# Summer School Exercises

Conference Date:
Monday, July 18, 2016 (All day) to Friday, July 29, 2016 (All day)
Pirsa Collection:
Scientific Areas:
Quantum Fields and Strings
Quantum Gravity
Quantum Information

In recent years, compelling evidence has emerged that information theory provides a powerful way to structure our thinking about quantum gravity and quantum field theory. In turn, fundamental physics provides new classes of fascinating questions for quantum information theorists to address.

In spite of these exciting developments, high energy physics and quantum information theory remain distinct disciplines and communities, separated by significant barriers to communication and collaboration. This school has been organized by the "It from Qubit" Simons Collaboration to promote communication and learning between the two research communities. In particular, we strongly encourage applications from interested students and junior researchers whose background is limited to either of the two fields but who are interested in reaching across disciplinary boundaries.  The school will include both lectures and hands-on tutorials.

Courses will cover a full range from basic to advanced topics, including:

## qubit.png

The school will be held concurrently with a workshop of the "It from Qubit" Simons Collaboration. Advanced students will have the opportunity to attend the seminars organized for the workshop.

Registration for this event is now closed.  However, we refer interested researchers to the "Remote Participation" tab below.

Sponsorship for this event has been provided by:

Main Lecturers:

• Dorit Aharonov, The Hebrew University of Jerusalem
• Horacio Casini, Centro Atomico Bariloche
• Daniel Gottesman, Perimeter Institute
• Daniel Harlow, Harvard University
• Thomas Hartman, Cornell University
• Patrick Hayden, Stanford University
• Veronika Hubeny, University of Califonia, Davis
• Stephen Jordan, National Institute of Standards and Technology
• Mukund RangamaniUniversity of Califonia, Davis
• Robert Spekkens, Perimeter Institute
• Douglas Stanford, Institute for Advanced Study
• Guifre Vidal, Perimeter Institute
• John Watrous, University of Waterloo & IQC

Focus Lecturers:

• Alice Bernamonti, Perimeter Institute
• Adam Bouland, Massachusetts Institute of Technology
• Xi Dong, Institute for Advanced Study
• Markus Hauru, Perimeter Institute
• Isaac Kim, IBM
• David Kubiznak, Perimeter Institute
• Mark Mezei, Princeton University
• Markus Mueller, Perimeter Institute & University of Western Ontario
• Jonathan Oppenheim, University College London
• Fernando Pastawski, California Institute of Technology
• Daniel Roberts, Massachusetts Institute of Technology
• Michael Walter, Stanford University
• Beni Yoshida, Perimeter Institute

• Scott Aaronson, Massachusetts Institute of Technology
• Aysha Abdel-Aziz, Stanford University
• Nima Afkhami-Jeddi, Cornell University
• Cesar Agon, Brandeis University
• Dorit Aharonov, The Hebrew University of Jerusalem
• Alvaro Alhambra, University College London
• Tibra Ali, Perimeter Institute
• Natacha Altamirano, Perimeter Institute
• Valentina Baccetti, Macquarie University
• Vijay Balasubramanian, University of Pennsylvania
• Ning Bao, California Institute of Technology
• Matt Beach, University of British Columbia
• Alice Bernamonti, Perimeter Institute
• Adam Bouland, Massachusetts Institute of Technology
• Fernando Brandao, California Institute of Technology
• Daniel Brod, Perimeter Institute
• Pablo Bueno, KU Leuven
• Nele Callebaut, Columbia University
• Joan Camps. University of Cambridge
• Pawel Caputa, NORDITA
• John Cardy, University of California, Berkeley
• Dean Carmi, Perimeter Institute
• Horacio Casini, Centro Atomico Bariloche
• Christopher Chamberland, Institute for Quantum Computing
• Shira Chapman, Perimeter Institute
• Wissam Chemissany, Leibniz University of Hannover
• Lin-Qing Chen, Perimeter Institute
• Christina Cirstoiu, Imperial College London
• Joshua Combes, Perimeter Institute
• Jordan Cotler, Stanford University
• Matthew Coudron, Massachusetts Institute of Technology
• Jason Crann, University of Waterloo
• Shawn Cui, University of California, Santa Barbara
• Timothy de Jonckhere, Free University of Brussels
• Clement Delcamp, Perimeter Institute
• Anton de la Fuente, University of Maryland
• Lidia Del Rio, University of Bristol
• Giuseppe Di Molfetta, IFIC - Universitat de Valencia
• Dawei Ding, Stanford University
• Xi Dong, Institute for Advanced Study
• Netta Engelhardt, University of California, Santa Barbara
• Zachary Fisher, Univeristy of California, Berkeley
• Zicao Fu, University of California, Santa Barbara
• Cohl Furey, Cambridge University
• Damian Galante, Perimeter Institute
• Federico Galli, Perimeter Institute
• Simon Gentle, University of California, Los Angeles
• Hrant Gharibyan, Stanford University
• Yan Gobeil, McGill University
• Can Gokler, Harvard University
• Daniel Gottesman, Perimeter Institute
• Brianna Grado-White, University of California, Santa Barbara
• Stephen Green, Perimeter Institute
• Tarun Grover, Kavli Institute for Theoretical Physics
• Felix Haehl, Durham University
• Daniel Harlow, Harvard University
• Thomas Hartman, Cornell University
• Markus Hauru, Perimeter Institute
• Patrick Hayden, Stanford University
• Ashwin Hedge, University of California, Los Angeles
• Michal Heller, Perimeter Institute
• Eliot Hijano, University of California, Los Angeles
• Philipp Hoehn, Institute for Quantum Optics and Quantum Information
• Timothy Hsieh, Kavali Institute for Theoretical Phyics
• Qi Hu, Perimeter Institute
• Kuo-Wei Huang, Stony Brook University
• Veronika Hubeny, University of Califonia, Davis
• Ling Yan Hung, Fudan University
• Nick Hunter-Jones, California Institute of Technology
• Ted Jacobson, University of Maryland
• Robert Jefferson, University of Amsterdam
• Tomas Jochym-O'Connor, University of Waterloo
• Robert Jonsson, University of Waterloo
• Stephen Jordan, National Institute of Standards and Technology
• Philipp Kammerlander, ETH Zurich
• Daniel Kapec, Harvard University
• Arjun Kar, University of Pennsylvania
• Adrian Kent, University of Cambridge
• Isaac Kim, IBM
• Jason Koeller, Univeristy of California, Berkeley
• Dax Koh, Massachusetts Institute of Technology
• Ryszard Kostecki, Perimeter Institute,
• Shauna Kravac, University of California, San Diego
• Marius Krumm, University of Western Ontario
• Aleksander KubicaCalifornia Institute of Technology
• David Kubiznak, Perimeter Institute
• Lampros Lamprou, Stanford University
• Hun Hee Lee, Seoul National University
• Jaehoon Lee, University of British Columbia
• Debbie Leung, University of Waterloo & IQC
• Aitor Lewkowycz, Princeton University
• Jie Lin, University of Waterloo
• Zi-Wen Liu, Massachusetts Institute of Technology
• Simon Loewe, Cornell University
• Matteo Lostaglio, Imperial College London
• Javier Martinez Magan, Utrecht University
• Raghu Mahajan, Stanford University
• Juan Maldacena, Institute for Advanced Study
• Alexander Maloney, McGill University
• Ipsita Mandal, Perimeter Institute
• Donald Marolf, University of California, Santa Barbara
• Henry Maxfield, McGill University
• Alex May, University of British Columbia
• Sam McCandlish, Stanford University
• Lauren McGough, Princeton University
• Marco Meineri, Perimeter Institute
• Mark Mezei, Princeton University
• Benjamin Michel, University ofo Califronia, Santa Barbara
• Ashley Milsted, Perimeter Institute
• Eric Mintun, University of California, Santa Barbara
• Masamichi Miyaji, Kyoto University
• Markus Mueller, Perimeter Institute & University of Western Ontario
• Robert Myers, Perimeter Institute
• Anand Natarajan, Massachusetts Institute of Technology
• Gim Seng Ng, McGill University
• Yuezhen Niu, Massachusetts Institute of Technology
• Masahiro Nozaki, University of Chicago
• Hirosi Ooguri, California Institute of Technology
• Jonathan Oppenheim, University College London
• Maria Papageorgiou, Perimeter Institute
• Onkar Parrikar, University of Illinois
• Fernando Pastawski, California Institute of Technology
• Geoffrey Penington, Stanford University
• Natalia Pinzani Fokeeva, Israel Institute of Technology
• Roji Pius, Perimeter Institute
• Nicholas Pomata, Stony Brook University
• Diego Pontello, Centro Atómico Bariloche
• John Preskill, California Institute of Technology
• Xiaoliang Qi, Stanford University
• Charles Rabideau, Univesity of British Columbia
• Mukund RangamaniUniversity of Califonia, Davis
• Pratik Rath, Perimeter Institute
• Renato Renner, ETH Zurich
• Jess Riedel, Perimeter Institute
• Julian Rincon, Perimeter Institute
• Daniel Roberts, Massachusetts Institute of Technology
• Massimiliano (Max) Rota, Durham University
• Subir Sachdev, Harvard University
• Grant Salton, Stanford University
• Fabio Sanches, University of California, Berkeley
• Krishan Saraswat, University of British Columbia
• Gabor Sarosi, Budapest University of Technology and Economics
• Volkher Scholz, Ghent University
• Stephen Shenker, Stanford University
• Ralph Silva, University of Geneva
• Sang-Jin Sin, Hanyang University
• Alexander Smith, University of Waterloo & Macquarie University
• Robert Spekkens, Perimeter Institute
• Antony Speranza, University of Maryland
• Douglas Stanford, Institute for Advanced Study
• Josephine Suh, University of British Columbia
• Brian Swingle, Stanford University
• Eduardo Teste Lino, Centro Atomico Bariloche / Balseiro Institute
• Gonzalo Torroba, Centro Atómico Bariloche
• Yonathan Touati, The Hebrew University of Jerusalem
• Ioannis Tsiares, McGill University
• Mark van Raamsdonk, University of British Columbia
• Guillaume Verdon-Akzam, University of Waterloo
• Ruben Verresen, Max Planck Institute for the Physics of Complex Systems
• Guifre Vidal, Perimeter Institute
• Michael Walter, Stanford University
• Chenjie Wang, Perimeter Institute
• Jian Wang, University of Michigan
• Tian Wang, California Institute of Technology
• Yihong Wanng, Stonybrook University
• Kento Watanbe, Yukawa Institute for Theoretical Physics
• John Watrous, University of Waterloo & Institute for Quantum Computing
• Silke Weinfurtner, University of Nottingham
• Jason Wien, University of California, Santa Barbara
• Shai Wyborski, The Hebrew University of Jerusalem
• Shuo Yang, Perimeter Institute
• Zhao Yang, Stanford University
• Beni Yoshida, Perimeter Institute
• Henry Yuen, Massachusetts Institute of Technology
• Ying Zhao, Stanford University
• Yechao (Elton) ZhuMassachusetts Institute of Technology
• Claire Zukowski, Columbia University

## Monday, July 18, 2016

 Time Event Location 8:30 – 9:00am Registration Reception 9:00 – 9:10am Welcome and Opening Remarks Theater/Bob 9:10 – 10:30am Patrick Hayden, Stanford UniversityQI Basics Theater 9:10 – 10:30am Veronika Hubeny, University of California, DavisGravity Basics Bob Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Rob Spekkens, Perimeter InstituteEntanglement Theater 12:30 – 2:30pm Lunch Atrium 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 4:30pm – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm David Kubiznak, Perimeter InstituteGR: Actions and Equations(Focus Lecture for Gravity Basics Course) Alice Room 5:00 – 6:00pm Adrian Kent, Cambridge UniversityBell’s Theorem(Focus Lecture for Entanglement Course) Bob Room 5:00 – 6:00pm Matthew Headrick, Brandeis UniversityA new perspective on holographic entanglement Theater

## Tuesday, July 19, 2016

 Time Event Location 9:00 – 10:30am John Watrous, University of WaterlooQI Basics Theater 9:00 – 10:30am Thomas Hartman, Cornell UniversityQFT Basics Bob Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Rob Spekkens, Perimeter InstituteEntanglement Theater 12:30 – 2:30pm Lunch Atrium 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 2:30 – 4:30pm Patrick Hayden, Stanford UniversityAdrian Kent, Cambridge UniversityQuantum Information in Spacetime Theater 4:00 - 4:30pm Bianca Dittrich, Perimeter InstituteEntanglement Entropy in nonAbelian Gauge Theories Bob Room 4:30 – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm Mark Mezei, Princeton UniversityQFT in Rindler Space(Focus Lecture for QFT Basics Course) Alice Room 5:00 – 6:00pm Fernando Pastawski, California Institute of TechnologyGrover’s Algorithm(Focus Lecture for QI Basics Course) Bob Room 5:00 – 6:00pm Hirosi Ooguri, California Institute of TechnologyGravitational Positive Energy Theorems from Information Inequalities Theater

## Wednesday, July 20, 2016

 Time Event Location 9:00 – 10:30am Daniel Gottesman, Perimeter InstituteQuantum Error Correction Theater 9:00 – 10:30am Veronika Hubeny, University of California, DavisGravity Basics Bob Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Horacio Casini, Centro Atomico BarilocheEntanglement in QFT Theater 12:30 – 2:30pm Lunch Atrium 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 2:30 – 4:30pm Thomas Harrtman, Cornell UniversityMark van Raamsdonk, University of British ColumbiaConstraints on Entanglement Dynamics Theater 4:30 – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm David Kubiznak, Perimeter InstituteBlack Hole Thermodynamics(Focus Lecture for Gravity Basics Course) Alice Room 5:00 – 6:00pm Jonathan Oppenheim, University College LondonQuantum Thermodynamics(Focus Lecture for Entanglement Course) Bob Room 5:00 – 6:00pm Daniel Roberts, Massachusetts Institute of TechnologyHolographic complexity by design Theater

## Thursday, July 21, 2016

 Time Event Location 9:00 – 10:30am Thomas Hartman, Cornell UniversityQFT Basics Theater 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Horacio Casini, Centro Atomico BarilocheEntanglement in QFT Theater 12:30 – 2:30pm Lunch Atrium 1:00 - 2:00pm Daniel Harlow, Harvard UniversityThe Ryu-Takayanagi Formula from Quantum Error Correction Theater 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 2:30 – 4:30pm Scott Aaronson, Massachusetts Institute of TechnologyDaniel Roberts, Massachusetts Institute of TechnologyComplexity Theater 4:30 – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm Mark Mezei, Princeton UniversityA Calculation of EE in Free QFT(Focus Lecture for Entanglement in QFT Course) Alice Room 5:00 – 6:00pm Beni Yoshida, Perimeter InstituteSubsystem Codes(Focus Lecture for QEC Course) Bob Room 5:00 – 6:00pm Fernando Brandao, California Institute of TechnologyBoundary States and Entanglement Spectrum from Strong Subadditivity Theater 6:30 - 7:00pm Veronika Hubeny, University of California, Davis"Introduction to Ads Space" Bob Room 7:30pm Movie Night:Star Trek Theater

## Friday, July 22, 2016

 Time Event Location 9:00 – 10:30am Daniel Gottesman, Perimeter InstituteQuantum Error Correction Theater 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Mukund Rangamani, University of California, DavisAdS/CFT correspondence Theater 12:30 – 2:30pm Lunch Atrium 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 2:30 – 4:30pm Michal Heller, Perimeter InstituteLampros Lamprou, Stanford UniversitySam McCandlish, Stanford UniversityKinematic Space Theater 4:30 – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm Alice Bernamonti, Perimeter InstituteHolographic Correlation Functions(Focus Lecture for AdS/CFT Course) Alice Room 5:00 – 6:00pm Isaac Kim, IBMAnyons and Topological Codes(Focus Lecture for QEC Course) Bob Room 5:00 – 6:00pm Netta Engelhardt, University of California, Santa BarbaraTowards a Reconstruction of General Bulk Metrics Theater 7:30pm Movie Night:Star Trek: Into the Darkness Theater

## Saturday, July 23, 2016

 Time Event Location 9:00 – 10:30am Stephen Jordan, National Institute of Standards and TechnologySimulation of Quantum Hamiltonians Theater 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Horacio Casini, Centro Atomico BarilocheEntanglement in QFT Theater

## Sunday, July 24, 2016

 Time Event Location 9:00 – 11:00am Depart Perimeter Institute and Travel to Niagara Falls Bus 11:00 – 1:00pm Table Rock Niagara Falls 1:00 – 1:30pm Drive to Niagara-on-the-Lake Bus 1:30 – 3:00pm Lunch at Trius Vineyard 3:00 – 4:00pm Tour of Vineyard Vineyard 4:00pm Depart for Waterloo Bus

## Monday, July 25, 2016

 Time Event Location 9:00 – 10:30am Stephen Jordan, National Institute of Standards and TechnologySimulation of Quantum Hamiltonians Theater 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Mukund Rangamani, University of California, DavisAdS/CFT correspondence Theater 12:30 – 2:30pm Lunch Atrium 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 2:30 – 4:30pm Stephen Jordan, National Institute of Standards and TechnologyJohn Preskill, California Institute of TechnologyQuantum Simulations Theater 4:30 – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm Xi Dong, Institute for Advanced StudyA Primer on Bulk Reconstruction: Part 1(Focus Lecture for AdS/CFT Course) Alice Room 5:00 – 6:00pm Adam Bouland, Massachusetts Institute of TechnologyEquivalence of Adiabatic and Circuit Based Quantum Computing(Focus Lecture for Simulation of SQH Course & Complexity Courses) Bob Room 5:00 – 6:00pm Douglas Stanford, Institute for Advanced StudyThe Sachdev-Ye-Kitaev model and AdS2/CFT1 Theater 7:00 – 9:00pm Gong Show Theater

## Tuesday, July 26, 2016

Please note room change for Workshop Discussion Session at 2:30

 Time Event Location 9:00 – 10:30am Patrick Hayden, Stanford UniversityQuantum Shannon Theory Theater 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Mukund Rangamani, University of California, DavisAdS/CFT correspondence Theater 12:30 – 2:30pm Lunch Atrium 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 2:30 – 4:30pm Juan Maldacena, Institute for Advanced StudyStephen Shenker, Stanford UniversityChaos Time Room 4:30 – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm Xi Dong, Institute for Advanced StudyA Primer on Bulk Reconstruction: Part 2 (Focus Lecture for AdS/CFT Course) Alice Room 5:00 – 6:00pm Michael Walter, Stanford UniversityQuantum Information and Symmetry(Focus Lecture for Quantum Shannon Theory Course) Bob Room 5:00 – 6:00pm Guifre Vidal, Perimeter InstituteTensor Networks for Quantum fFelds:Conformal Invariance and Emergent de Sitter Space Theater 7:00 – 9:00pm Gong Show Theater

## Wednesday, July 27, 2016

 Time Event Location 9:00 – 10:30am Guifre Vidal, Perimeter InstituteTensor Networks Theater 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Daniel Harlow, Harvard UniversityBlack Hole Information Paradox Theater 12:30 – 2:30pm Lunch Atrium 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 2:30 – 4:30pm Xi Dong, Institute for Advanced StudyAitor Lewkowycz, Princeton University,Beni Yoshida, Perimeter InstituteBulk Reconstruction Theater 4:30 – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm Dan Roberts, Massachusetts Institute of TechnologyIntegrals over Unitary Matrices(Focus Lecture for BH Information Paradox Course) Alice Room 5:00 – 6:00pm Markus Hauru, Perimeter InstituteMERA: A tensor network for scale invariant systems(Focus Lecture for Tensor Networks Course) Bob Room 5:00 – 6:00pm Renato Renner, ETH ZurichAn Extension of the Wigner’s Friend Gedankenexperiment Theater 6:30pm onwards BBQ Atrium

## Thursday, July 28, 2016

 Time Event Location 9:00 – 10:30am Dorit Aharonov, The Hebrew University of JerusalemQuantum NP and the Complexity of Ground States Theater 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Daniel Harlow, Harvard UniversityBlack Hole Information Paradox Theater 12:30 – 2:30pm Lunch Atrium 2:30 – 4:30pm Summer School Problem Solving Bistro 2nd FloorSpace Room 2:30 – 4:30pm Vijay Balasubramanian, University of PennsylvaniaXiaoliang Qi, Stanford UniversityBrian Swingle, Stanford UniversityTensor Network Holography Theater 4:30 – 5:00pm Coffee Break Bistro 1st Floor 5:00 – 6:00pm Adam Bouland, Massachusetts Institute of TechnologyWhy physicists should care about the complexity zoo(Focus Lecture for Complexity Course) Alice Room 5:00 – 6:00pm Markus Mueller, Western University/Perimeter InstituteEigenstate Thermalization Hypothesis(Focus Lecture for BH Information Paradox Course) Bob Room 5:00 – 6:00pm John Cardy, University of California, BerkeleyModular hamiltonians in 2d CFT Theater

## Friday, July 29, 2016

 Time Event Location 9:00 – 10:30am Stephen Shenker, Stanford UniversityQuantum Gravity and Quantum Chaos Theater 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:30pm Daniel Harlow, Harvard UniversityToy Holography Theater 12:30 – 2:30pm Lunch Atrium

Fernando Brandao, California Institute of Technology

Boundary States and Entanglement Spectrum from Strong Subadditivity

In this talk I will consider quantum states satisfying an area law for entanglement (e.g. as found in quantum field theory or in condensed matter systems at sufficiently low temperature). I will show that both the boundary state and the entanglement spectrum admit a local description whenever there is no topological order. The proof is based on strong subadditivity of the von Neumann entropy. For topological systems, in turn, I'll show that the topological entanglement entropy quantifies exactly how many extra bits are needed in order to have a local description for the boundary state. This latter result is based on a recent strengthening of strong subadditivity.

Based on joint work with Kohtaro Kato (University of Washington)

John Cardy, University of California, Berkeley

Modular hamiltonians in 2d CFT

I enumerate the cases in 2d CFT when the modular hamiltonian (log of the reduced density matrix) may be written as an appropriate integral over the energy-momentum tensor times a local weight. This includes known examples as well as new time-dependent ones. In all these cases the entanglement spectrum is that of an appropriate boundary CFT. I point out the obstruction to the existence of such a result for more complicated bipartitions of the space. This is joint work with Erik Tonni.

Netta Engelhardt, University of California, Santa Barbara

Towards a Reconstruction of General Bulk Metrics

I will describe a procedure for reconstructing the metric of a general holographic spacetime (up to an overall conformal factor) from distinguished spatial slices - “light-cone cuts” - of the conformal boundary. This reconstruction can be applied to bulk points in causal contact with the boundary. I will also discuss a prescription for obtaining the light-cone cuts from divergences of correlators in the dual field theory.

A new perspective on holographic entanglement

The by-now classic Ryu-Takayanagi formula associates the entanglement entropy of a spatial region in a holographic field theory with the area of a certain minimal surface in the bulk. Despite its simplicity and beauty, this formula raises a number of stubborn conceptual problems. I will present a reformulation which does not involve the areas of surfaces. This reformulation leads to a picture of entanglement in the field theory being carried by Planck-thickness "bit threads" in the bulk. I will argue that this picture helps to resolve a number of the conceptual difficulties surrounding the RT formula.

Renato Renner, ETH Zurich

An Extension of the Wigner’s Friend Gedankenexperiment

In this talk I consider the following principle that one may impose on any physical theory T:
"If an agent uses T to describe a system which includes another agent who herself uses T then no logical contradictions should arise.”
I then propose a gedankenexperiment, which can be regarded as an extension of the Wigner’s Friend experiment, to test whether this principle holds for quantum mechanics. The conclusion is that this is indeed the case for “plain" quantum theory, but that the principle is violated by many of its common interpretations and extensions.

Daniel Roberts, Massachusetts Institute of Technology

Holographic complexity by design

Douglas Stanford, Institute for Advanced Study

The application of holography to fundamental problems in quantum gravity has been hindered by the lack of a solvable model. However, building on work by Sachdev and Ye, Kitaev has proposed a solvable QM system as a dual to an AdS2 black hole. I will discuss the model and its possible bulk interpretation.

Guifre Vidal, Perimeter Institute

Tensor Networks for Quantum Fields:
Conformal Invariance and Emergent de Sitter Space

The multi-scale entanglement renormalization ansatz (MERA) is a tensor network that efficiently represents the ground state wave-function of a lattice Hamiltonian. Similarly, its extension to the continuum, the continuous MERA [proposed by Haegeman, Osborne, Verschelde and Verstraete, Phys. Rev. Lett. 110, 100402 (2013), arXiv:1102.5524], aims to efficiently represent the vacuum state wave-functional of a quantum field theory. In this talk I will first review MERA and cMERA, with emphasis on why we should care about these two constructions, including their conjectured connection to the AdS/CFT correspondence. Then, using the simplified context of the free boson CFT in 1+1 dimensions, I will discuss two new results: (1) the cMERA wave-function, which has an explicit UV cut-off, is nevertheless invariant under the conformal group (but with modified Virasoro generators: the stress tensor is non-local at short distances); (2)  cMERA can be regarded as an evolution in de Sitter space. Talk based on joint work with Qi Hu, in preparation.

There was a tremendous amount of interest for the “It from Qubit” summer school being hosted at Perimeter Institute from July 18-29, 2016.  As we were not able to accept everyone into the program, arrangements have been made for livestreaming, and satellite workshops have been established in some select locations. More information regarding these options is listed below:

Main Lectures: Live Streaming Setup and Chat

Perimeter will be live-streaming the conference talks to allow satellite schools and remote attendees to follow the proceedings - see the URL below.  The Livestream service supports all Flash playing browsers.

Streaming and Chat URLs
http://perimeterinstitute.ca/it-qubit-summer-school/live-stream-session-1 (Main page)
http://perimeterinstitute.ca/it-qubit-summer-school/live-stream-session-2 (Secondary page)

The main page will live stream all lectures and seminars taking place in the Theatre, ie, at 9am, 11am and 5pm (Waterloo time) -- see the Schedule. The secondary page will only be active for the 9am lecture on Monday July 18th, Tuesday July 19th and Wednesday July 20th and will show the lecture given in the Bob Room.

If you would like to submit questions through the Live Chat, we ask that you apply the following Etiquette:

1. Introduce yourself - Start your comment with your name and location (eg, "Lenny Susskind, Stanford: I'd like to ask ..." so we know who you are.
2. Be concise - keep comments or questions short so we have a chance to read and respond to them without a long delay.
3. Avoid abbreviations - avoid abbreviations and acronyms unless they are standard physics conventions.
4. Avoid follow-up questions, thanks or good byes - keep to a single comment or question to respect time constraints

If you have difficulties viewing the live stream, please, contact: Jeff Leithwood <jleithwood@perimeterinstitute.ca>

All lectures (including focus lectures) will be recorded and the recordings will be available on PIRSA at the URL below. Every effort will be made to have the recordings posted within a few hours of presentation

http://pirsa.org/C16003

Remote Participants

Remote participants will be able to both watch the live video feed and send questions and comments via the chat feature at the links above. Remote participants are also invited to consider the practice problems which will be posted to the conference website, as the school progresses. (Solution sets will also be provided in due course.)

Satellite Schools

The satellite schools will be organized at select locations to allow students view the lectures and work on the practice problems in a group. If you are interested in participating in one of the satellite schools, we kindly request that you contact the following individuals at the location most convenient for you. If you are interesting in organizing a new satellite school and have it advertised here, please contact Stephanie Mohl at smohl@perimeterinstitute.ca

Germany:  Albert Einstein Institute (Golm)

Netherlands:  University of Amsterdam

Germany:  Ludwig-Maximilians-Universität München

Israel:  University of Tel Aviv

California:  UC Berkeley

Massachusetts:  MIT

The following social events have been set up for the “It from Qubit” summer school.  We hope you will be able to take advantage of some of these opportunities.

## Movie NightS

Calling all Star Trek Enthusiasts!  As a prelude to the new Star Trek movie premiering in the first week of the school, we will show the first two installments in the main lecture theatre at 7:30 pm on Thursday and Friday night. We encourage you to visit a local theatre to see the third movie on Saturday, July 23.

 Thursday, July 21 Star Trek Friday, July 22 Star Trek: Into the Darkness Saturday, July 23 Star Trek Beyond

Star Trek Beyond will be showing at the following two theatres in Waterloo.  You may pre-purchase tickets in the hyperlinks below.

1. Galaxy Cinemas Waterloohttp://www.cineplex.com/Showtimes/any-movie/waterloo-on?Date=7/23/2016

• 8:00 pm
• 10:50 pm

To get to this theatre please take Bus Route 202 on University/Seagram (Stop 1090) to get to Conestoga Mall.  The cost to take the bus is $3.25 and you must have the exact change. Time: approximately 30 minutes. 2. Landmark Cinemashttps://www.landmarkcinemas.com/waterloo/film-info?film=3485 3D - • 1:15 pm • 7:15 pm • 10:15 pm ​Regular - • 4:15 pm To get to this theatre please take Bus Route 29 at University/Seagram (Stop 2676) to the Boardwalk Medical Centre (Stop 1293) and walk across the parking lot to Landmark Cinemas. The cost to take the bus is$3.25 and you must have the exact change. Time:  approximately 30 minutes.

For approximate timing of these routes you may use the GRT website to plan your trip: http://web.grt.ca/hastinfoweb/

## Excursion to Niagara Falls

Niagara Falls is best known as one of the seven natural wonders of the world.  An excursion has been planned to visit the falls and then continue on to Trius vineyard in Niagara-on-the-Lake for lunch and wine tasting. The cost of the excursion is \$25.00 and anyone interested in participating must contact Stephanie, smohl@perimeterinstitute.ca by Friday, July 8

 Sunday, July 24: Itinerary is as follows (timing approximate) 9:00 am Depart Perimeter Institute 11:00 – 1:00 pm Table Rock, Niagara Falls 1:00 – 1:30 pm Drive to Niagara-on-the-Lake 1:30 – 3:00 pm Lunch at Trius Winery at Hilldebrand 3:00 – 4:00 pm Best in Glass Vineyard and Winery Tour 4:00 pm Depart for Waterloo (Perimeter Institute)

## It from Qubit BBQ

A BBQ will be held on Wednesday, July 27.  All summer school students and workshop participants are invited to attend and break bread with one another. Who doesn’t like a good BBQ?  Yummm!

Wednesday, July 27:      Black Hole Bistro, 6:30 pm

Building Access:

• Monday – Friday
• The front door of the building will be open from 8:00 am until 5:00 pm.  However, access to common areas within the building will be open until 8:00 pm
• Library hours are from 8:30 am – 5:00 pm
• Saturday, July 23
• The institute will be open for the morning to accommodate lectures taking place in the theater from 9:00 am – 12:30 pm.  Breakfast and lunch will not be available in the bistro on this day
• The institute will be open from 8:30 – 9:00 am to allow check in for the excursion.  The bistro will not be open to serve breakfast or provide any other snacks.
• Sunday, July 24
• During the hours not listed, the building will be locked.  There is security onsite 24 hours.  You are welcome to work in the library or common areas.  Please identify yourself as a conference attendee and they will let you into the building.

Computer Access:

• It is no longer necessary to have a username or password to log on to the PI wireless network.
• To connect to the PI network, open your ‘Wireless Networks Available’ window and connect to PI_Public.
• If you have any questions or IT needs during you stay, please contact them at tech@pitp.ca

Washrooms:

• Washrooms are located on every floor of the building on the south side, as well as in the Atrium area near the Mike Lazaridis Theater of Ideas.

Lunches:

Questions:

• If you have questions regarding your travel, or would like more information about the area, please see Stephanie Mohl or Emma Nichols in office 129.  Alternatively, Stephanie can be reached at extension 6062 or by email at smohl@perimeterinstitute.ca.  Emma may be reached at enichols@perimeterinstitute.ca

Morning Lectures:

Generally, the morning lectures will take place in the Mike Lazaridis Theatre on the 1st floor. The first lecture begins at 9am and the second lecture, at 11am. Please ensure that you arrive promptly in order to guarantee a seat and to cause no disruption to the lecture. The lectures will also be shown in the Bob Room on the 4th floor, in case the seating in the theatre reaches maximum capacity.

At 9am on the first three days of the conference, there will be an exception to the above arrangements and instead there will be two simultaneous lectures. The first will be in the Bob Room and will be directed at QI students interested in learning more about gravity and quantum field theory. The second will be in the Theatre and will be directed at HE students interested in learning about quantum information basics.

Summer School Problem Solving sessions:

Due to the number of students who will be participating in the “It from Qubit” summer school, it was necessary to hold the problem solving session in two separate rooms: the 2nd Floor Bistro or the Space Room (on the 4th floor).  On the back of your nametag, you will see to which of these two rooms you have be assigned.  Please go to the room indicated as there is a limited number of spaces in each room and the spaces have been set up based on your placement.

You will also see a coloured dot on the front of your nametag.  A red dot indicates that our information was that your primary background was in Quantum Information whereas a blue dot indicates a High Energy background. Please, do not worry if you feel we have made an error in this assignment. Both of the rooms are arranged with tables for 8 students each. We are going to ask you to arrange yourselves so that each table seats (roughly) 4 QI students and 4 HE students. A few printed copies of the problem sets will be provided at each table. The problem sets can also be on the conference website. (Solutions will also be posted there in due course.)

Further we are encouraging the students to help each other in these sessions. So feel free to discuss the problems (as well as the morning’s lectures) in your group and seek advice from someone with a different background than yours. There will also be two tutors supervising each session and so you can also ask them when you get stuck. Each of the morning’s lecturers will also visit the problem solving sessions at some point in the afternoon and so again we encourage you to ask them about the problems (as well as the morning’s lectures).

Focus Lectures:

Two focus lectures have been scheduled for each day from 5–6pm; one in the Alice Room (3rd floor) and one in the Bob Room (4th floor).  These are supplementary lectures which we hope will help provide a greater understanding of the material presented in the morning courses.   Please feel free to attend which ever lecture you think you will benefit from the most. Advanced students should also feel free to attend the workshop seminar which will be taking place at the same time in the Theatre.

Final Note:

This summer school has been organized by the "It from Qubit" Simons Collaboration to promote communication and learning between the high energy physics and quantum information theory communities. Hence, we are catering to a very broad spectrum of students and we have arranged a diverse set of activities. The school is also being held concurrently with a research workshop of the "It from Qubit" Collaboration. However, you will simply not be able to attend all of the lectures, seminars and other activities that are taking place here at Perimeter in the next two weeks! You will have to make choices. So we are asking each of you to choose to participate in those activities that you think will maximally benefit your own learning. As a side note, let us add that all of the lectures and seminars will be recorded and should appear at http://pirsa.org/C16003 within a few hours of their completion.

July 18

Hayden: Quantum Information Basics
Problem Set
Solution

Chapters 2 and 3 (and a small part of chapter 10) in John Preskill's Lecture Notes on Quantum Computation (http://www.theory.caltech.edu/people/preskill/ph229/)

Hubeny: Gravity Basics
Problem Set
Solution

Lecture Notes for this Lecture
Sean Carroll, "Lecture Notes on General Relativity" (http://arxiv.org/pdf/gr-qc/9712019)

Spekkens: Entanglement
Problem Set
Solution

Nielsen and Chuang Quantum Computation and Quantum Information'', Section 12.5
Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki, Quantum entanglement'', Rev. Mod. Phys. 81, 865 (2009), Sections I, II, and IIIA-D
Marshall, Olkin, and Arnold "Inequalities: Theory of Majorization and Its Applications"

July 19

Watrous:  QI Basics
Problem Set
Solution

A similar presentation of Shor's algorithm can be found in:
P. Kaye, R. Laflamme, and M. Mosca, "An Introduction to Quantum Computing" (Oxford University Press 2007)
or
R. Cleve, A. Ekert, C. Macchiavello and M. Mosca, "Quantum algorithms revisited," Proceedings of the Royal Society A (1998) [arXiv:quant-ph/9708016]

Hartman:  QFT Basics
Problem Set
Solution

Sections 4-5 of my course notes at http://www.hartmanhep.net/topics2015/
Section 1 of Rychkov's lectures at
https://arxiv.org/abs/1601.05000

Spekkens:  Entanglement
Problem Set
Solution

July 20

Gottesman:  Quantum Error Correction
Problem Set
Solution

Daniel Gottesman, "An Introduction to Quantum Error Correction," arXiv:quant-ph/0004072
<https://www.perimeterinstitute.ca/personal/dgottesman/QECC-resources.html>

Hubeny:  Gravity Basics
Problem Set
Solution

Lecture Notes for this Lecture

Casini:  Entanglement in QFT
Problem Set
Solution
Bonus Question
Bonus Question Solution

H. Casini and M. Huerta, "Entanglement entropy in free quantum field theory" (https://arxiv.org/abs/0905.2562)
P. Calabrese and J. Cardy, "Entanglement Entropy and Quantum Field Theory" (http://arxiv.org/abs/hep-th/0405152)

July 21

Hartman:  QFT Basics
Problem Set
Solution

Casini:  Entanglement in QFT
Problem Set
Solution
Bonus Question
Bonus Question Solution

July 22

Gottesman:  Quantum Error Correction
Problem Set
Solution

Problem Set
Solution

July 23

Jordan:  Simulation of Quantum Hamiltonians

Lecture Notes for this Lecture

July 25

Jordan:  Simulation of Quantum Hamiltonians
Problem Set
Solution

Lecture Notes for this Lecture

Problem Set
Solution

July 26

Hayden:  Quantum Shannon Theory
Problem Set
Solution

Chapter 10 of Preskill’s quantum computation lecture notes: http://www.theory.caltech.edu/~preskill/ph219/chap10_6A.pdf
B. Czech, P. Hayden, N. Lashkari and B. Swingle, "The Information Theoretic Interpretation of the Length of a Curve" (
http://arxiv.org/pdf/1410.1540.pdf)

Problem Set
Solution

M. Rangamani "Holographic Entanglement Entrophy"
https://ucdavis.box.com/v/eebookpi
https://arxiv.org/pdf/1609.01287v1.pdf

July 27

Vidal:  Tensor Networks
Problem Set
Solution

Slides for this Lecture:  Tensor Networks

Problem Set
Solution

July 28

Aharonov:  Complexity
Problem Set

Survey of the circuit-to-Hamiltonian construction and Kitaev's proof that local Hamiltonian is QMA complete:
Dorit Aharonov, Tomer Naveh, "Quantum NP - A Survey" (https://arxiv.org/abs/quant-ph/0210077)
More conceptual explanations of the above in Sections 1-3 of Dorit Aharonov, Itai Arad and Thomas Vidick, "The Quantum PCP Conjecture" (http://arxiv.org/abs/1309.7495)
(section 1.3 explains the connection between QMA hardness and the time of relaxation to the Gibbs state or ground state. Section 3 explains the difficulties in Kitaev's proof of QMA completeness of the local Hamiltonian problem)
Long list of QMA-complete problems:
Adam D. Bookatz, "QMA-complete problems" (https://arxiv.org/abs/1212.6312)

More specialized material:

Hardness of physically motivated Hamiltonians (2D Hubbard and 2D Heisenberg):
Norbert Schuch and Frank Verstraete, "Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory" (http://arxiv.org/abs/0712.0483)
QMA completeness of the Consistency of density matrices problem:
Yi-Kai Liu, "Consistency of Local Density Matrices is QMA-complete" (https://arxiv.org/abs/quant-ph/0604166)
1D translationaly invariant hamiltonians are hard:
Daniel Gottesman and Sandy Irani, "The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems" (https://arxiv.org/abs/0905.2419

July 29

Shenker:  Quantum Gravity and Quantum Chaos

J. Maldacena, S.H. Shenker and D. Stanford, "A bound on chaos," arXiv:1503.01409 [hep-th].
S.H. Shenker and D. Stanford, "Stringy effects in scrambling," arXiv:1412.6087 [hep-th].
D.A. Roberts, D. Stanford and L. Susskind, "Localized shocks," arXiv:1409.8180 [hep-th].

Harlow:  Toy Holography

Additional minicourse by Aaron Wall on entanglement entropy and black hole physics available here: http://www.wall.org/~aron/STmini.htm

## Toy Holography

Friday Jul 29, 2016
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## Quantum Gravity and Quantum Chaos

Friday Jul 29, 2016
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## Eigenstate Thermalization Hypothesis

Thursday Jul 28, 2016
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## Modular hamiltonians in 2d CFT

Thursday Jul 28, 2016
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I enumerate the cases in 2d CFT when the modular hamiltonian (log of the reduced density matrix) may be written as an appropriate integral over the energy-momentum tensor times a local weight. This includes known examples as well as new time-dependent ones. In all these cases the entanglement spectrum is that of an appropriate boundary CFT. I point out the obstruction to the existence of such a result for more complicated bipartitions of the space. This is joint work with Erik Tonni

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## Why physicists should care about the complexity zoo

Thursday Jul 28, 2016
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## Tensor Network Holography

Thursday Jul 28, 2016
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## Black Hole Information Paradox - 2

Thursday Jul 28, 2016
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## Quantum NP and the Complexity of Ground States

Thursday Jul 28, 2016
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## An Extension of the Wigner’s Friend Gedankenexperiment

Wednesday Jul 27, 2016
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In this talk I consider the following principle that one may impose on any physical theory T:
"If an agent uses T to describe a system which includes another agent who herself uses T then no logical contradictions should arise.”
I then propose a gedankenexperiment, which can be regarded as an extension of the Wigner’s Friend experiment, to test whether this principle holds for quantum mechanics. The conclusion is that this is indeed the case for “plain" quantum theory, but that the principle is violated by many of its common interpretations and extensions.

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## Integrals over Unitary Matrices

Wednesday Jul 27, 2016
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## Pages

Scientific Organizers:

• Patrick Hayden, Stanford University