Patrick Hayden, Stanford University
Matthew Headrick, Brandeis University
The 2022 Simons Collaboration on It from Qubit annual meeting was 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; gravitational wormholes and their information-theoretic implications; calculable lower-dimensional models of quantum gravity; the entanglement structure of semi-classical states in quantum gravity; quantum error-correcting codes in quantum field theory and quantum gravity; complexity in field theory and gravity; the black-hole information puzzle; and quantum simulation and measurement-induced phase transitions.
The It from Qubit Collaboration met on December 8th and 9th at the Simons Foundation in New York City. For many participants, it was their first opportunity to see each other in person in several years, and the excitement translated into a gratifying hubbub of scientific activity. During the breaks, all available blackboards and whiteboards were occupied by participants eager to discuss ideas and collaborative projects.
The formal part of the program consisted of seven presentations ranging from pure quantum information through quantum field theory and AdS/CFT all the way to more speculative explorations of holographic formulations of cosmology.
In the first talk of the program, Tadashi Takayanagi introduced a quantity he called “pseudo-entropy.” In general, this pseudo-entropy can take complex values, complicating its physical interpretation as a potential measure of uncertainty. In certain holographic contexts, however, it is guaranteed to be real, and Takayanagi displayed his signature intuition by identifying a compelling dual formulation as the area of a minimal surface appearing in a Euclidean time-dependent geometry. It was a contribution perfectly suited to the final annual meeting given that Ryu and Takayanagi’s identification of the bulk dual of von Neumann entropy was one of the foundational results that made the It from Qubit Collaboration possible.
The next talk, focusing on quantum field theory, was similarly valedictory. Over the course of the past several years, Horacio Casini and his collaborators have resolved myriad confusions and problems in our understanding of entanglement entropy in quantum field theory while using those tools to develop a deeper understanding of field theory itself. One source of confusion that they addressed was the ambiguity in assigning an algebra to a physical region in gauge field theories. In his talk, Horacio explained how a tool they developed to resolve that ambiguity, namely the notion of duality defects, provides a precise way to understand generalized symmetries in quantum field theories.
The theme in the afternoon shifted to cosmology. The AdS/CFT correspondence has provided a well-defined concrete arena in which to develop the relationship between information theoretic ideas and quantum gravity. Ultimately, however, we need to understand quantum gravity in cosmological spacetimes more like our own. The first talk, by Lenny Susskind, discussed a conjectured duality between de Sitter space in 2+1 dimensions and the double-scaled limit of the SYK model at infinite temperature. His talk showed how four length scales in the cosmological theory, namely the cosmic, Planck, micro and string scales, behave identically to and should be considered dual to four length scales in the SYK model.
Susskind’s talk was followed immediately by Mark Van Raamsdonk’s very different proposal for embedding a cosmological spacetime as a bubble in a theory with a negative cosmological constant. He showed that even with a negative cosmological constant, the positive potential energy of time-dependent scalar fields can drive an expansion matching some features of our universe. The advantage of Van Raamsdonk’s approach is that it is more amenable to analysis via AdS/CFT duality.
The emphasis on the second day of the workshop shifted towards quantum information. Dorit Aharonov opened the session with a wide-ranging discussion on the difficulty of performing an experiment definitively demonstrating the computational superiority of quantum mechanics. Her highly pedagogical development exposed the string theorists in the group to new concepts like delegated quantum computation before coming to random circuit “quantum supremacy” experiments of the type first performed at Google in 2019. Recent work had come close to establishing that such experiments cannot lead to a refutation of the strong Church-Turing thesis because, in the presence of depolarizing noise, the state of the computer converges exponentially to uniform noise, obliterating the signal. A potential loophole remained, however. The so-called “sweet spot” consisted of circuits of logarithmic depth. Such circuits could still have nontrivial signal in the asymptotic limit while evading existing simulation methods. Aharonov presented a new simulation algorithm showing that classical computers can simulate log-depth random circuit sampling in polynomial time. The sweet spot is no more.
Aharonov’s talk generated the most discussion of any at the conference, likely because of the multiple ways that complexity has entered our understanding of AdS/CFT. We have learned that some entries in the AdS/CFT dictionary are almost certainly computationally intractable to evaluate, akin to the kinds of random circuit sampling questions Aharonov was discussing. On the other hand, nontrivial simulation algorithms could correspond to dictionary entries more tractable to evaluate than previously thought.
John Preskill spoke next, summarizing work in his group over the past several years on efficiently learning quantum states and dynamics. Ideas at the core of quantum information science, namely error correction and complexity, have played surprising and outsized roles in our developing understanding of holography. Preskill suggested that there are further deep unexploited discoveries in quantum information awaiting their application in quantum gravity. When faced with an uncharacterized quantum system, the vastness of Hilbert space suggests that it should be completely hopeless to efficiently characterize it. Preskill explained how for most practical purposes, the opposite is true: relatively simple and parsimonious measurement procedures coupled with efficient prediction algorithms exist provided the questions asked about the system are weakly constrained.
Patrick Hayden gave the last talk of the conference. From the point of view of a quantum information theorist, one of the most remarkable features of AdS/CFT is that it realizes local computations executed in the bulk spacetime as distributed computations in the boundary theory. Better understanding the duality offers the promise of new and more efficient procedures for distributed quantum computation. In his talk, Hayden took a step in that direction, presenting the first efficient algorithm for one of the theoretical workhorses of quantum distributed computation, a protocol known as port-based teleportation.
This was the final annual meeting of the It from Qubit Collaboration and many participants expressed how exhilarating the past seven years have been. A true intellectual convergence occurred leading to major advances in our understanding of fundamental physics. It from Qubit has seeded an entire community that will ensure that the science continues, but there was nonetheless an undercurrent of sadness at the conference. A truly remarkable enterprise is coming to an end.
That said, we were pleased to learn during the conference that there will be a reunion meeting in 2025. We look forward to seeing you then!
THURSDAY, DECEMBER 8
9:30 AM Tadashi Takayanagi | Pseudo Entropy and AdS(dS)/CFT 11:00 AM Horacio Casini | Duality Defects, Entropic Order Parameters, and Noether's Theorem 1:00 PM Leonard Susskind | The Semiclassical Limit of De Sitter Space In (2+1)-Dimensions and the Double-Scaled Limit of SYK at Infinite Temperature 2:30 PM Poster Session | IFQ Postdocs 4:00 PM Mark Van Raamsdonk | Cosmology via Holography
9:30 AM Dorit Aharonov | A Polynomial-Time Classical Algorithm for Noisy Random Circuit Sampling 11:00 AM John Preskill | Learning Quantum Dynamics 1:00 PM Patrick Hayden | Entanglement, Complexity and Teleportation
Abstracts & Slides
A Polynomial-Time Classical Algorithm for Noisy Random Circuit Sampling
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The field of quantum computation heavily relies on the belief that quantum computation violates the extended Church Turing thesis, namely, that quantum many body systems cannot be simulated by classical ones with only polynomially growing overhead. What experimental evidence do we have for this assumption? Dorit Aharonov will overview the inherent difficulty in collecting such evidence. A major effort towards providing evidence for quantum advantage concentrates on “quantum supremacy” experiments via quantum random circuit sampling (RCS).
These experiments can be modeled as sampling from a random quantum circuit where each gate is subject to a small amount of noise. Aharonov will give a polynomial time classical algorithm for sampling from the output distribution of a noisy random quantum circuit in the regime of anti-concentration to within inverse polynomial total variation distance. It should be noted that our algorithm is not practical in its current form, and does not address finite-size RCS based quantum supremacy experiments. Our result gives strong evidence that random circuit sampling (RCS) cannot be the basis of a scalable experimental violation of the extended Church-Turing thesis.
Based on recent joint work with Xun Gao, Zeph Landau Yunchao Liu and Umesh Vazirani, arxiv: 2211.03999
CONICET, Instituto Balseiro
Duality Defects, Entropic Order Parameters, and Noether’s Theorem
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Horacio Casini will review aspects of the existence of duality defects in quantum field theories. These appear in theories where the assignment of algebras to regions is not unique and give a precise way to understand completeness and the existence of generalized symmetries. Casini will show how entropic order parameters can be defined through the existence of the multiple algebras and the entropic certainty relation obeyed by dual order parameters. Casini will sketch the way different phases of QFT show up in terms of these order parameters. The interplay between duality defects and global symmetries leads to possible obstructions to strong forms of the Noether theorem and illuminates the reason behind known cases where this theorem does not apply. Several further consequences are suggested, such as the impossibility of charge-less electrodynamics.
Entanglement, Complexity and Teleportation
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The boundary realization of a quantum computer operating in the bulk of anti-de Sitter space is a distributed computation that implements the same computation without ever assembling all the input data in one place. Attempts to understand the power of those distributed computations led Alex May to prove that the complexity of the bulk computation can be bounded in terms of the boundary entanglement. In this talk, Patrick Hayden will describe a computationally efficient implementation of port-based teleportation, a protocol at the heart of those arguments, that leads to an exponential tightening of May’s bound.
California Institute of Technology
Learning Quantum Dynamics
When the It from Qubit collaboration launched in 2015, we were just beginning to appreciate the value of quantum information concepts like error correction and complexity for explorations of quantum gravity. Now these ideas are widely recognized as essential to the subject. What concepts from computer science will guide us in the next seven years? The answer is: I don’t know. But I think the IFQ community might benefit from learning about recent applications of learning theory to quantum systems, so I will describe some of these developments. I won’t explain how these ideas will be useful in quantum gravity — that’s for you to figure out. The talk draws from a recent paper with Robert Huang and Sitan Chen (https://arxiv.org/abs/2210.14894) and earlier papers referenced there.
The Semiclassical Limit of De Sitter Space In (2+1)-Dimensions and the Double-Scaled Limit of SYK at Infinite Temperature
Leonard Susskind will explain the four important length scales that occur in dS(2+1) — the cosmic, Planck, micro, and string scales, and why they are dual to the SYK scales Lc = 1/J, Lp = 1/JN, Lc = 1/JN(1/2), Ls = 1/(Jq) in the semi-classical limit. The consistency of these correspondences is further evidence for the conjectured duality between de Sitter space in 3-dimensions and the double-scaled limit of SYK at infinite temperature.
Pseudo Entropy and AdS(dS)/CFT
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Pseudo entropy is a generalization of entanglement entropy such that it depends on both an initial and final state. It has a clear gravity dual via the AdS/CFT, namely the minimal surface area in a Euclidean time-dependent AdS background. In this talk, Tadashi Takayanagi will explain the definition and basic properties of pseudo entropy as well as discuss recent applications of pseudo entropy to quantum phase transition and to dS/CFT.
Mark Van Raamsdonk
University of British Columbia
Cosmology via Holography
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Mark Van Raamsdonk will describe how the standard tools of holography might be used to define microscopic models of big-bang cosmology. Van Raamsdonk will consider models where a bubble of the cosmological spacetime is embedded in an asymptotically AdS spacetime, and models where an asymptotically AdS Euclidean spacetime obtained by analytically continuing the cosmological spacetime is described via a Euclidean CFT construction. While the effective field theories we consider have negative cosmological constant, they can describe realistic accelerating cosmologies via the positive potential energy of time-dependent scalar fields.
- Princeton/IAS IFQ Workshop, December 5-7