Simons Collaboration on It from Qubit Annual Meeting 2019

Simons Foundation Lecture
Wednesday, December 4, 2019

Leonard Susskind, Stanford University
The Quantum Origins of Gravity
Tea 4:15-5:00 PM
Lecture 5:00-6:15 PM

Participation is optional; separate registration is required.

Separate registration is required. Please click the link below for additional information:
https://www.sns.ias.edu/quantum-information-workshop-2019

Matthew Headrick
Brandeis University

Bit Threads and Holographic Entropy Inequalities
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Entanglement entropies in holographic theories as computed by the Ryu-Takayanagi formula are known to obey many inequalities beyond those required of general quantum states. Headrick will explain how these special properties can be understood in the language of bit threads and what they might imply for the entanglement structure of the underlying states.
 

Don Marolf
University of California, Santa Barbara

The Universal Structure of Holographic Quantum Codes
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Don Marolf argues that the structure of holographic quantum codes is related to a simple splitting into two parts of the bulk gravitational path integrals. In particular, treating the bulk as an effective field theory means that we are given an effective Lagrangian \(L_\Lambda\) associated with a cut-off energy scale \(\Lambda\). We show that aspects of the code are then determined by classical computations involving \(L_\Lambda\), while the path integral over fluctuations below the scale \(\Lambda\) determines the states to be encoded. As a result, in each superselection sector, all such codes turn out to have flat entanglement spectrum up to corrections of order \(G\) (i.e., up to corrections of order \(G^2\) times the leading term, which is itself of order \(1/G\)). This statement holds for any \(L_\Lambda\), no matter what higher derivative terms it may contain. Marolf also comments on other applications of fixed-area states or more generally of states with fixed geometric entropy.
 

Vijay Balasubramanian
University of Pennsylvania

Quantum Complexity of Time Evolution with Chaotic Hamiltonians

Balasubramanian studies the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, Balasubramanian demonstrates that there is always a geodesic between the identity and the time evolution operator e−iHt, whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. Balasubramanian identifies a criterion — the Eigenstate Complexity Hypothesis (ECH) — which bounds the overlap between off-diagonal energy eigenstate projectors and the k-local operators of the theory — and uses it to show that the linear geodesic will at least be a local minimum for exponential time. He shows numerically that the large-N SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, he also studies the case with N=2 fermions (which is integrable) and finds short-time linear complexity growth followed by oscillations. His analysis relates complexity to familiar properties of physical theories, like their spectra and the structure of energy eigenstates, and has implications for the hypothesized computational complexity class.
 

Christine Muschik
University of Waterloo

How to Simulate Lattice Gauge Theories on Quantum Computers
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Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. Muschik will talk about proposals for quantum simulations of gauge theories and their recent implementation on a trapped ion quantum computer. Considering one-dimensional quantum electrodynamics, Muschik and collaborators addressed the real-time evolution of particle-antiparticle pair production in a digital quantum simulation [Nature 534, 516-519 (2016)] as well as hybrid classical-quantum algorithms [Nature 569, 355 (2019)] to simulate equilibrium problems. Muschik will also discuss recent results on extending this work beyond one spatial dimension.
 

Alex Maloney
McGill University

CFT Universality, Black Holes and Chaos
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We describe universal statistical constraints on the dynamical data of two dimensional conformal field theories. These should be regarded as a CFT version of the gravitational “no hair” theorem which captures the intuitive notion that black hole geometries emerge from the coarse graining of quantum microstates. They provide a precise formulation of, as well as potential extensions to, the eigenstate thermalization hypothesis which characterizes chaos in two dimensional CFT. To further study the relation between black holes and chaos, we present a toy model of quantum gravity in 2+1 dimensions where black hole microstates are constructed by quantizing geometry. At the perturbative level, these microstates are represented by wave functions on a moduli space of Riemann surfaces. These can be computed numerically, where we find evidence that the resulting level statistics match those of a random matrix in the GOE.
 

Stephen Shenker
Stanford University

Black Holes, Random Matrices, Baby Universes and D-branes
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The energy spectrum of generic large AdS black holes is discrete because their entropy is finite. The explanation for this is clear from the boundary field theory point of view in AdS/CFT — it is just the discrete spectrum of a bound quantum system. But the explanation for this discreteness from the bulk gravitational point of view remains a mystery. We will discuss some progress on a simpler related problem: the gravitational origin of the statistical properties of this discrete spectrum in an ensemble of quantum systems. Because black holes are quantum chaotic systems, we expect these statistics to be described by random matrix ensembles. Shenker’s analysis will focus on the simple model black hole described by the Sachdev-Ye-Kitaev (SYK) model and, in particular, on its low-energy limit, Jackiw-Teitelboim (JT) gravity. We will be led to consider an asymptotic expansion described by space-time manifolds with an arbitrary number of handles and its completion by an analog of D-branes. We will close by discussing some of the questions this analysis raises — based on joint work with Phil Saad and Douglas Stanford.
 

Jonathan Oppenheim
University College London

A Post-Quantum Theory of Classical Gravity?
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Oppenheim presents a consistent theory of classical gravity coupled to quantum field theory. The dynamics are linear in the density matrix, completely positive and trace preserving, and reduce to Einstein’s equations in the classical limit. The constraints of general relativity are imposed as a symmetry on the equations of motion. The assumption that gravity is classical necessarily modifies the dynamical laws of quantum mechanics; the theory must be fundamentally stochastic involving finite-sized and probabilistic jumps in space-time and in the quantum field. Nonetheless, the quantum state of the system can remain pure, conditioned on the classical degrees of freedom. The measurement postulate of quantum mechanics is not needed since the interaction of the quantum degrees of freedom with classical space-time necessarily causes collapse of the wave function. More generally, Oppenheim derives a form of classical-quantum dynamics using a noncommuting divergence, which has as its limit deterministic classical Hamiltonian evolution and which doesn’t suffer from the pathologies of the semi-classical theory. The theory can be regarded as fundamental or as an effective theory of QFT in curved space where back-reaction is consistently accounted for.