- Organized by
Matthew Headrick, Ph.D.Brandeis University
Patrick Hayden, Ph.D.Stanford University
The It from Qubit Simons Collaboration held its fourth annual meeting December 5–6, 2019, bringing together the program’s Principal Investigators, the It from Qubit Fellows (postdoctoral scholars) and a large contingent of students and distinguished guests.
The meeting was immediately preceded by a two-day It from Qubit workshop at the Institute for Advanced Study, providing a full week of exciting scientific interaction. One of the major advances of the past year has been the development of tools to track the flow of information in dynamic space-times, including those of evaporating black holes. That advance has resulted in a flood of insights. The IAS meeting focused on taking the next step, understanding the detailed process enabling nonlocal movement of information in some circumstances.
The meeting at the Simons Foundation had seven speakers, split between five collaboration PIs and two external speakers. The first external speaker, Christine Muschik, educated the collaboration on using cold atom experiments to artificially simulate gauge theories, focusing on her recently published work using trapped ions to simulate one-dimensional quantum electrodynamics. The possibility of simulating interacting quantum systems that do not otherwise exist in nature is an exciting new direction that some collaboration members have already begun to pursue. The other external speaker, Steve Shenker, is a close colleague of It from Qubit who has been a leader in understanding the role of quantum chaos in gravitational systems. He dazzled the audience with an account of the relationship between two-dimensional gravity, random matrix theory and wormhole geometries.
Other highlights included Vijay Balasubramanian’s demonstration that complexity in the SYK model will grow linearly for exponential time, barring global obstructions; Matt Headrick’s guide to the bit thread formulation of holographic entanglement; Don Marolf’s explanation of how fixed-area states in quantum gravity can be used to probe the holographic error-correcting codes; Alex Maloney’s description of how universal statistical constraints on CFT data illuminate the structure of black hole microstates; and, last but not least, Jonathan Oppenheim’s contrarian presentation of a dissipative theory of quantum fields coupled to gravity.
In addition, a poster session gave the IFQ postdocs the opportunity to present their latest research. As usual, the time between the talks was filled with intense scientific discussion, which continued into the night across the street at the Flatiron Institute. After four years, It from Qubit has become a vibrant community whose members are eager to make use of every opportunity to learn from each other.
Thursday, December 5
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Matthew Headrick | Bit Threads and Holographic Entropy Inequalities 10:30 AM BREAK 11:00 AM Don Marolf | The Universal Structure of Holographic Quantum Codes 12:00 PM LUNCH 1:00 PM Vijay Balasubramanian | Quantum Complexity of Time Evolution with Chaotic Hamiltonians 2:00 PM BREAK 2:30 PM Poster Session | IFQ Postdocs 3:30 PM BREAK 4:00 PM Christine Muschik | How to Simulate Lattice Gauge Theories on Quantum Computers 5:00 PM DAY ONE CONCLUDES
Friday, December 6
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Alex Maloney | CFT Universality, Black Holes and Chaos 10:30 AM BREAK 11:00 AM Stephen Shenker | Black Holes, Random Matrices, Baby Universes and D-branes 12:00 PM LUNCH 1:00 PM Jonathan Oppenheim | A Post-Quantum Theory of Classical Gravity? 2:00 PM MEETING CONCLUDES 2:30 PM Continued Discussions @ Flatiron Institute
- Public Lecture
- IAS Workshop on Qubits and Spacetime
Abstracts and Slides
Bit Threads and Holographic Entropy Inequalities
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.
University of California, Santa Barbara
The Universal Structure of Holographic Quantum Codes
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.
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.
University of Waterloo
How to Simulate Lattice Gauge Theories on Quantum Computers
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.
CFT Universality, Black Holes and Chaos
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.
Black Holes, Random Matrices, Baby Universes and D-branes
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.
University College London
A Post-Quantum Theory of Classical Gravity?
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.