- Organized by
Matthew Headrick, Ph.D.Brandeis University
Patrick Hayden, Ph.D.Stanford University
The 2019 annual meeting of It from Qubit: Simons Collaboration on Quantum Fields, Gravity, and Information will be devoted to recent developments at the interface of fundamental physics and quantum information theory, spanning topics such as chaos and thermalization in many-body systems and their realization in quantum gravity; traversable wormholes and their information-theoretic implications; calculable lower-dimensional models of quantum gravity; the entanglement structure of semi-classical states in quantum gravity; complexity in field theory and gravity; the black-hole information puzzle; and applications of near-term quantum devices to problems in high-energy physics.
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 | De Sitter Quantum Gravity in 2 and 3 Dimensions 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
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.
De Sitter Quantum Gravity in 2 and 3 Dimensions
Maloney will discuss aspects of JT gravity in two-dimensional nearly de Sitter (dS) space-time and pure de Sitter quantum gravity in three dimensions. Both are essentially topological theories of gravity where it is possible to study precisely the wave function of the universe following the Hartle-Hawking construction. The wave function can be computed by analytic continuation to Euclidean AdS, rather than the sphere; this allows us to compute all of the perturbative and (in two dimensions) nonperturbative corrections to the wave function and to formulate the theory as a Matrix integral and provides a connection with the quantization of the moduli space of Riemann surfaces.
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.
Air and Train
Groups A & BThe foundation will arrange and pay for all air and train travel to the conference for those in Groups A and B. Please provide your travel specifications by clicking the registration link above. If you are unsure of your group, please refer to your invitation sent via email.
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Personal CarFor participants in Groups A & B driving to Manhattan, the Roger Hotel offers valet parking. Please note there are no in-and-out privileges when using the hotel’s garage, therefore it is encouraged that participants walk or take public transportation to the Simons Foundation.
Participants in Groups A & B who require accommodations are hosted by the foundation for a maximum of three nights at The Roger hotel. Any additional nights are at the attendee’s own expense.
The Roger New York
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