and blurring the boundary between them. The 2018 annual meeting of It from Qubit: Simons Collaboration on Quantum Fields, Gravity, and Information served as an opportunity to review progress, assess where we stand today and develop strategies to tackle the outstanding challenges as we see them now.

### Meeting Report

The annual meeting of It from Qubit: Simons Collaboration on Quantum Gravity, Fields and Information brought together all 18 principal investigators, 21 IFQ Fellows and around 50 guests for two days at the Simons Foundation headquarters in New York. The meeting featured eight 45-minute talks by PIs, covering — in a broad sense — the range of topics studied by the collaboration. The talks were largely devoted to overviews of the most important progress over the past three years at the interface of fundamental physics and quantum information theory. Each talk was followed by a lively 15-minute discussion period, addressing both the finer points of the science and the the most exciting future research directions in the area.

Patrick Hayden, director of the collaboration, kicked off the meeting with a review of applications of quantum error correction to holographic dualities, focusing on three important developments: First, it was shown that complementary recovery allows the full entanglement wedge, and not just the causal wedge, to be reconstructed from a given boundary region and, therefore, in particular allows observables behind causal horizons to be reconstructed. Second, error correction helped to resolve a tension inherent in the Ryu-Takayanagi formula, which equates the entropy, a nonlinear function of the state, to the area, an observable in gravity. And, third, error correction has been used to show, as has been argued previously on other grounds, that theories of quantum gravity do not admit global symmetries. Hayden also discussed how nature (or at least AdS/CFT) gets around one of the fundamental no-go theorems in quantum fault tolerance to make time evolution possible.

Leonard Susskind motivated and presented evidence for a connection in holographic theories between circuit complexity and spatial volume or action in the bulk. He then explained the notion of complexity geometry and how it can be used to redefine complexity as an entropy with respect to an auxiliary system. He then raised a series of provocative questions regarding complexity and physics, such as: Can the principle of least action be formulated as a principle of minimal computation? Can we formulate quantum chaos as the tendency for relative complexity to grow? What happens to geometry when complexity maxes out? Does it lead to firewalls? Finally, and most provocatively, does GR = QM?

Alexei Kitaev gave an overview of the SYK model and its connection to black-hole physics. He started by reviewing the physics of Hawking radiation and Dray–’t Hooft shock waves in black-hole backgrounds, and then described the behavior of out-of-time-order correlators (OTOCs), whose Lyapunov exponent saturates the Maldacena-Shenker-Stanford bound. The Sachdev-Ye-Kitaev (SYK) model also saturates the bound; in other words, it exhibits the strongest possible quantum chaos. Even more remarkably, its collective mode has the same effective action as 2D dilaton gravity. Kitaev then described recent developments, including the Lorentzian version of the duality and effective Hilbert space models, to model the behavior on time scales short compared to the scrambling time.

Scrambling and OTOCs were also a main theme of Brian Swingle’s talk. In particular, he described information scrambling in extended quantum systems in the language of operator spreading. Defining an information speed, he showed that, in chaotic systems, it equals the butterfly speed and illustrated it with the case of a particle falling into a black-hole horizon in a holographic theory. He then explained several experiments that are currently being undertaken to measure scrambling in trapped ion and NMR systems. Finally, he described simulations of scrambling and information spreading in Brownian coupled clusters and spin chains, and proposed that these exhibit a universal form of information spreading.

Mark Van Raamsdonk explained holographic connections between gravitational physics and field-theory entanglement and, in particular, the constraints on space-time that follow from properties of entanglement. A by-now-classic example is the derivation of the linearized Einstein equation from the first law of entanglement. Since then, there have been developments on several fronts, including the extension of this relation to second order, which leads to new constraints on field theories that are dual to Einstein gravity and new positive-energy theorems. He then described several open problems in this area, such as whether there is a connection between entanglement and geometry in systems without an a priori spatial structure, such as matrix models.

On the second day, Horacio Casini explained how quantum mechanics constrains relativistic quantum field theories and especially their renormalization-group flows. The starting point here is the Markov property of the vacuum of any relativistic QFT for regions with boundary on a common null hyperplane. This property can be used to prove the irreversibility of the RG flow (so-called ‘C-theorems’) in 2, 3 and 4 space-time dimensions. It is also connected to the average null energy condition (ANEC) and quantum null energy condition (QNEC), two generalizations of the usual null energy condition used in proofs of important theorems in classical general relativity, such as singularity theorems and the area theorem. Finally, Casini described interesting future directions, including the effort to unify different axiomatic approaches to quantum field theory from the perspective of entanglement entropy.

Dorit Aharonov then gave the theoretical computer scientist’s view on quantum mechanics, emphasizing four essential ingredients. The first is computational complexity, in particular the notion of universal computational hardness and the map of (classical and quantum) complexity classes. The definition of these classes in turn relies on reduction of one problem to another. It also leads to the question of robustness, both of entanglement and of computational hardness. Finally, Aharonov emphasized the concept of interaction, which, for example, would allow us to check whether a putative quantum computer is functioning correctly even when it is performing a calculation that is too hard for a classical computer and therefore cannot be directly checked. She stressed that a new theory of reductions and complexity is required to capture the power of the analog quantum simulators being used to explore many-body physics, including many phenomena of interest to It from Qubit.

Finally, Juan Maldacena explained recent breakthroughs associated with traversable wormholes in general relativity. For a long time, it was believed that such wormholes were forbidden. However, it was shown recently that cleverly coupling the two sides of a standard eternal black hole would allow an observer to pass from one side to the other, and that this process is a holographic realization of quantum teleportation. This effect allows external observers to see the previously inaccessible interior region of the black hole. It also sheds new light on the Hayden-Preskill process for decoding the state of a black hole from the emitted Hawking radiation and, in particular, suggests that the quantum computer that carries out the decoding also has a gravity dual, which is connected to the interior of the original black hole. Finally, Maldacena explained how traversable wormholes can be constructed both in the toy-model SYK/nearly-AdS2 duality and in our 4D world.

The beautiful science descibed in these talks, together with the animated conversations among the participants during the breaks, confirmed that the interface between quantum information theory and fundamental physics continues to be a fruitful and exciting field of research.

### Talks

Patrick Hayden
Stanford University

Holographic Quantum Error Correction: What, How and Why?
(Slides PDF)

The bulk to boundary mapping in AdS/CFT has a surprising built-in redundancy: it is a quantum error-correcting code. That simple observation resolved a number of conceptual puzzles, including nonlinearities and redundancies in the correspondence. More recently, the algebra of error-correction property has provided the first detailed argument for the existence of localized quantum degrees of freedom in the bulk theory. In an even more striking advance, the proof of the entanglement wedge reconstruction hypothesis has illustrated how to extract information from beyond a horizon. In this talk, Hayden will summarize these and other advances, ending with a discussion of further challenges and opportunities. The talk will also contain a brief overview of the It from Qubit Simons Collaboration and its activities over the past three years.

Leonard Susskind
Stanford University

Complexity Behind the Horizon
(Slides PDF)

Susskind will explain aspects of the application of quantum complexity to the dynamics of the interiors of black holes. These will include the complexity-action correspondence and the importance of the second law of complexity to the evolution of the bulk geometry of black hole interiors.

Alexei Kitaev
California Institute of Technology

The SYK Model and Black Holes
(Slides PDF)

Information scrambling in black holes is special because (up to stringy effects) it is operated by few collective degrees of freedom, ’t Hooft’s ‘shock waves.’ A similar situation occurs in the Sachdev-Ye-Kitaev model, where the relevant collective mode is described by the Schwarzian action. Kitaev will give a quick overview of the SYK model, including some recent developments. The main focus will be on mapping SYK observables, microstates, and more to the Schwarzian model, which is itself a consistent quantum theory.

Brian Swingle
University of Maryland

Scrambling and Quantum Spacetime
(Slides PDF)

Swingle will first review information scrambling and its relation to chaos and the geometry of space-time in the context of AdS/CFT. Scrambling can also be related to a kind of many-body spin echo, which opens a route to potentially measuring scrambling in the lab by effectively controlling the flow of time, as demonstrated in five preliminary experiments already carried out. Swingle will then comment on current directions, including a new definition of a spectrum of quantum Lyapunov exponents, a new universal structure for the spread of chaos in spatially extended systems, and the generation of macroscopic superpositions of space-times via quantum chaos. Swingle will close with a discussion of experiments to probe quantum space-time in toy universes and our own.

Mark Van Raamsdonk
University of British Columbia

Gravitational Physics from Quantum Information Constraint
(Slides PDF)

In this talk, Mark Van Raamsdonk will review some of the remarkable connections between gravitational physics and the physics of entanglement in conformal field theories. He will describe how the structure of entanglement in a conformal field theory can be captured by the geometry of an asymptotically Anti-de Sitter (AdS) space-time and how constraints on entanglement imply (at least to second order in perturbation theory around AdS) that this space-time must satisfy Einstein’s equations. Further quantum information-theoretic constraints suggest new results in classical gravity, including a family of positive energy theorems for gravitational subsystems.

Horacio Casini
Centro Atómico Bariloche

Entanglement Entropy in Quantum Field Theory: Recent Results and Future Prospects
(Slides PDF)

Entanglement entropy offers a nonstandard view of quantum field theory where the focus is on the statistical properties of the state, rather than the ones of a particular set of operators — the traditional approach based on correlation functions. We will review the main recent results in this approach. In particular, we now have a unification of all theorems of irreversibility of the renormalization group for dimensions d=2, 3 and 4 (c, F and A theorems) based on the property of strong subadditivity of entanglement entropy. This proof offers, for the first time, a simple conceptual understanding of the quantum information theory meaning of these theorems and highlights the role of relativity. The Markovian property of the vacuum state, a new general property of relativistic quantum field theories, was discovered in this context. We will also discuss the quantum null energy condition that deepens our understanding of the relations between energy and entropy. We will end with an outlook of future possibilities.

Dorit Aharonov
Hebrew University

Minimizing Resources for Analog Quantum Simulations
(Slides PDF)

The goal of analog quantum simulation, where a Hamiltonian $$H$$ is simulated by another Hamiltonian $$H’$$ that is simpler or more easily implemented, was identified by Feynman as a main motivation for quantum computers as early as 1981 and is considered to be one of the more practical and useful applications in the era of noisy intermediate-scale quantum technology (NISQ). The minimal resources required for such analog simulations will play a crucial role in such applications. We prove two results in this context: one, we prove that reducing the degree to a constant in analog simulations is, in general, impossible in the quantum world; this is due to the special nature of quantum correlations and stands in stark contrast to the classical world, where degree reduction is possible. Two, we significantly improve the requirements on the spatial dimension required for such analog simulations. Based on joint work with Leo Zhou.

Juan Maldacena