Website address: http://insti.physics.sunysb.edu/~twei/Courses/Fall2024/PHY568/

Lecture time: 2:00-3:20PM Monday & Wednesday, in person in Physics Building P123

Instructor: Tzu-Chieh Wei <tzu-chieh.wei[at]stonybrook[dot]edu> Office: Math 6-115B, Office Phone: 631-632-7966

Office hours: (beginning from Sep. 6th) tentatively 11:30am to 12:30pm Friday via Zoom (see Brightspace for the link).

Grader: Shuyu Zhang <shuyu.zhang.1[at]stonybrook[dot]edu>

Technical and Software Requirement: Zoom meeting will be used for office hours. Internet is needed. Microphone needed to participate verbally.

(a) The best way to communicate with the instructor is to attend the weekly office hour, the next is (b) to email the instructor (you may expect an aswer about 24-48 hours)

Qualification of the instructor: (1) He has ample research experience in Quantum Information Science since when he was a PhD student, and has supervised a few PhD students, master students, and undergraduate students on related research projects. See the publication list here.

(2) He is constantly motivated to improve his teaching skills and recently completed a 5-week Online Teaching Workshop held by CELT, Stony Brook and obtained an electronic badge for that: Online Teaching Certificate (OTC): Summer 2021 (Stony Brook University).

(3) To keep updated with the fast evolving design of the quantum programming software, the instructor was also diligent in attending IBM Qiskit Summer Schools and other events for the past two years so as to design up-to-date programming materials for this course. See the certificates and badges he earned:

1. IBM 2020 Qiskit Global Summer School: (a) Certificate of Participation and (b) Certificate of Quantum Excellence

2. IBM Quantum Challenge 2021

3. IBM 2021 Qiskit Global Summer School on Quantum Machine Learning

4. IBM Quantum Challenge - Fall 2021 - Advanced

5. IBM Quantum Spring Challange 2022 Achievement - Advanced

6. IBM Qiskit Global Summer School 2023 - Quantum Excellence

(4) This past summer (2024), he co-organized a C2QA Summer School QIS303: Quantum Error Mitigation with Prof. Dmitri Kharzeev

(5) He has worked on the creation of a Quantum Information Science and Technology Master's Program, which was recently approved by SUNY and NYSED in July 2022.. There are a few exciting new courses to be added. This course is one in the series and PHY 605 Quantum Programming is another. He aims to make Stony Brook University become a major contributor of Quantum-Ready Workforce that is highly demanded from academia, industries and national labs.

Course description:

This is a survey of the fast evolving field of quantum information, ranging from Bell inequality, quantum teleportation to quantum algorithms and quantum programming frameworks. It aims to cover the essential knowledge of quantum information science and helps to bridge the gap to the current research activities of the field. Some emphasis will be placed on solid-state platforms of quantum computers, topological error correction codes, and applications. Other systems will be introduced when necessary. Some illustration of quantum programming will be done on IBM's transmon-type cloud quantum computers.

Course level: senior undergraduates and beginning graduate students (Master/PhD); students from other departments such as Chemistry, Math, CS and Engineering who have learned linear algebra should find the course accessible. The materials covered in this course are interdisciplinary anyway. The required knowledge of quantum mechanics is also minimal, e.g. superposition, unitary evolution, and measurement described in the first chapter of a standard quantum mechanics textbook. But these will be reviewed in the first week as well. [Over the past two years in the precursor PHY682, there were students from Applied Math, CS & Mechanical Engineering, in addition to Physics. They were all doing better as the course progressed.]

For undergraduates: This course may be taken by upper-level undergraduates with Prerequisite: PHY 251 or Corequisite: PHY 308. It needs the permission and the signature of the instructor in order to register for this course; permission form can be downloaded here.

Breadth course or not (for Physics & Astronomy PhD students): this can count as a breadth course; if you have any question on the breadth courses, please consult the Graduate Program Director.

Learning outcomes:

Students who have completed this course

• Should be able to understand the physical principles of quantum computation and how quantum algorithms work such as Shor's factoring and Grover's searching

• Should be able to understand various frameworks of quantum computation, such as the standard circuit model, topological quantum computation, adiabatic quantum computation and measurement-based quantum computation.

• Should be able to understand the basics of information theory and their relation to statistical mechanics and quantum entanglement

• Should be able to understand the working principles of sold-state qubits and be able to perform simple programming on publicly available quantum computers such as IBM Q

Required Textbooks:

There is no required textbook. The instructor is working lecture notes and they will be provided when available (see below; current one file collection of notes is here [with less frequent update than each separate unit; see below).

[PHY568 is evolved under PHY682 Special Topics in Solid-State Physics(Fall 2020 and Fall 2021) and now has its own course number and title (since Fall 2022);

Moreover: All the 25 lectures from PHY682 Fall 2020 are now available to watch online on YouTube; link to Fall 2023's website

Recommended Textbooks/Resources:

Quantum Computation and Quantum Information, M. Nielsen and I. Chuang (Cambridge University Press)

An Introduction to Quantum Computing, P. Kaye, R. Laflamme and M. Mosca (Oxford)

J. Preskill lecture notes (http://www.theory.caltech.edu/~preskill/ph229/#lecture)

The Feynman Lectures on Physics, Vol. 3 (which can be read online here)

Learn Quantum Computation using Qiskit (free digital textbook)

Cirq tutorial (from Cirq documentation)

Quantum Computing: An Applied Approach, Jack D. Hidary (Springer)

Online book by Andy Matuschak and Michael Nielsen on "Quantum computing for the very curious"

IBM Quantum Learning is a collection of learning materials (e.g. recorded videos, codes, etc.) maintained by IBM.

Math needed in this course: e.g. The Mathematics of Quantum Mechanics by Dr. Martin Laforest (University of Waterloo)

Python Notebooks will be distributed to illustrate how to program quantum computers. Minimal prior programming experience is needed. We will learn from examples and you can modify and play with codes. The Qiskit book Learn Quantum Computation using Qiskit (free digital textbook) gives an extensive coverage. In PHY568 there will be only minimal quantum programming. PHY605 Quantum Programming covers various aspects of programming (first offered in Spring 2024).

Grades: (tentative)

(1) Homework 50% [main purpose is to enhance understanding of lecture materials; will be posted as pdf on Brightspace]

(2) Participation (possible extra 5%) [(a) attendance of lectures is required; more importantly, this is to encourage active participation and learning; asking questions helps the instructor to clarify and in turn helps you and others to understand; sharing with others how you understand a particular concept is useful. (b) Office hours are encouraged to attend. (c) Brightspace discussion board is also encouraged to use]

(3) Mid-term exam 25% [to gauge how your learning goes]

(4) Final presentation (for suggested topics/papers, see below) 25%

The letter grade assignment is based on: A (90-100), A- (85.01-89.99), B+ (80.01-85.00), B (75.01-80.00), B-(70.01-75.00), C+(65.01-70.00), C (60.01-65.00), C-(55.01-60.00), D+(50.01-55.00), D(45.01-50.00), Fail: 45 or below

Homework policy: no late homework (must be turned in on the due day by submitting it in Brightspace); exception must be requested two days or earlier before the deadline

Topics to be covered and tentative syllabus

(This is a tentative syllabus, based on last year's version. Due dates may change. Check later for update.)

[All the 25 lectures from Fall 2020 are now available to watch online on YouTube; link to Fall 2023's website]

Lectures will be given in person and the coverage of topics may differ from last year's.

The topics are still being updated; lecture notes can be downloaded by clicking the unit titles; current one file collection is here (file size can be large and less often updated).

Learning Units | Topics | Selected Learning Goals | Dates |

Unit 0: The appetizer of quantum behavior Unit 1: The history of Q |
Review of Math, Basics of Quantum Principles, Concepts of qubits, gates and quantum algorithms | You'll be ready to embark on a QIS journey | 8/26, 8/28 |

Unit 2: From foundation to science-fiction teleportation | Bell inequality, teleportation of states and gates, entanglement swapping, remote state preparation, superdense coding, and superdense teleportation | You'll be able understand basic and important procotols of information processing | 9/4, 9/9 |

Unit 3: Information is physical | Superconducting qubits, solid-state spin qubits, photons, trapped ions, and topological qubits | You'll get to know various physical systems and candidates to realize qubits and quantum computers | 9/11, 9/16 |

Unit 4: Grinding gates in quantum computers | Quantum gates and circuit model of quantum computation, introduction to IBM's Qiskit, Grover's quantum search algorithm, amplitude amplification | You'll be able to understand what quantum computation is and specific quantum algorithm on searching | 9/18, 9/23 |

Unit 5: Programming through quantum clouds | Quantum programming on IBM's quantum computers, variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA) [will not focus too much on programming in Fall 2024;see PHY605; may be replaced with other topics] | You'll be able to modify example Python Notebooks to run variational quantum eigensolvers for applications | 9/25 |

Unit 6: Dealing with errors | Error models, Quantum error correction, topological stabilizer codes and topological phases, error mitigations | You'll be able to understand why quantum information is fragile but quantum correction codes can be used to reduce error rates in logical qubits | 9/30, 10/2 |

Unit 7: Quantum computing by braiding & Unit 8: More topological pleas | Anyons and topological quantum computation, Fibonacci anyons, Majorana fermions, Kitaev's chain, toric/surface code | You'll be able to say what anyons are and how they can be used for quantum computing | 10/7, 10/9 |

Midterm | 10/16 | ||

Unit 7: Quantum computing by braiding & Unit 8: More topological please | Anyons and topological quantum computation, Fibonacci anyons, Majorana fermions, Kitaev's chain, toric/surface code | You'll be able to say what anyons are and how they can be used for quantum computing | 10/21 |

Unit 9: Quantum computing by evolution and by measurement | Other frameworks of quantum computation: adiabatic and measurement-based; D-Wave’s quantum annealers | You'll be able to understand alternative approaches for quantum computation | 10/23 |

Unit 10: Quantum en-tangles | Entanglement of quantum states, entanglement of formation and distillation, entanglement entropy, Schmidt decomposition, majorization, quantum Shannon theory | You'll be able to understand the basics of quantum information and entanglement theory | 10/28, 10/30 |

Unit 11: No clones in quantum | No cloning of quantum states, non-orthogonal state discrimination, quantum tomographic tools, quantum cryptography: quantum key distribution from transmitting qubits and from shared entanglement | You'll be able to understand why no cloning actually helps to distribute secret keys | 11/4, 11/6 |

Unit 12: Show me your phase, Mr. Unitary | Quantum Fourier Transform, quantum phase estimation, Shor’s factoring algorithm, and quantum linear system (such as the HHL algorithm) | You'll be able to understand and apply one of the most important functions: Quantum Fourier Transform and algorithms: Quantum Phase Estimation. | 11/11, 11/13,11/18 |

Unit 13: The quantum Matrix | Quantum
simulations and quantum sensing and metrology |
You'll be able to get some glimpses to quantum simulations and sensing and metrology and to explain them | 11/20, 11/25 |

Students presentation | Topics to be chosen by students (in discussion with the instructor and among students in groups) | You'll be able to learn a specific topic and present it to the class | 12/2, 12/4, 12/9 & final exam day (if needed) |

For basic linear algebra: see Laforest's online book, Chapter 2 of Kaye, Laflamme & Mosca (KLM), or Chapter 2 (2.1 to 2.2.3) of Nielsen and Chuang (N&C) including review of quantum mechanics needed in this course.

(week 1) [8/26,8/28] Unit 0: The appetizer of quantum behavior Unit 1 The history of Q: Overview of this course and review of linear algebra, basics of quantum mechanics, quantum bits and mixed states, taste of quantum algorithms.

suggested reading: N&C 1.2-1.4, 2.2, 2.4; KLM 1.4, 1.6, chapter 3, 6.2-6.4; Qiskit book (Qb) chapter 1, 2.1-2.3;

(weeks 2 & 3) [Labor Day 9/4, 9/9] Unit 2 From foundation to science-fiction teleportation: Bell inequality, teleportation of states and gates, entanglement swapping, remote state preparation, superdense coding, and superdense teleportation.

suggested reading: N&C 2.3, 2.6; KLM chapter 5; Qb 3.1-3.5

further reading: Nonlocality beyond quantum mechanics, Sandu Popescu, http://www.nature.com/doifinder/10.1038/nphys2916

Genuine Quantum Nonlocality in the Triangle Network by Marc-Olivier Renou, Elisa Bäumer, Sadra Boreiri, Nicolas Brunner, Nicolas Gisin, and Salman Beigi, Phys. Rev. Lett. 123, 140401 (2019)

(weeks 3 & 4) [9/11, 9/16] Unit 3 Information is physical---Physical systems for quantum information processing:

Superconducting qubits, solid-state spin qubits, photons, trapped ions, and topological qubits (p-wave superconductors, fractional quantum Hall systems, topological insulators, etc.)

suggested reading: N&C chap 7

Some refs for further reading:

Majorana zero mode and topological quantum computing, Das Sarma, Friedman and Nayak, npj Quantum 1, 15001 (2015)

Diamond NV centers for quantum computing and quantum networks, Childress and Hanson, MRS Bulletin 38, 134 (2013)

Quantum Control over Single Spins in Diamond, V.V. Dobrovitski, G.D. Fuchs, A.L. Falk, C. Santori, and D.D. Awschalom, Annual Review of Condensed Matter Physics 4, 23 (2013)

Quantum computing with neutral atoms, David S. Weiss, and Mark Saffman, Physics Today 70, 7, 44 (2017); doi: 10.1063/PT.3.3626

A quantum engineer's guide to superconducting qubits, P. Krantz , M. Kjaergaard , F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Appl. Phys. Rev. 6, 021318 (2019)

Superconducting Qubits and the Physics of Josephson Junctions, J. Martinis and K. Osborne, Les Houches Lecture Notes

Photonic quantum information processing: A concise review, Sergei Slussarenko and Geoff J. Pryde, Appl. Phys. Rev. 6, 041303 (2019)

Building logical qubits in a superconducting quantum computing system, Jay M. Gambetta, Jerry M. Chow & Matthias Steffen, npj Quantum Information volume 3, Article number: 2 (2017)

Co-designing a scalable quantum computer with trapped atomic ions, Kenneth R Brown, Jungsang Kim & Christopher Monroe, npj Quantum Information volume 2, Article number: 16034 (2016)

Engineering the quantum-classical interface of solid-state qubits, David J Reilly, npj Quantum Information volume 1, Article number: 15011 (2015)

A quantum engineer's guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019), P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver

Single-qubit quantum memory exceeding ten-minute coherence time, Wang et al. Nature Photonics volume 11, pages646–650(2017)

(weeks 4 & 5) [9/18,9/23] Unit 4 Grinding gates in quantum computers: Quantum gates and circuit model of quantum computation, introduction to IBM's Qiskit, Grover's quantum search algorithm, amplitude amplification.

Other circuit-model based quantum computers and their programming frameworks: Rigetti and Forest, Google and Cirq (We focus on using Qiskit in this course)

For construction of quantun gates, there is a milestone paper worth reading:

"Elementary gates for quantum computation", Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter,

Phys. Rev. A 52, 3457 (1995).

J. Zhang, J. Vala, S. Satry, K. B. Whaley, Exact Two-Qubit Universal Quantum Circuit, Phys. Rev. Lett. 91, 027903 (2003).

Bremner MJ, Dawson CM, Dodd JL, Gilchrist A, Harrow AW, Mortimer D, Nielsen MA, Osborne TJ, Practical scheme for quantum computation with any two-qubit entangling gate, Phys. Rev. Lett. 89, 247902 (2002)

suggested reading: N&C chap 4; KLM chap 4; Qb 1.4; 2.4, 2.5

(week 5) [9/25] Unit 5 Programming through quantum clouds: Computational complexity, Quantum programming on IBM's superconducting quantum computers, including the use of the variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA) for optimization, hybrid classical-quantum neural network.

suggested reading: Qb chap 4;

(week 6) [9/30,10/2] Unit 6 Dealing with errors: Error models, Quantum error correction, error mitigations (brief discussions on topological stabilizer codes and topological phases).

suggested reading: N&C chap 10; KLM chapter 10; Qb chap 5.1-5.2

Useful references:

"An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation", Daniel Gottesman, arXiv:0904.2557

"Quantum Error Correction" by Todd Brun in Oxford Research Encyclopedia in Physics

"Key ideas in quantum error correction" by Robert Raussendorf, Phil. Trans. R. Soc. A (2012) 370, 4541–4565

doi:10.1098/rsta.2011.0494

(weeks 7,8,9) [10/7, 10/9, 10/14 Fall break, 10/16 mid term, 10/21] Unit 7 Quantum computing by braiding: Toric code in more detail, Anyons and topological quantum computation, Fibonacci anyons, Majorana fermions, Kitaev's chain and Unit 8 More topological please: (The two units will be combined to one: Topological Quantum Computing)

[in-class midterm exam on 10/16]

Useful references:

Majorana zero modes and topological quantum computation, Sankar Das Sarma, Michael Freedman & Chetan Nayak, npj Quantum Information volume 1, Article number: 15001 (2015)

Kitaev & Laumann, arXiv:0904.2771

Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321 (2006) 2–111

Simon Trebst, Matthias Troyer, Zhenghan Wang, Andreas W.W. Ludwig, A short introduction to Fibonacci anyon models, arXiv:0902.3275

Lahtinen & Pachos, A Short Introduction to Topological Quantum Computation, arxiv:1705.04103

Nayak et al. Rev. Mod. Phys. 80, 1083 (2008)

Fujii, arXiv:arXiv:1504.01444

(week 9) [10/23] Unit 9 Quantum computing by evolution and by measurement: Other frameworks of quantum computation: adiabatic and measurement-based; D-Wave’s quantum annealers

Refs:

"Adiabatic Quantum Computing and Quantum Annealing" by Erica K. Grant and Travis S. Humble in Oxford Research Encyclopedia in Physics

"Measurement-Based Quantum Computation", an article I wrote for Oxford Research Encyclopedia of Physics, the article link is here.

D-Wave tutorials: https://www.dwavesys.com/resources/tutorials

For Blind quantum computation and related subjects, see a review by J. Fitzsimons

A series of recorded lectures by Prof. Robert Raussendorf on MBQC are here.

(weeks 9 & 10) [10/28,10/30] Unit 10 Quantum entangles: Entanglement of quantum states, entanglement of formation and distillation, entanglement entropy, Schmidt decomposition, majorization, quantum Shannon theory

suggested reading: N&C 12.2, 12.5

additional reading:

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, ``Quantum entanglement,'' Rev. Mod. Phys. 81, 865 (2009)

Quantum Data Compression of a Qubit Ensemble, Lee A. Rozema, Dylan H. Mahler, Alex Hayat, Peter S. Turner, and Aephraim M. Steinberg, Phys. Rev. Lett. 113, 160504 – Published 17 October 2014

(week 11) [11/4,11/6] Unit 11 No clones in quantum: No cloning of quantum states, non-orthogonal state discrimination, quantum tomographic tools, quantum cryptography: quantum key distribution from transmitting qubits and from shared entanglement

suggested reading: N&C 12.1, 12.6; Qb chap 3.12

Refs:

Barnett & Croke, Quantum state discrimination, arXiv:0810.1970

Bae & Kwek, Quantum state discrimination and its applications, arXiv: 1707.02571

Progress in satellite quantum key distribution, Robert Bedington, Juan Miguel Arrazola & Alexander Ling, npj Quantum Information volume 3, Article number: 30 (2017)

Practical challenges in quantum key distribution, Eleni Diamanti, Hoi-Kwong Lo, Bing Qi & Zhiliang Yuan, npj Quantum Information volume 2, Article number: 16025 (2016)

[book] Principles of Quantum Communication Theory: A Modern Approach, by Sumeet Khatri and Mark M. Wilde, arXiv2011.04672

(weeks 12, 13) [11/11,11/13,11/18] Unit 12 Show me your 'phase', Mr. Unitary: Quantum Fourier Transform, quantum phase estimation, Shor’s factoring algorithm, and quantum linear system (such as the HHL algorithm) and programming with IBM Qiskit again

suggested reading: N&C chap 5, 6.3; KLM chapter 7, 8.4; Qb chap 3.8, 3.9, 3.11

Refs:

Quantum algorithms: an overview, Ashley Montanaro, npj Quantum Information volume 2, Article number: 15023 (2016)

Quantum sampling problems, BosonSampling and quantum supremacy, A. P. Lund, Michael J. Bremner & T. C. Ralph, npj Quantum Information volume 3, Article number: 15 (2017)

(weeks 13 & 14) [11/20,11/25, 11/27 no class: Thanksgiving Break] Unit 13 The quantum 'Matrix': Quantum simulations and quantum sensing and metrology

additional reading:

"Entropic uncertainty relations and their applications", Patrick J. Coles, Mario Berta, Marco Tomamichel, and Stephanie Wehner, Rev. Mod. Phys. 89, 015002 – Published 6 February 2017

"Cross-Platform Verification of Intermediate Scale Quantum Devices", by Andreas Elben, Benoît Vermersch, Rick van Bijnen, Christian Kokail, Tiff Brydges, Christine Maier, Manoj K. Joshi, Rainer Blatt, Christian F. Roos, and Peter Zoller, Phys. Rev. Lett. 124, 010504 (2020)

See also the article by Steve Flammia on "Quantum Computer Crosscheck"

Physics article on "The Certainty of Uncertainty" by David Voss

"Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements" by L.A. Rozema, A. Darabi, D. H. Mahler, A. Haya, Y. Soudagar, and A. M. Steinberg, Phys. Rev. Lett. 109, 100404 (2012)

"Quantum Optical Metrology -- The Lowdown on High-N00N States", J. P. Dowling, arXiv:0904.1063

"Nonclassical Light and Metrological Power: An Introductory Review", K.C. Tan, H. Jeong, arXiv:1909.00942

"Minimizing back-action through entangled measurements", K.D. Wu et al., Phys. Rev. Lett. 125, 210401 (2020)

Other refs:

Richard Feynman's paper "Simulating Physics with Computers", Int. J. Theor. Physics, vol 21, no.6/7, p467-488 (1982). Some quotes from Feynman on quantum physics and computer simulation.

Review article on "Tools for quantum simulation with ultracold atoms in optical lattices" by Florian Schäfer, Takeshi Fukuhara, Seiji Sugawa, Yosuke Takasu & Yoshiro Takahashi, Nature Reviews Physics volume 2, pages411–425(2020) [link to arXiv version]

Collection of review papers in Nature Physics on quantum simulations in 2012

(weeks 14 & 15 & 16) [12/2,12/4,12/9 (last class)] Additional topics and Student Presentation

Python and Qiskit

Qiskit requires Python 3 and you can install Qiskit according to the instruction here at the documentation. Python (in particular Python 3) can be installed in Mac, Windows and Linux (Mac and Linux may come with it). We need at least Python 3.6 or later. It is recommended to install on your own PC or laptop.

You can also sign up a free IBM Q account; in order to run programs on real qantum computers, you need to have an account with IBM Q. They used to have "Quantum Lab" with which you can write and run codes on their web server. However, they discontinued that service in May 2024. Additionally, you can sign up for a "CoCalc" account at here: https://cocalc.com/ or a Google Colab account at https://colab.research.google.com/. Note that Qiskit is evolving fast. It is likely that by the end of this course, the Qiskit version may have changed quite a bit.

May 2021: Here is the link to "Introduction to Quantum Computing and Quantum Hardware" from the Qiskit Summer School 2020

Suggested topics and papers for presentation (click to see the incomplete list, to be updated)

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Announcement, Update and Additional Information

Other useful resources:

Youtube lectures by Umesh Vazirani

Leonard Susskind's lecture series on Modern Physics: Quantum Mechanics

Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lecture 10

Minicourse on quantum-information thermodynamics: link is here

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