__July 18__

**Hayden: Quantum Information Basics **

Problem Set

Solution

Supplementary reading for this course:

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

Supplementary reading for this course:

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

**Spekkens: Entanglement**

Problem Set

Solution

Supplementary reading for this course:

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

Supplementary reading for this course:

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

Supplementary reading for this course:

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

Supplementary reading for this course:

Daniel Gottesman, "An Introduction to Quantum Error Correction," arXiv:quant-ph/0004072

See also a longer list of resources at the following webpage:

<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

Supplementary reading for this course:

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

**Rangamani: AdS/CFT Correspondence**

Problem Set

Solution

Supplementary reading for this course:

M. Rangamani "The AdS/CFT Correspondence"

http://mukund.physics.ucdavis.edu/research/resources/adscft.pdf

**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

**Rangamani: AdS/CFT Correspondence**

Problem Set

Solution

**July 26**

**Hayden: Quantum Shannon Theory**

Problem Set

Solution

Supplementary reading for this course:

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)

**Rangamani: AdS/CFT Correspondence**

Problem Set

Solution

Supplementary reading for this course:

M. Rangamani "Holographic Entanglement Entrophy"

http://mukund.physics.ucdavis.edu/research/resources/eebook-pi.pdf

**July 27**

**Vidal: Tensor Networks**

Problem Set

Solution

Slides for this Lecture: Tensor Networks

**Harlow: Black Hole Information Paradox**

Problem Set

Solution

**July 28**

**Aharonov: Complexity**

Problem Set

Supplementary reading for this course:

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)

**Harlow: Black Hole Information Paradox**

Problem Set

**July 29**

**Shenker: Quantum Gravity and Quantum Chaos**

Supplementary reading for this course:

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