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Quantum Grading, Tue 2021-12-15

Table of contents

1 Grade computation

  1. It is now too late to protest grades that were uploaded to gradescope before the last class.

  2. Weights are based on the syllabus.

  3. Since there was only 1 in-class presentation, it was deleted from the grading weights and everything else was multiplied by 1.111.

  4. Some things labeled as homeworks for convenience were really presentation or project.

  5. The final project/paper grade was subdivided as follows:

    1. 2 reports (homework 12 and 13): 10% each

    2. talk: 40%

    3. report and/or paper: 40%

  6. The real homeworks were numbers 1-4, 6-9, 11. They were weighted equally.

  7. Homework 5 was an in-class presentation and weighted as 11.1%

  8. For the 4000 version:

    1. all homeworks: 55.6%

    2. in-class presentation: 11.1%

    3. project: 33.3%

  9. For the 4000 version:

    1. all homeworks: 33.3%

    2. in-class presentation: 11.1%

    3. project/paper: 55.6%

  10. Students who chose to present a homework solution or who corrected or supplemented something I said got a few extra points.

  11. The grade cutoffs were at 95, 90, 85, ... for A, A-, B+, ...

  12. I uploaded the most important columns to LMS.

  13. LMS computes a required column called TOTAL. Ignore it. You want FINAL POINTS.

  14. I've uploaded the letter grades to SIS.

Quantum Class 28, Thu 2021-12-09

1 Final project presentations, session 3

  1. Brian W

  2. Richard M

  3. Saad B A R & Zhizhuo L

  4. Alex E

  5. Osama M R

2 Quantum news

  1. https://www.aps.org/publications/apsnews/202112/quantum.cfm

    The best part of the story is the several links to news.

  2. https://event.on24.com/wcc/r/3164012/F0A56160CA6D62535C9EA2C60AD9299B

3 Good luck in the future

Perhaps you found this course worthwhile; it was fun to teach.

If so, could you fill out the course survey; that helps me.

I'm available in the future, even after you leave RPI, to discuss any legal and ethical topic.

Quantum Class 27, Mon 2021-12-06

1 Final project presentations, session 2

  1. Fanny C

  2. Athreya M & Alejandro N T & Misha S

  3. Pavankumar R V

  4. Matthew Y & Justin M H & Lauren T

2 Quantum computing at RPI

RPI's Quantum Blueprint group would like to know: what would you like to see, in courses and research?

  1. a lower level course?

  2. fewer prereqs in this course?

  3. a minor?

  4. different topics in this course?

I email you about the focus group session, this Wed at 4. Please try to attend; this will help to strengthen quantum computing at RPI.

I will not be present; so you can be frank.

3 Quantum physics explains USB behavior

/files/quantum_usb_behavior.png

4 Course material

4.1 Feynman

  1. Feynman was the first to propose the theoretical idea of a quantum computer.

    Richard Feynman - Quantum Mechanics 4:01.

    Extracted from HD Feynman: FUN TO IMAGINE complete 1080p 1:06:49. Recorded in 1983.

4.2 Honeywell

  1. Competitor to IonQ

  2. https://techhq.com/2021/12/quantinuum-is-the-worlds-largest-integrated-quantum-computing-company/

  3. https://www.zdnet.com/article/quantinuum-launches-as-honeywell-quantum-cambridge-quantum-deal-closes/

    There are several links to other interesting stories in this.

  4. https://arstechnica.com/science/2021/04/honeywell-releases-details-of-its-ion-trap-quantum-computer/

4.3 Microsoft

  1. https://azure.microsoft.com/en-us/solutions/quantum-computing/

  2. https://www.microsoft.com/en-us/research/research-area/quantum-computing/?facet%5Btax%5D%5Bmsr-research-area%5D%5B0%5D=243138&sort_by=most-recent

  3. Note what architectures they do not use.

  4. https://www.wired.com/story/microsoft-win-quantum-computing-error/

  5. https://www.hpcwire.com/2021/06/15/isc-keynote-glimpse-into-microsofts-view-of-the-quantum-computing-landscape/

  6. https://cloudblogs.microsoft.com/quantum/2020/12/09/microsoft-practical-quantum-computing-q2b/

  7. Disentangling hype from reality: Achieving practical quantum advantage https://www.youtube.com/watch?v=ybmKJBTXudk (14:28) Mar 26, 2021 Join distinguished Microsoft Scientist Matthias Troyer in his session on achieving practical quantum advantage from the 2020 Q2B event.

4.4 List of algorithms

https://quantumalgorithmzoo.org/

4.5 Nasty probability distributions and failures in financial modeling

  1. This expands my comments a few classes ago.

  2. Consider the Cauchy probability distribution.

    1. It's smooth and unimodal.

    2. It can happen in real experiments like spinning a pointer.

    3. However it has no moments. The integral to compute the mean diverges.

    4. The law of large numbers fails here.

    5. No paramatric sampling techniques are valid.

    6. See wikipedia.

  3. Generally, fat-tailed distributions have this problem; see wikipedia.

  4. There are good arguments that stock market numbers might be like this/

  5. So, all the usual market analysis tools are invalid.

  6. This might be the math behind black swans, i.e., unusual events that happen more often than the models predict.

  7. Deleting extreme outlying observations might shrink the tails enough that the moments now are finite. However it's hard to put a formal foundation on this.

  8. Another problem with the models is that they can fail when you need them most.

    1. Their job is to compute prices, at which people will both buy and sell.

    2. In a panic, no one is buying; the market can break down.

  9. Read https://en.wikipedia.org/wiki/Long-Term_Capital_Management where models developed by 2 Nobel Econ winners failed and nearly caused a major financial market crash. To stop that, the Fed had to bail it out.

  10. Quantum computing will allow all this to happen faster.

Quantum Homework 14 - Final Project

Due Fri Dec 10, 1159 pm

This is your final project, with paper, code, whatever. Upload a PDF or zip file to gradescope.

This deadline will be enforced. I will grade what I have at that time.

Presentation to Quantum Blueprint group 2021-12-02

This talk's web site is https://wrf.ecse.rpi.edu/Teaching/quantum-f2021/posts/bluetalk.html

1 ECSE-4964/6964 Quantum Computer Programming

1.1 Context

  1. I asked and was permitted to create this course for Fall 2020. This semester (F2021) is the 2nd running.

  2. Based on a suggestion from Dr. Chandrasekhar Narayanaswami, Distinguished Research Staff Member, Member IBM Academy of Technology, Member IBM Industry Academy, Thomas J. Watson Research Center, Yorktown Heights.

    1. my former PhD student.

    2. now on the ECSE advisory board.

  3. It replaced ECSE-4750 Computer Graphics, which I'd taught for about 40 years.

  4. It's not the 1st or 2nd quantum course at RPI, but might be in the SoE.

  5. Like all my courses, QCP has a blog: https://wrf.ecse.rpi.edu/Teaching/quantum-f2021/

    1. that runs on my virtual web server: wrf.ecse.rpi.edu

      1. hosted by ECSE

      2. I'm root, and update and manage it.

      3. This takes my time, but I can configure it as I want.

      4. RPI is protected from any security problems I might introduce.

      5. although historically I'm more secure than RPI.

    2. the blog is readable by anyone.

      that's only fair since I use so much free material.

    3. created with Nikola, https://getnikola.com/, a static site generator.

  6. this year's running of the course:

    1. 16 students: 9 undergrad, 7 grad.

    2. from 6 different majors:

      1. AERO

      2. CBIO

      3. CSCI

      4. CSYS

      5. ELEC

      6. MATH

1.2 Content

  1. The idea was not to compete with, but to supplement the other courses.

  2. I assume that the physicists will deliver ever better quantum computers

    1. how to use them?

    2. hence the title: Quantum Computer Programming.

  3. Catalog:

    Intro to quantum mechanics. Various physical realizations of quantum computing, such as transmon qubit (IBM Q), trapped ion (IonQ), and quantum annealing (D-Wave). Quantum states and qubits. Quantum gates including Hadamard, Pauli-XYZ, Toffoli, Fredkin. Qiskit. Quantum algorithms such as Grover, and Shor. Programming quantum computers using IBM qiskit and Microsoft Quantum.

  4. Pre-requisites:

    1. ECSE-2610 (CPTR COMPONENTS & OPER),

    2. CSCI-2200 (FOUNDATIONS OF COMPUTER SCI), and

    3. PHYS-1200 (PHYSICS II) or permission.

    The prereqs select for ECSE seniors. Maybe they could be relaxed.

  5. Source material:

    1. Suggested textbooks:

      1. Noson S. Yanofsky and Mirco A. Mannucci, Quantum Computing for Computer Scientists, 2008;

      2. Abraham Asfaw et al, Learn Quantum Computation using Qiskit, http://community.qiskit.org/textbook, 2020

        There's an old and a new version. The old version was more comprehensive.

        1. David Mermin, Quantum Computer Science An Introduction, 2006.

      We used pieces from each of them.

    2. Web sites:

      1. IBM's detailed online stuff. Not just qiskit but algorithms etc.

      2. Other universities provided inspiration.

      3. Misc quantum research centers, like Delft

      4. Many videos.

    3. I tried to show the principals themselves describing their work and their opinions. E.g., Peter Shor talking about his algorithm and about quantum computing in general.

    4. My main job was to be a curator selecting the best material for the class.

  6. Learning Outcomes:

    1. Demonstrate proficiency with the mathematics behind quantum computing.

    2. Understand important quantum computing algorithms.

    3. Understand the three main quantum platforms: transmon qubit, trapped ion, and quantum annealing.

    4. Apply that to write and run programs on those platforms.

  7. Lecture technique: primarily show videos and ask questions. Approx 4 of 28 classes were student presentations.

  8. Course content, by lecture

    1. Intro to quantum physics, qubit, state as complex vector, superposition, reversibility, no cloning, measurement, entanglement, history.

    2. 1 and 2 qubit operators, quantum computation vs classical circuits

    3. more on math, operators, no cloning

    4. more on entanglement with Toffoli gate, complexity theory, history of theoretical CS, intro to hw

    5. abstract computation models, complexity classes, theory preceded implementation, hw, IBM qiskit

    6. IBM quantum computing

    7. quantum computing 2021 update, misc from qiskit textbook

    8. Grover's algorithm

    9. Student presentations

    10. Student presentations ctd

    11. Student presentations ctd, Shor's algorithm

    12. Shor's algorithm, ctd

    13. Qiskit applied algorithms: HHL to solve linear systems

    14. Qiskit applied algorithms ctd: simulating chemistry, image processing

    15. Amazon Braket

    16. Amazon Braket ctd, D-Wave, IonQ

    17. D-Wave ctd

    18. D-Wave ctd, quantum compution compiler optimization

    19. quantum compution compiler optimization ctd, quantum commununication

    20. quantum commununication ctd, secret sharing

    21. What can Quantum do for AI?

    22. Quantum machine learning

    23. cryo-CMOS control, IonQ

    24. IBM Quantum State of the Union, quantum computers in financial risk analysis

    25. NYU reaction to IBM Eagle, Tristan Meunier slides (which start by nicely summarizing quantum computing)

    26. student presentations etc

    27. student presentations

    28. student presentations

  9. Lectures contain many links to current news stories.

  10. Homeworks:

    1. math etc

    2. programming actual quantum computers of three architectures:

      1. IBM with qiskit

      2. D-wave and IonQ on Amazon Braket

  11. Grades: many homeworks, in class presentation, final project with writeup and presentation

    Extra work for 6000 level: more research content in project, documented.

2 Difference from last year and next year

  1. This year I added more non-IBM stuff: IonQ, D-Wave, Amazon Braket etc.

  2. Next year (if I don't retire) I'd add more student presentations (they're good) and be more polished.

3 Other interesting stuff

3.1 IBM Announcement

  1. Eagle: 127 qubit

  2. better software tools

  3. roadmap: 432 qubits in a year.

3.2 Amazon Braket

  1. https://aws.amazon.com/braket/

  2. run on 3 different quantum architectures

  3. software tools

  4. Microsoft has a similar service; Amazon's looks better.

Quantum Class 25, Mon 2021-11-29

1 Quantum News

  1. https://news.slashdot.org/story/21/11/24/1933200/us-blacklists-chinese-quantum-computing-companies

  2. https://www.theregister.com/2021/11/29/china_quantum_ai_offensive/

2 Homework presentation

  1. Misha will talk on the transmond qubit question.

3 Actual course material

3.1 IBM Eagle

  1. IBM's 127 qubit Eagle quantum computer breakdown and reaction to release (25:22) Nov 20, 2021

    NYU Quantum Technology Lab. We take a look at IBM's new 127 qubit Eagle quantum computing chip, and look at its specifications, ranging from decoherence times, gate fidelities, and other available information from their website

    We'll continue at 8 minutes.

3.2 Dr. Tristan Meunier, CNRS – Néel Institute

The Quantum Spin Grenoble Initiative For Large Scale Quantum Computing

https://ny-creates.org/dr-tristan-meunier-cnrs-neel-institute/

This is the recent talk that I mentioned. He has kindly made his slides available; they are linked on the above page.

The talk starts with an excellent hi-level summary of quantum computing.

Quantum Class 24, Mon 2021-11-22

1 Qiskit updates

FYI

Assorted new things in Qiskit 0.32, Qiskit Runtime API, which provided users with the possibility for some experiments to be executed significantly faster within an improved hybrid quantum/classical process, etc.

2 Select your prefereed talk date

If you have a preference for when to give your talk, write me by the end of today. Tomorrow I will assign dates, and post it on this blog. This is necessary to give people enough time to prepare their talks.

3 Volunteers to present homework answers to class

If you would like to present your solution to the following homeworks to the class next Mon 11/29, for extra points, write me. The first person to write gets it. A reasonable talk is 5-15 minutes.

  1. homework 10, q1, Grover

  2. homework 10, q2, transmon qubit

  3. homework 11

4 My spring class in parallel computing

If you liked this class, in Spring 2022, I am teaching ECSE-4740-01 APPL PARALLEL COMP FOR ENGRS. Poster

5 Videos

  1. Using quantum computers in financial risk analysis | ZDNet (5:05) Apr 12, 2019

    Stefan Woerner, global leader quantum finance and optimization at IBM Research - Zurich, talks to Tonya Hall about quantum computing and how models must be specifically tuned for quantum computers.

  2. The IBM Quantum State of the Union (32:54) Nov 17, 2021

    The IBM Quantum team will take you on an unprecedented technological deep dive into the future of quantum computing. Using our Development Roadmap as our guide, the team will be sharing many new technological breakthroughs from 2021, making more announcements for 2022, charting a course to quantum advantage, client value and beyond.

  3. IBM's 127 qubit Eagle quantum computer breakdown and reaction to release (25:22) Nov 20, 2021

    NYU Quantum Technology Lab. We take a look at IBM's new 127 qubit Eagle quantum computing chip, and look at its specifications, ranging from decoherence times, gate fidelities, and other available information from their website

    We saw 8 minutes today.

Quantum Class 23, Thu 2021-11-18

1 Missing project proposals - repeat

Several students have still not submitted project proposals. It will be difficult to pass the course w/o a project. Projects will be due on the last class day; there will be no extensions.

There are many missing homeworks.

I've reopened gradescope to take old submissions until Sunday 11pm.

Do not send submissions to me; upload them to gradescope.

2 Project presentation signup

The last 3 class days will be student presentations of your projects. That is, Dec 2, 6, 9.

Sign up by emailing me your preferred dates (in preferred order if you care). It's helpful if the subject contains quantum. In your email, give me the names of your whole team.

A single person talk should be 10-15 minutes. For 2 or more people: 15-20.

3 Steve Dombrowski tribute

https://ecse.rpi.edu/news/ecse-mourns-passing-long-time-ecse-staff-steve-dombrowski

4 New videos

  1. Cryo-CMOS Quantum Control: from a Wild Idea to Working Silicon, Prof. Edoardo Charbon (38:36), Oct 18, 2021.

    The core of a quantum processor is generally an array of qubits that need to be controlled and read out by a classical processor. This processor operates on the qubits with nanosecond latency, several millions of times per second, with tight constraints on noise and power. This is due to the extremely weak signals involved in the process that require highly sensitive circuits and systems, along with very precise timing capability. We advocate the use of CMOS technologies to achieve these goals, whereas the circuits will be operated at deep-cryogenic temperatures. We believe that these circuits, collectively known as cryo-CMOS control, will make future qubit arrays scalable, enabling a faster growth in qubit count. In the lecture, the challenges of designing and operating complex circuits and systems at 4K and below will be outlined, along with preliminary results achieved in the control and read-out of qubits by ad hoc integrated circuits that were optimized to operate at low power in these conditions. The talk will conclude with a perspective on the field and its trends.

    See also https://www.quantumsilicon-grenoble.eu/cryogenic-cmos-electronics/

  2. Barriers to building scalable quantum computers, Joe Fitzsimons, Chris Monroe and John Morton, (10:00), Oct 4, 2021.

  3. What IonQ Inc. Provides In Quantum Computing? (5:04), Oct 1, 2021.

    TD Ameritrade Network. IonQ is a quantum computing hardware and software. President and CEO, Peter Chapman, weighs in on the stock opening for trading today on the NYSE. He says that quantum systems are available through the cloud on Amazon Braket, Microsoft Azure, and Google Cloud. The company recently completed a business combination with DMY Tech Group (DMYI), and has partnerships with Accenture, Fidelity, and the University of Maryland.

    If you're thinking of investing in this, or any other stock, remember the Wall Street proverb about how to make a small fortune in the stock market.

  4. Every Major Quantum Computing Breakthroughs in 2021 So Far (8:07) Aug 12, 2021.

    From developing high-level quantum computers to keeping qubits stable at room temperature, let’s look at some of the most amazing quantum breakthroughs in 2021! Subscribe to Futurity.

5 Possible future topics

  1. Quantum Isomer Search

  2. quantum info processing

  3. Daniel Gottesman - Quantum Error Correction and Fault Tolerance (Part 1) - CSSQI 2012 (54:13) Nov 23, 2012

    Institute for Quantum Computing. Dr. Daniel Gottesman, Research Scientist at the Perimeter Institute for Theoretical Physics, gave a lecture about Quantum Error Correction and Fault Tolerance.

    The lecture is the first of two parts, and was filmed at the Canadian Summer School on Quantum Information, held at the University of Waterloo in June of 2012.

    For More:

    1. http://iqc.uwaterloo.ca

    2. http://www.facebook.com/QuantumIQC

    3. http://www.twitter.com/QuantumIQC

    4. QuantumFactory Blog: http://quantumfactory.wordpress.com

Quantum Class 22, Mon 2021-11-15

1 Missing project proposals

Several students have not submitted project proposals. It will be difficult to pass the course w/o a project. Projects will be due on the last class day; there will be no extensions.

There are many missing homeworks. I can take late homeworks up through the end of this week - email me to let you submit.

2 Quantum machine learning

  1. Quantum Machine Learning (1:14:13), Jun 30, 2016.

    A special lecture entitled " Quantum Machine Learning " by Seth Lloyd from the Massachusetts Institute of Technology, Cambridge, USA.

  2. SymCorrel2021 Quantum Machine-Learning for Electronic Structure Calculations , (37:55), Oct 8, 2021.

    Sabre Kais (Purdue University) - Quantum Machine-Learning for Electronic Structure Calculations

    Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. In this talk, I will present our developed quantum algorithm that can be used to obtain accurate ground and excited states for molecules and two-dimensional materials. Our technique is based on a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs- Boltzmann distribution using a quantum circuit with the resource requirements of our algorithm is strictly quadratic. Then, I will show our implementation of the developed algorithm on the actual IBM-Q quantum devices. The results of the quantum simulations for simple molecules and two-dimensional materials such as graphene and transition metal- dichalcogenides are in good agreement with the results procured from conventional electronic structure calculations. The quantum machine learning approach is general and can be used to calculate band structure different materials.

  3. The Future of Quantum Machine Learning, (1:33:54) Jul 23, 2021

    To commence our second annual Qiskit Global Summer School attended by over 5,000 students, in over 110 countries, we will be hosting a panel discussion regarding the future of quantum machine learning.

    00:00 Starting Soon 05:18 Commencement 14:55 Panel

    Our panelists will discuss what the current state of quantum machine learning is and where they believe the most promising applications will arise. They will also address some of the major concerns surrounding quantum machine learning, such as whether or not its potential will be reached by painting a picture of the field's landscape, and elaborating on what still needs to be achieved.

    The panel will include quantum experts such as: Ewin Tang, Quantum Algorithms, University of Washington; Maria Schuld, Senior Researcher and Quantum Software Developer, Xanadu; Aram Harrow, Associate Professor of Physics, MIT; Kristan Temme, QC Researcher, IBM Quantum

    Moderated by Amira Abbas, IBM Quantum

Quantum Class 21, Thu 2021-11-11

1 Another ECSE death

Steve Dombrowski died last night. He'd been in ECSE since 1979. Jerry Dziuba died last month; he'd been here longer. Not ECSE but close, Peter Fox died a few months ago. Then there are the unusual number of retirees who've died recently. This is getting horrible.

The relevance to you is that you had better like what you're doing, at least on balance. Or, do something else. I'm still here because I like learning and talking to bright people. Also, it's fun seeing what my former students have succeeded at.

2 The Quantum Spin Grenoble Initiative For Large Scale Quantum Computing

https://ny-creates.org/news-events/ny-creates-events/

This looks good. You must preregister.

Dr. Tristan Meunier, CNRS – Néel Institute November 18 (Thursday), 2021 11:00 am to 12:00 pm (EST) Virtual via Zoom

Should this replace the class?

3 Your opinion on class format wanted

I'd like your opinion about requiring in-person attendance in class next spring vs taping the lecture and letting students watch it later.

One complexity: if it can be made to work, I'd like to interrupt the lectures with a poll every 20 minutes or so. This is pedagogically good. However that wouldn't work for students watching later.

Also, recording might be impossible when there are several source media. How could I record if, in the same lecture, I showed a video and pages from the book using my thinkpad and then wrote something on my ipad?

If I dumbed down my techniques to accommodate the remote students, then this hurts the in-person ones.

Your opinions? Thanks.

4 Today's videos

I might show only the start; you can watch the rest on your own if you're interested.

  1. Panel: What can Quantum do for AI? (47:57),Nov 16, 2018.

    Inaugural AI Research Week, hosted by the MIT-IBM Watson AI Lab. Panel discussion on research directions at the intersection of AI and Quantum Computing.

    Panelists: Yoshua Bengio, Head of the Montreal Institute for Learning Algorithms (MILA), Aram Harrow, Associate Professor of Physics, MIT, Peter Shor, Professor of Applied Mathematics, MIT, Kristan Temme, Research Staff Member, IBM Research.

Quantum Class 20, Mon 2021-11-08

1 My computer problems

On Wed, my main laptop computer's power brick failed (2 hours before chairing a virtual session of ACM SIGSPATIAL 2021). I've never seen a power brick fail before. Oh well, that's what backups and extra laptops are for. Concerning them, the question is, am I paranoid enough?

So I could create Thursdays's blog page on another machine, and showed it in class, but couldn't sync everything enough to get it on the web server and update gradescope. I'm now using an old power brick while Lenovo ships out a new one. Things are mostly back to normal.

Concerning backups, for a serious installation, it's insufficient just to copy all the files. The HW is too expensive to have a spare just sitting around, and various licenses and passwords are keyed to the particular HW and have to be reset. I've considered going virtual on AWS but that has other problems.

2 Quantum communication, 2

  1. Theoretical Tutorial: Quantum communications (40:00) May 19, 2020

    Centre for Quantum Computation and Communication Technology (CQC2T) Program Manager Prof. Tim Ralph from the University of Queensland presents a quantum computing theoretical tutorial on quantum communications.

    We'll start at minute 15, which starts a new topic, Quantum repeaters.

3 Quantum secret sharing

  1. Secret Sharing Explained Visually (7:56). Oct 22, 2019.

    The IEEE Information Theory Society presents an overview of Adi Shamir's 1979 paper on secret sharing. This is part of our series on the greatest papers from information theory.

  2. How to keep an open secret with mathematics (10:35). Dec 31, 2019.

    This is a little less technical. You can watch on your own.

  3. Oblivious transfer (14:14).

    This educational video is part of the course Quantum Cryptography available for free via http:/www.online-learning.tudelft.nl ©️ TU Delft, released under a CC BY NC SA license.

Quantum Class 19, Thu 2021-11-04

1 Quantum computing compiler optimization, 2

  1. Using SAT Solvers for Quantum Computing Design: Potential and Challenges (48:03) Oct 25, 2021.

    We'll watch the last 10 minutes.

  2. Quantum circuit optimisation, verification, and simulation with PyZX, (33:26), by John van de Wetering at: FOSDEM 2020

    affiliated sites:

    1. https://zxcalculus.com

    2. https://github.com/Quantomatic/pyzx Python library for quantum circuit rewriting and optimisation using the ZX-calculus

    Looking for a term project topic? Browse their sample projects.

  3. Compilers for the NISQ era, Ross Duncan, #QRST (30:12), Oct 6, 2020.

    So you have a new quantum computer? What now? I’ll present t|ket⟩, a quantum software development platform produced by Cambridge Quantum Computing Ltd which will help you get the best out of your new machine. The heart of t|ket⟩ is a language-agnostic optimising compiler designed to generate code for a variety of NISQ devices, which has several features designed to minimise the influence of device error. The compiler has been extensively benchmarked and outperforms most competitors in terms of circuit optimisation and qubit routing. This talk will cover roughly the same ground as our recent paper (arXiv:2003.10611) but such is the nature of the field, that paper is already obsolete, so I will cover some of the hot new sh*t we have done since then.

2 Quantum communication, 1

  1. Taking quantum key distribution out of the lab (1:40) Mar 13, 2019.

    Members of the Quantum Photonics Lab, led by Institute for Quantum Computing (IQC) researcher Thomas Jennewein, designed and constructed a working portable demonstration of Quantum Key Distribution (QKD). The QKD demo used hardware components designed by Excelitas Technologies, an industry partner who provides customized optoelectronics and advanced electronic systems.

    QKD enables secure communication between two parties. QKD establishes highly secure keys between distant parties by using single photons to transmit each bit of the key. Since single photons behave according the laws of quantum mechanics they cannot be tapped, copied or directly measured without detection.

    The huge benefit for users of such systems is the peace of mind of knowing that any attack, manipulation or copying of the photons can be immediately detected and overcome. QKD solves the long-standing problem of securely transporting cryptographic keys between distant locations. Even if they were to be transmitted across hostile territory, their integrity could be unambiguously verified upon receipt.

  2. Quantum Link: Building the U.S. Quantum Superhighway (3:48) Oct 25, 2018

    Argonne National Laboratory

    The Quantum Link is an ambitious project by Argonne, Fermilab and the University of Chicago to bring the property of entanglement into the real world.

    Entangling objects 30 miles apart, between Argonne and Fermi, the Quantum Link seeks to answer questions like, “What is the meaning of entanglement?” and “Can you use entangled states, separated 30 miles apart, as a type of superhighway to transfer information from one point to the other?”

    Using an optical fiber network built 12 years ago by the state of Illinois to link hi-speed data centers, the project gives researchers a real-world view of what a quantum network might look like.

  3. Theoretical Tutorial: Quantum communications (40:00) May 19, 2020

    Centre for Quantum Computation and Communication Technology (CQC2T) Program Manager Prof. Tim Ralph from the University of Queensland presents a quantum computing theoretical tutorial on quantum communications.

    We saw the 1st 15 minutes.

Quantum Class 18, Mon 2021-11-01

1 D-wave, 3

  1. Quantum Programming 101: Solving a Problem From End to End | D-Wave Webinar (54:25), starting around 10:00.

2 Quantum computing compiler optimization

  1. Quantum-assisted quantum compiling paper (enrichment)

    Discussion (26:04) We'll watch the 1st 4 minutes.

    Popular summary (copied from the paper)

    Ordinary computers require a compiler that converts one's code into a machine-level language. Quantum computers require a compiler as well. However, a new challenge for such "quantum compilers" is that they should be optimal, i.e., they should return a machine-level program that has as few operations as possible. This optimality is crucial for current noisy quantum devices, where longer programs accumulate more errors while shorter programs avoid errors. In this work, we introduce an algorithm for optimal quantum compiling. The key feature that allows for optimality is that we propose to use quantum computers themselves to assist in the compiling process. Hence, our algorithm is called quantum-assisted quantum compiling (QAQC, pronounced "Quack").

    The idea is that one needs to quantify the distance between the original program and the compiled program, with the goal of trying to minimize this distance. We prove that this distance calculation cannot be done efficiently on a classical computer. On the other hand, we provide an efficient quantum circuit for computing it.

    In addition to shortening the length of one's quantum program, QAQC can be used to learn algorithms that compensate for a given quantum computer's noise and also to benchmark the noise processes occurring on a quantum computer. We successfully implement QAQC for small programs using currently available quantum computers from IBM and Rigetti, and we use simulators to explore the compilation of larger programs. Overall, QAQC appears to be a promising tool for mitigating errors in the era of noisy intermediate-scale quantum computers.

  2. Using SAT Solvers for Quantum Computing Design: Potential and Challenges (48:03) Oct 25, 2021.

    We'll watch the 1st 20 minutes.

  3. Quantum circuit optimisation, verification, and simulation with PyZX, (33:26), by John van de Wetering at: FOSDEM 2020

    affiliated sites:

    1. https://zxcalculus.com

    2. https://github.com/Quantomatic/pyzx Python library for quantum circuit rewriting and optimisation using the ZX-calculus

    Looking for a term project topic? Browse their sample projects.

  4. Compilers for the NISQ era, Ross Duncan, #QRST (30:12), Oct 6, 2020.

    So you have a new quantum computer? What now? I’ll present t|ket⟩, a quantum software development platform produced by Cambridge Quantum Computing Ltd which will help you get the best out of your new machine. The heart of t|ket⟩ is a language-agnostic optimising compiler designed to generate code for a variety of NISQ devices, which has several features designed to minimise the influence of device error. The compiler has been extensively benchmarked and outperforms most competitors in terms of circuit optimisation and qubit routing. This talk will cover roughly the same ground as our recent paper (arXiv:2003.10611) but such is the nature of the field, that paper is already obsolete, so I will cover some of the hot new sh*t we have done since then.

3 Possible future topics

  1. Quantum Isomer Search

Quantum Class 17, Thu 2021-10-28

1 QuTech Academy videos

  1. The maze (0:42)

  2. NV center qubits (6:34). Another tech.

2 Superconducting quantum computing, ctd

There are alternatives to how IBM does it. This Wikipedia article is a good summary.

3 D-wave ctd

  1. Quantum Computing: Top Players 2021 (13:23)

  2. Quantum Annealer vs Universal Gate Based Quantum Computers | Is D-Wave a Real Quantum Computer? (12:02) Anastasia Marchenkova

  3. What is Quantum Annealing? (6:14)

  4. How The Quantum Annealing Process Works (6:09)

  5. Quantum Programming 101: Solving a Problem From End to End | D-Wave Webinar (54:25), 1st 10 minutes

  6. https://www.dwavesys.com/build/getting-started/

  7. D-Wave System Documentation

  8. https://docs.dwavesys.com/docs/latest/doc_getting_started.html

4 Term project

Homework 12 asks for your topic.

Deliverable include writeup, class presentation, code if you're programming.

5 Due dates

During the semester, I've been lenient with due dates because this is a small class. However, RPI's last class day will be a firm due date for everything. The registrar will want the grades early because there is no final exam.

Quantum Homework 12, Thu 2021-10-28

Due Thu Nov 4

Form teams and pick a term project topic. Give me names and title.

The topic can be anything vaguely related to quantum computer programming.

Programming, surveys or tutorials are all good topics.

If you're in the 6000 version of this class, to make things easier, this may be an addon to your paper.

Quantum Class 16, Mon 2021-10-25

1 Term project

Time to start thinking of a term project, on a topic at least vaguely related to the course. Teams of any size ok. This is separate from the paper for the 6000 version of the course.

2 Programming notes

2.1 WSL

(I mentioned this last time.)

  1. This is Windows Subsystem for Linux 2.

  2. I've just used it a little, but it looks quite good.

  3. It's a basically full Ubuntu running under Windows.

  4. It's a lightweight virtualization, not full like, say, Vmware.

  5. It starts faster and uses fewer resources.

  6. You can a have Windows and linux tabs simultaneously.

  7. You can access either file system from the other OS.

  8. You can even run either OS's executables under the other OS, e.g., in linux:

    notepad.exe /tmp/foo

  9. The linux VM can create graphics windows, e.g., xeyes and firefox.

  10. I can ssh from another computer into the linux vm, but so far have to use password authentication.

  11. I can ssh out from the linux vm with public-private keys.

  12. However I still don't understand or trust windows security. (That may be me, not MS.)

Summary: WSL looks potentially excellent.

2.2 Why I hate linux (almost as much as I hate MS)

Intel Tiger Lake, which my Thinkpad x12 has, doesn't play well with ubuntu linux. The buttons and sound don't work. This continues linux's trend of basically never working properly with new hw, such as: hdpi displays, dual graphics, fingerprint readers, half the printers ever I've used, sometimes even Nvidia GPUs, ...

The problem is a standoff between linux (and ubuntu...) and the commercial HW people over who should pay to add the HW to the OS. Even when a HW company is willing to pay, the linux kernel is a nonstandardized undocumented API-breaking moving target. I can document every adjective in the previous sentence.

2.3 Old C++ joke

https://webhome.phy.duke.edu/~rgb/Beowulf/c++_interview/c++_interview.html

3 Amazon Braket, ctd

  1. https://docs.aws.amazon.com/braket/latest/developerguide/braket-get-started-create-notebook.html

  2. https://aws.amazon.com/blogs/aws/amazon-braket-go-hands-on-with-quantum-computing/

4 D-Wave

  1. Getting Started with D-Wave through Amazon Braket (40:17). Continuing at 15 min.

5 IonQ and trapped ions

  1. Christopher Monroe Quantum Computing with Trapped Ions (1:03:13). We'll start around 17:00 and continue for about 1/2 hour.

  2. One advantage is that any two qubits can be operated on. There is complete connectivity.

  3. One problem with trapped ions is that only one multi-qubic gate can operate at a time.

  4. IonQ is not increasing the number of qubics as fast as IBM is.

Quantum Class 15, Thu 2021-10-21

Quantum Homework 11, Thu 2021-10-21

Due Thu Oct 28

Groups of any size are ok; submit one answer to gradescope.

For each question, I am soliciting a volunteer to present the answer to the class. That will give you some extra points.

  1. Introduce yourself to quantum computing on Amazon Braket . Wander around the web site. Set up an account.

    1. Try to run your Grover's program on the Rigetti, which is similar to IBM.

    2. Simulate it. Try to run on a real machine. Write a report on your observations.

    3. Try it on the IonQ.

This will probably cost you a few dollars, but not too much. If you feel that I'm being unfair to ask this, contact me. I'll give you a replacement homework.

Total: 10

Quantum Class 14, Mon 2021-10-18

1 Quantum current events

None of these are a formal part of this course, but still look interesting.

  1. IBM Quantum Challenge Fall 2021.

    Oct 27 at 9:00 AM (local) — Nov 05 at 12:00 PM (local)

  2. (reminder) Fundamentals of Quantum Computation Using Qiskit v0.2X Developer, C1000-112 IBM Quantum.

  3. D-Wave Clarity Roadmap Webinar, Wednesday October 20, 9-10am PT. https://www.dwavesys.com/

2 Qiskit Applied Algorithms, ctd

  1. https://qiskit.org/textbook/ch-applications/algs_for_apps_index.html

2.1 Simulating chemistry

  1. https://www.qutube.nl/quantum-algorithms/simulating-chemistry

    simple video 3:53.

  2. Quantum Computation for Chemistry and Materials (57:39). Dr. Jarrod McClean Google’s Quantum Artificial Intelligence Lab.

    We'll start at 16:00 and play for awhile.

  3. https://qiskit.org/textbook/ch-paper-implementations/vqls.html

2.2 Image processing

  1. Quantum Edge Detection - QHED Algorithm on Small and Large Images

  2. Image processing in quantum computers Aditya Dendukuri and Khoa Luu.

    Quantum Image Processing (QIP)is an exciting new field showing a lot of promise as a powerful addition to the arsenal of Image Processing techniques. Representing image pixel by pixel using classical information requires an enormous amount of computational resources. Hence, exploring methods to represent images in a different paradigm of information is important. In this work, we study the representation of images in Quantum Information. The main motivation for this pursuit is the ability of storing N bits of classical information in only log(2N) quantum bits (qubits). The promising first step was the exponentially efficient implementation of the Fourier transform in quantum computers as compared to Fast Fourier Transform in classical computers. In addition, images encoded in quantum information could obey unique quantum properties like superposition or entanglement.

3 Amazon Braket

If you want to read ahead, look here: https://aws.amazon.com/braket/

Quantum Class 13, Thu 2021-10-14

1 Qiskit Applied Algorithms

  1. https://qiskit.org/textbook/ch-applications/algs_for_apps_index.html

1.1 HHL to solve linear systems

  1. Original paper. Quantum algorithm for solving linear systems of equations Aram W. Harrow, Avinatan Hassidim, Seth Lloyd.

  2. QuTech Academy: https://www.qutube.nl/quantum-algorithms/solving-linear-equations-with-quantum-computers 6:24. Rather simple.

  3. Quantum Machine Learning - 37 - Overview of the HHL Algorithm 5:58.

    Quantum Machine Learning MOOC, created by Peter Wittek from the University of Toronto in Spring 2019.

    Lecture 37: Overview of the HHL Algorithm

    "Peter disappeared in the Himalayas due to an avalanche in September 2019. I upload those videos as a tribute to him and his passion for open knowledge. Thanks Peter for everything you've done for us!"

  4. Quantum algorithm for solving linear equations 36:31

    A special lecture entitled "Quantum algorithm for solving linear equations" by Seth Lloyd from the Massachusetts Institute of Technology, Cambridge, USA. Feb 8, 2011

    Lloyd is the L in HHL.

  5. Quantum Algorithms for Systems of Linear Equations (Quantum Summer Symposium 2020) 19:22

    Rolando Somma from the Theoretical Division of the Los Alamos National Laboratory talks about quantum algorithms for systems of linear equations. This presentation was recorded on Day 2 of Google's Quantum Summer Symposium 2020 (July 23, 2020).

    Google’s Quantum Summer Symposium 2020 playlist → https://goo.gle/2Z149sN

  6. https://en.wikipedia.org/wiki/Quantum_algorithm_for_linear_systems_of_equations

  7. https://quantumcomputing.stackexchange.com/questions/2697/what-could-be-the-possible-future-applications-for-hhl-algorithm

Quantum Homework 9, Thu 2021-10-14

Due Thu Oct 21

Groups of 2 are ok; submit one answer to gradescope.

For each question, I am soliciting a volunteer to present the answer to the class. That will give you some extra points.

  1. (10 pts) Take your Grover's algorithm simulation and run it on a real IBM quantum computer.

    Include enough to show how it works. Compare the real computer to the simulation. Mention any interesting observations.

  2. (10 pts) Watch this video, and write 100 words (that are different from the abstract below) about something interesting in it.

    Control of transmon qubits using a cryogenic CMOS integrated circuit (QuantumCasts) 35:47.

    presented by Research Scientist Joe Bardin, Google AI Quantum and UMass Amherst, for the APS March Meeting 2020.

    Superconducting quantum processors are controlled and measured in the analog domain and the design of the associated classical-to-quantum interface is critical in optimizing the overall performance of the quantum computer. Control of the processor is achieved using a combination of carefully shaped microwave pulses and high-precision time varying flux biases. Measurement of quantum states is typically achieved using dispersive readout, which requires a low-power pulsed microwave drive and a near quantum-limited readout chain. For control of a single qubit, a typical system employs two high-speed high-resolution (e.g., 1 Gsps/14 bit) digital-to-analog converters (DACs) and a single-sideband modulator to generate microwave control pulses. A third DAC with similar specifications is used for flux-bias control. A typical readout channel may service on the order of five qubits and contains yet another pair of DACs, with a single-sideband modulator employed to generate a stimulus signal. For measurement, the readout chain also employs a series of cryogenic amplifiers followed by further amplification, IQ demodulation, and high-speed digitization at room temperature. For today’s prototype systems with on the order of 50-100 qubits, keeping most of the electronics at room temperature makes sense. However, achieving fault tolerance—a long term goal of the community—will require implementing systems with on the order of 10^6 qubits and today’s brute force control and readout approach will not scale to these levels. Instead, a more integrated approach will be required. In this talk, we will present a review of recent work towards implementing a scalable cryogenic quantum control and readout system using silicon integrated circuit technology. After motivating the work, we will describe the design and characterization of a prototype cryogenic XY controller for transmon qubits. Detailed measurement results will be presented. The talk will conclude with a discussion of future work.

Total: 20

Quantum Homework 10, Thu 2021-10-21

Due Thu Oct 21

(This is a separate homework to allow for different groupings.)

Groups of any size are ok; submit one answer to gradescope.

If you are taking the grad version of the course, then your extra work to justify the 6000-level is a research or tutorial paper or Python notebook with some vague relation to this course. It might overlap with another course or your research, if you tell everyone involved.

Give a proposed title and summary of your paper.

If you are taking the 4000 version of this course, then just submit a note saying that. (This is because I cannot assign a grade in GS unless there is a handin.)

Total: 10

Quantum Class 12, Thu 2021-10-07

1 Shor's algorithm to factor an integer, ctd

1.1 Videos

  1. Umesh Vazirani's lecture, 2018.

    1. This jumps into the middle of things a little. However the alternatives are worse: not to show Vazirani at all, or to also show all the earlier videos.

    2. Lecture 10 2 Shor's Factoring Algorithm (25:42)

      continue at 13:00.

1.2 IBM Quantum

https://quantum-computing.ibm.com/composer/docs/iqx/guide/shors-algorithm

2 Sampling the Qisit textbook

  1. https://qiskit.org/textbook/ch-algorithms/quantum-fourier-transform.html

  2. https://qiskit.org/textbook/ch-algorithms/shor.html

  3. https://qiskit.org/textbook/ch-algorithms/teleportation.html

  4. https://qiskit.org/textbook/ch-algorithms/quantum-key-distribution.html

Quantum Class 11, Mon 2021-10-04

1 Student talks, round 1, part 3

2 Another view of superposition

The quantum states of some system are solutions of a linear PDE. There is a basis set of solutions. Linear combos are also solutions. That's superposition.

3 Shor's algorithm to factor an integer

3.1 Notes

  1. This is the most famous quantum algorithm.

  2. It's the one that has the potential to break much public key crypto.

  3. This is the deepest topic of this course so far.

  4. Takeaways from this algorithm are that some serious math is involved, and the quantum version is unlike the classical version.

  5. If you don't absorb all the details, then absorb the its flavor.

  6. I'm showing videos because they present the idea better than me.

  7. OK to ask questions and make comments during the videos. I'll pause the video and try to answer.

  8. I'm spending less time on this topic than some other courses to make room for other topics, like coding and other platforms.

3.2 Videos

  1. Shor on, what is Shor's factoring algorithm? (2:09)

    It's good to listen to the inventor of a big idea.

  2. Umesh Vazirani's lecture, 2018.

    1. This jumps into the middle of things a little. However the alternatives are worse: not to show Vazirani at all, or to also show all the earlier videos.

    2. Lecture 10 1 Period Finding (19:27)

    3. Lecture 10 2 Shor's Factoring Algorithm (25:42)

  3. Hacking at Quantum Speed with Shor's Algorithm (16:35). Optional to watch on your own.

  4. The Story of Shor's Algorithm, Straight From the Source | Peter Shor (31:27) 2021-07-02 Gives the history. Optional to watch on your own.

3.3 IBM Quantum

https://quantum-computing.ibm.com/composer/docs/iqx/guide/shors-algorithm

4 IBM sites reminder

  1. https://qiskit.org/

  2. https://www.ibm.com/quantum-computing/

  3. https://quantum-computing.ibm.com/

Quantum Homework 7, Thu 2021-09-30

Due Thu Oct 7

Groups of 2 are ok; submit one answer to gradescope.

Simulate Grover

Run, on a simulator, the 3-SAT test of Grover's algorithm shown here:

https://github.com/Qiskit/qiskit-tutorials/blob/master/tutorials/algorithms/07_grover_examples.ipynb

You may use the online simulator or install it locally. You don't need to install Jupyter if you don't want.

Upload the output histogram, or otherwise convince me that you got it to work.

Students taking the grad version of this course

Start thinking about what you'll do to earn grad credit. I propose an extra paper, preferably researching something relevant. Nothing to hand it yet, just think

Quantum Class 8, Thu 2021-09-23

Quantum Class 7, Mon 2021-09-20

1 Homework 6 is online

here.

2 Homework signup

Go to

https://doodle.com/poll/my45k5euc5zmxq77?utm_source=poll&utm_medium=link

Pick a preferred date from 9/23, 9/27 or 9/30.

In the participant name field, enter your topic and enough of your name(s) that I can identify you.

I fill out unused class time with new material.

3 Thurs 9/30 class will end early

for Pres Jackson's faculty reception. I asked her what to do about the conflict. This is it.

4 Video

Quantum Computing 2021 Update by Christopher Barnett in ExplainingComputers. 13:12.

5 IBM Quantum Developer Certificate

https://www.ibm.com/blogs/research/2021/03/quantum-developer-certification/

https://www.ibm.com/certify/exam?id=C1000-112#associatedCerts

Should I try to cover the material in class so you can write the exam?

6 Online Qiskit textbook

This is the new material today. We'll work through part of it.

https://qiskit.org/textbook-beta

Quantum Class 6, Thr 2021-09-16

1 Homework 5

here.

2 Videos

  1. Quantum Algorithms (2:52).

    "Which problems can quantum computers solve exponentially faster than classical computers? David Gosset, IBM quantum computing research scientist, explains why algorithms are key to finding out."

  2. Benchmarking Quantum Systems (1:58)

    "As we build ever larger quantum computers capable of performing increasingly complex algorithms, it is important to define a metric to quantify their power. IBM quantum computing research scientist Lev Bishop has defined a new metric called Quantum Volume that characterizes what a quantum computer is capable of “calculating.” The metric is architecturally neutral and can be applied to all types of quantum systems."

3 Apply for a summer 2022 internship with IBM Quantum

https://www.research.ibm.com/blog/2022-quantum-internships

Apply by Monday, October 18, 2021 for the best chance at consideration.

4 IBM quantum computing ctd

  1. Topics from IBM's site, e.g.:

    1. https://research.ibm.com/blog/ibm-quantum-roadmap

    2. https://www.research.ibm.com/blog/quantum-advantage-limited-space

Quantum Homework 5, Thu 2021-09-16

Groups of 2 are ok; do one talk.

  1. Pick an interesting IBM quantum topic and present it for 5 minutes in a week.

  2. Sign up site to follow.

Total: 10

Quantum Class 5, Mon 2021-09-13

1 Homework 4

here, due Thurs.

2 Quantum computing in the news

(or at least on Slashdot).

  1. https://yro.slashdot.org/story/21/09/04/2147245/americas-nsa-isnt-sure-quantum-computers-will-ever-break-public-key-encryption

3 Abstract computation models ctd

  1. Original motivation was to discover an algorithm for proving (or disproving) theorems.

  2. That can be done in some simple cases, like first order predicate calculus with addition over the integers.

    1. and first order predicate calculus with addition and multiplication over the rationals or reals.

  3. This goal failed because it was proved that it is undecidable in some cases.

    1. like first order predicate calculus with addition and multiplication over the integers.

    2. Some theorems truth or falsity depends on the allowable domain of their variables.

    3. in a deep sense, ints are harder than reals.

    4. Long time ago I wrote a paper on this, in the context of computer graphics. Problems with Raster Graphics Algorithms.

4 Complexity classes

  1. Group problems into broad classes of considerably differing difficulty.

  2. P vs NP.

  3. Steve Cooks's paper first describing this was rejected.

  4. Quantum complexity classes.

5 Hardware implementations

  1. Quantum computation was theoretically started decades before actual quantum computers were designed.

  2. Just like classical computers.

  3. Many competing technologies.

  4. Let the strongest win.

5.1 Superconducting qubits

  1. Dilution fridge: cool by mixing He3 into He4.

  2. Cooper pairs of electrons: pairs of electrons in a metal weakly attract each other. It's a quantum effect.

  3. Josephson Junction:

  4. good ref: A Quantum Engineer's Guide to Superconducting Qubits

5.2 IBM quantum computing

  1. A Qubit in the Making (2:01) https://www.youtube.com/watch?v=2pB87H3_F_c&list=PLOFEBzvs-VvpzQnlazij7cL1mjKvJTAwk&index=10&t=0s

  2. Behold the Mighty Qubit (2:51) https://www.youtube.com/watch?v=_P7K8jUbLU0&list=PLOFEBzvs-VvpzQnlazij7cL1mjKvJTAwk&index=10

  3. They have several quantum computers.

  4. The older ones are freely available on the web.

  5. Those have 5, 15 or more qbits; see https://quantum-computing.ibm.com/

  6. Note that you can put gates between only adjacent qbits.

  7. You submit a batch job and get emailed when it runs.

  8. IBM github site: https://github.com/Qiskit with

    1. a free simulator.

      It doesn't match all the physical complexity of the real computer, but it's a good start.

    2. and tutorials and presentations.

  9. and a SW development framework. https://qiskit.org/

  10. You can create a quantum computation program either by

    1. designing a circuit, or

    2. using a programming language.

5.2.1 Sites

  1. https://qiskit.org/

    1. You can install it on your machine.

    2. Create and run the demo program.

    3. Try the Getting Started tutorial.

      Since I'm still learning, I have to say circ.draw() not circ.draw('mpl')

  2. https://www.ibm.com/quantum-computing/

    1. Browse around the website.

    2. Look at the topologies of some machines.

    3. Create an account for yourself.

    4. Play with the graphical composer.

    5. Submit a job.

    6. Look at the output.

Quantum Homework 4, Mon 2021-09-13

Due 2021-09-16 4pm in gradescope. Groups of 2 are ok; submit one answer set.

  1. Pick an approach to building quantum computers that is not used by a major company like IBM, Google, Microsoft, Amazon, Rigetti or D-wave. Hidary Chapter 5 has lots of suggestions. Describe the idea, and its major advantages and disadvantages.

Total: 10

Quantum Class 4, Thurs 2021-09-09

1 Homework 3

here, due Tues.

2 Singular value decomposition correction

The image of the circle or its higher dimensional analogues under any matrix mapping is an ellipse or the analogue of an ellipse in some other number of dimensions. The lengths of the principal axes of this ellipse give what are called the singular values of the matrix. Any matrix A can be written as $A = U S V^*$, where U and V are unitary and S is diagonal with its entries being the singular values. For a hermitian matrix, the SVD is also a eigenvalue decomposition (diagonalization). Thus we can apply the circle/ellipse visualization to the eigenvalues of hermitian matrices. For a unitary matrix, all of the singular values are 1. A unitary matrix only rotates the circle, and does not deform it.

-Richard McQueen

(to everyone: more suggestions and corrections are welcome.)

3 Entangling with Toffoli revisited

  1. Here's another way to look at this. Review:

  2. $x'=x \\ y'=y \\ z'= z \oplus xy$

  3. Use those equations only with classical bits, otherwise use the matrix multiplication.

  4. Let x=1, z=0. Then, x'= 1, y'= y, z'= y.

  5. So if y=0, then x'= 1, y'= 0, z'= 0.

  6. and if y=1, then x'= 1, y'= 1, z'= 1.

  7. If y is a superposition of 0 and 1, then the output will be a superposition of the above 2 cases.

  8. That is, 50% of the time, we measure y'= 0, z'= 0 and 50% of the time we measure y'= 1, z'= 1.

  9. We always measure y' and z' the same.

  10. Even if we transport z' a long distance away first.

4 Quantum parallel computation

  1. The above is also a first glimpse into parallel computation.

  2. You first create a superposition of states.

  3. Then the quantum operators operate on all the states in parallel.

  4. We haven't yet seen how to pick out the answer we want.

5 Complexity theory - Hidary chap 4

  1. Problems vs algorithms.

  2. Interesting types of resources: time, space, ...

  3. Worst case time, best case time.

  4. We want to group problems and algorithms into classes in a way that captures their important properties and ignores the others.

  5. competing formal ways to describe algorithms: Turing machine, Church's lambda calculus, ...

    1. different ones had different power (could describe different classes).

    2. the ones listed above seemed to all have the same power.

  6. Universal Turing machine.

  7. Church-Turing Thesis (CTT): If an algorithm can be performed on any piece of hardware (say, a modern personal computer), then there is an equivalent algorithm for a Universal Turing Machine (UTM) which performs exactly the same algorithm [161, p. 5].

  8. Strong Church-Turing Thesis (SCTT) Any algorithmic process can be simulated efficiently using a Universal Turing Machine (UTM)

  9. randomness can sometimes lead to a faster algorithm.

  10. Extended Church-Turing Thesis (ECTT) Any algorithmic process can be simulated efficiently using a Probabilistic Turing Machine (PTM) [161, p. 6].

  11. Quantum Extended Church-Turing Thesis (QECTT) Any realistic physical computing device can be efficiently simulated by a fault-tolerant quantum computer.

6 Hardware implementations

  1. Quantum computation was theoretically started decades before actual quantum computers were designed.

  2. Many competing technologies.

  3. Let the strongest win.

Quantum Homework 3, Thurs 2021-09-09

Due 2021-09-13 4pm in gradescope. Groups of 2 are ok; submit one answer set.

(These questions are from Hidary.)

  1. (10 points) Investigate the Stern-Gerlach experiment of 1921. What was the expectation from classical theory for the outcome and what actually occurred?

  2. (10 points) What does non-separable mean for two states and what does that tell us about these states?

  3. (10 points) For the CZ gate, does it matter which qubit is the control qubit and which is the target?

  4. (10 points) What is the final state of the following circuit, in Dirac notation?

/files/hidary-hw-3-1b.png

Total: 40

Quantum Class 3, Tues 2021-09-07

1 Homework 3

is out, due Thurs. It's short.

2 New material

Various things designed to solidify your understanding of the fundamentals.

2.1 Math review from Quantum Computing for Computer Scientists

  1. Chapter 2:

    1. Complex vector space, page 34.

      1. n-dim vector $\begin{vmatrix} c_0 \\ \cdots \\ c_{n-1}\end{vmatrix}$

      2. Add 2 vectors.

      3. Multiply vector by scalar.

      4. etc.

    2. Set of $m\times n$ complex matrices, $\mathbb{C}^{m\times n}$, is also a complex vector space.

      1. Transpose, conjugate, adjoint.

      2. Matrix mult is $\star$ in book.

    3. $\mathbb{C}^{m\times n}$ is a complex algebra.

    4. Set of polynomials in one variable of degree $le n$ is a complex vector space.

    5. State of a quantum system is a complex vector.

    6. You can make new vector spaces from combos of old ones.

      1. Cartesian product or direct sum.

      2. Just an ordered pair.

      3. $(v_1, v_2)$.

    7. Set of basis vectors for the vector space.

      1. Every vector $v$ in the space is a linear combo of the basis vectors.

      2. Represent $v$ as the list of weights.

      3. There are many possible basis sets.

      4. Each different basis set causes a different representation for the vectors.

      5. Convert: change of basis.

      6. Cartography example: NAD27, WGS84.

        A bridge between Switzerland and Germany across the Rhine River at Laufenberg had its two ends at different elevations because of a conversion error between two different basis systems.

        https://www.science20.com/news_articles/what_happens_bridge_when_one_side_uses_mediterranean_sea_level_and_another_north_sea-121600

      7. Hadamard matrix is an example.

    8. Section 2.4 Inner product, etc, p 53

    9. Section 2.7 Tensor product of vector spaces, p 66.

      1. $\mathbb{V} \otimes \mathbb{V'}$.

      2. Let $dim(\mathbb{V})=p$ and $dim(\mathbb{V'})=q$ . Then $dim(\mathbb{V} \otimes \mathbb{V'}) = pq$.

      3. This is how quantum systems combine.

      4. Example 2.7.2 p 70.

  2. From end of section 2.3, p.52 to 2.6.

    1. P 52. Transition matrix to convert a vector representation from the canonical basis this another basis is the Hadamark matrix.

    2. Section 2.4. Add an inner product operator to the complex vector space. Note the conjugates in the rules; you don't see them with a real vector space.

    3. Norm, aka length.

    4. We won't need limits etc.

    5. Section 2.5 Eigenvalues and eigenvectors

      1. Eigenvalues don't depend on the representation. Converting to a new basis set doesn't change them.

      2. Geometrically, in 2D, in you transform a circle centered at origin, eigenvalues are lengths of the axes. Eigenvectors are the axes.

    6. Section 2.6 Hermitian and unitary matrices

    7. P 39. Adjoint: conjugate transpose of matrix.

    8. If you use its eigenvectors as a basis, then the matrix diagonalizes to a list of its eigenvalues.

    9. P 62. Hermitian matrix: it is its adjoint.

    10. Unitary: its inverse is its adjoint.

    11. Geometrically, they are rotations since they preserve distances.

    12. Notation confusion: the books uses capital letters both for matrices and vectors.

    13. P 71, tensor product of matrices.

      1. Chapter 3 through 3.2, p 74-88.

      1. p 80, doubly stochastic matrix.

      2. Multiplying it by a vector of probabilities gives a vector of probabilities (i.e., they sum to 1 and $0\le a_i \le 1$ ).

      3. P 88, Chapter 3, section 3.3 Quantum systems,

      4. Real probabilities add.

      5. When probabilities are norms of complex numbers, they might cancel.

    15. p 91, Ex 3.2.2

    16. p 93 double slit experiment

    17. p 97 Section 3.4, Assembling systems

2.2 2 slit experiment compared with real vs complex transitions

2.3 Two and three qubit operators

  1. https://en.m.wikipedia.org/wiki/Bloch_sphere:

    1. The state of a qbit can be represented as a point on or in a sphere of radius 1.

    2. E.g., |1> is the north pole, |0> the south pole.

    3. Many operations are rotations.

  2. Common operations (aka gates):

    https://en.wikipedia.org/wiki/Quantum_logic_gate

    1. Swap

    2. controlled not CNOT cX

      When input is general, it's more sophisticated that it looks.

    3. Hadamard.

      1-qbit creates a superposition.

      https://cs.stackexchange.com/questions/63859/intuition-behind-the-hadamard-gate

      2-qbit creates a uniform superposition

      https://en.wikipedia.org/wiki/Quantum_logic_gate

    4. Toffoli, aka CCNOT.

      Universal for classical boolean functions.

      (a,b,c) -> (a,b, c xor (a and b))

      https://en.wikipedia.org/wiki/Toffoli_gate

    5. Fredkin, aka CSWAP.

      https://en.wikipedia.org/wiki/Fredkin_gate

      3 inputs. Swaps last 2 if first is true.

      sample app: 5 gates make a 3-bit full adder.

  3. Bell state

    1. Maximally entangled.

    2. Hadamard then CNOT.

2.4 Entanglement of 2-qbit system

State is a 4-vector of length 1.

It was originally created as the exterior product of two 2-vectors, the states of two separate 1-qbit systems.

Originally the separate 1-qbit systems didn't affect each other. Either could be transformed and measured.

Then 2-qbit system was rotated with a transformation matrix.

Now, perhaps it can be decomposed into the exterior product of two 2-vectors. Perhaps not.

  1. Case 1: The 4-vector representing the new state can be decomposed.

    1. Then it's still really two separate 1-qbit systems.

    2. They can still either be transformed and measured.

    3. Measuring one qbit does not affect the other qbit.

  2. Case 2: The 4-vector representing the new state cannot be decomposed.

    1. So the 2 qbits are now entangled.

    2. That means that measuring one qbit affects what you will see when you measure the other.

    3. It might just bias the probabilities of measuring the other qbit as 0 or 1.

    4. Or, it might totally control what you will see.

2.5 No Cloning

I made some supplementary material on cloning (copying), which works in the classical world but not in the quantum world.

Classically, you can easily clone a bit. Consider a 2-bit system, $x, y$. Represent the state with a 4-vector

$s=\begin{vmatrix} a_0\\a_1\\a_2\\a_3\end{vmatrix}$

where exactly one $a_i=1$ and the other three are 0. E.g., if $a_3=1$ then $x=y=1$.

Here's a 2-input, 2-output circuit that clones the first bit.

$x'=x\\y'=x$

Its truth table is

x y | x'y'
0 0 | 0 0
0 1 | 0 0
1 0 | 1 1
1 1 | 1 1

The matrix M is:

1 1 0 0
0 0 0 0
0 0 0 0
0 0 1 1

That is, the final state is $s' = \sum_j M_{ij} b_j$

However, M is singular. So this is not a legal quantum circuit. Let's try again.

The better way is the 3-input Toffoli gate. The function is

$x'=x \\ y'=y \\ z'= z \oplus xy$

The truth table is

x y z | x'y'z'
0 0 0 | 0 0 0
0 0 1 | 0 0 1
0 1 0 | 0 1 0
0 1 1 | 0 1 1
1 0 0 | 1 0 0
1 0 1 | 1 0 1
1 1 0 | 1 1 1
1 1 1 | 1 1 0

The matrix is:

1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1
0 0 0 0 0 0 1 0

Let x=1, z=0. Then:

x'= 1
y'= y
z'= y

and we've cloned y in the classical case.

This matrix is nonsingular and so is legal in a quantum circuit.

Try $y= \frac{1}{\sqrt{2}} | 0> + \frac{1}{\sqrt{2}} | 1>$. Using x=1, z=0, the input will be

$\frac{ | 1, 0, 0> + | 1, 1, 0>}{\sqrt{2}}$

and the state is

$(0, 0, 0, 0, \frac{1}{\sqrt{2}} , 0, \frac{1}{\sqrt{2}} , 0)^T$

Multiplying that by the matrix gives

$\frac{ | 1, 0, 0> + | 1, 1, 1>}{\sqrt{2}}$

Instead of cloning y into z, this entangled y and z.

This isn't new; we already know how to engangle two qbits.

Engangling isn't the same as cloning. The point of cloning is that we could operate on the two bits separately. If they're engangled, operating on one affects the other.

Note that this changes $x$, not just $y$. Classically, $x$ is an input but that does not change.

Quantum Homework 2, Tues 2021-09-07

Due 2021-09-09 4pm in gradescope. Groups of 2 are ok; submit one answer set.

These are questions about the videos assigned in class 1.

  1. (10 points) What are the 2 ways that Talia Gershon says that quantum is different?

  2. (10 points) According to David Deutsch, what is the quantum theory of computation?

Total: 20

Quantum Class 2, Thurs 2021-09-02

1 Upcoming conferences etc

  1. IEEE Quantum Week 2021 October 17–22, 2021 October 17–22, 2021, IEEE International Conference on Quantum Computing and Engineering (QCE21)

    You might want to watch or submit a paper.

  2. free ACM TechTalk, "Quantum Computational Supremacy," presented on Thursday, September 9 at 12:00 PM ET/9:00 AM PT by Scott Aaronson, the David J. Bruton Centennial Professor of Computer Science at the University of Texas at Austin and recipient of the 2020 ACM Prize in Computing.

    I forwarded the email to the class.

  3. Workshop - Quantum Computing Opportunities in Renewable Energy and Climate Change.

    GE is organizing a workshop at the IEEE Quantum week focused on renewable energy and climate change. In case you are interested in submitting an abstract, this is the link to the call for abstract:

    https://qce.quantum.ieee.org/wp-content/uploads/2021/08/Call-for-Speakers-QCE21-Workshop-on-Quantum-Computing-Opportunities-in-Renewable-Energy-and-Climate-Change.pdf

2 My emails to class

  1. I've sent several emails to the class, most recently this morning. Has anyone received any of them?

  2. If you send me your non-RPI email, I'll also send to it.

3 Chapter 3: Qubits, Operators and Measurement

  1. Bloch sphere. Shows 1 qubit and makes it easy to see phases and rotations.

  2. Quantum circuit diagram shows how qubits interact and their states change over time.

    Contrast to classical circuits, where data moves around.

  3. Review and extend 1 qubit operators.

    1. Rotations by $\pi$ about major axes: NOT (X), Y, Z

    2. Hadamard (H)

    3. Other rotations

  4. Additional good ref: https://en.wikipedia.org/wiki/Quantum_logic_gate

  5. (from the text callout 3.1) qubit: a two-level quantum mechanical system.

  6. state at any given time is a vector in a 2-D complex Hilbert space.

3.1 Two qubit operators

  1. Now, let $q$ be a system with two qubits, i.e., a 2-vector of qubits.

  2. $q$ is now a linear combo of 4 basis values, $ | 00\!\!>$, $ | 01\!\!>$, $ | 10\!\!>$, $ | 11\!\!>$.

  3. $q = a_0 | 00\!\!> + a_1 | 01\!\!> + a_2 | 10\!\!> + a_3 | 11\!\!> $

  4. where $a_i$ are complex and $ \sum | a_i | ^2 = 1$.

  5. $q$ exists in all 4 states simultaneously.

  6. If $q$ is a vector with n component qubits, then it exists in $2^n$ states simultaneously.

  7. This is part of the reason that quantum computation is powerful.

  8. A measurement operator applied to $q$ will rotate it to a basis {00, 01, 10, 11}, so that it will be observed in one of those four cases, with probabilities $ | a_i | ^2$.

  9. You operate on $q$ by multiplying it by a 4x4 matrix operator.

  10. The matrices are all invertible (except for measurement matrices), and all leave $ | q | = 1$.

  11. You set the initial value of $q$ by setting its two qubits each to 0 or 1.

  12. How this is done depends on the particular hw.

  13. I.e., initially, $q_1 = \begin{pmatrix}a_1 | 0\!\!> \\b_1 | 1\!\!> \end{pmatrix}$ and $q_2 = \begin{pmatrix}a_2 | 0\!\!> \\b_2 | 1\!\!> \end{pmatrix}$, and so

    $$q = \begin{pmatrix} q_1 \\ q_2 \end{pmatrix} = \begin{pmatrix} a_1 a_2 | 00 \!\!> \\ a_1 b_2 | 01 \!\!> \\ a_2 b_1 | 10 \!\!> \\ b_1 b_2 | 11 \!\!> \end{pmatrix}$$.

  14. The combined state is the tensor product of the individual qubits.

  15. In this case, you could separate out the individual qubits again.

  16. However, sometimes after operating on the combo (i.e., multiplying by a matrix), you cannot any more separate out the result into a tensor product of individual qubits.

  17. For $n$ qubits, the tensor product is a vector with $2^n$ elements, one element for each possible value of each qubit.

  18. Each element of the tensor product has a complex weight.

  19. You transform a state by multiplying it by a matrix.

  20. The matrix is invertible.

  21. The transformation doesn't destroy information.

  22. When you measure a state, it collapses into one of the basis states. (aka component states)

  23. You don't need to bring in consciousness etc. The collapse happens because the measurement causes the state to interact with the outside world.

  24. The probability of collapsing into a particular state is the squared magnitude of its complex weight.

  25. For some sets of weights, particularly after a transformation, the combined state cannot be separated into a tensor product of individual qubits. In this case, the individual qubits are entangled.

  26. That is the next part of why quantum computation is powerful.

  27. Entanglement means that if you measure one qubit then what you observe restricts what would be observed when you measure the other qubit.

  28. However that does not let you communicate.

  29. The current limitations are that IBM does only a few qubits and that the operation is noisy.

4 No new homework

Finish 1 and enjoy Labor Day.

Quantum Class 1, Mon 2021-08-30

1 Misc

1.1 Syllabus

Read the syllabus, accessible from the top bar.

1.2 Gradescope

We'll use Gradescope for submitting homeworks and possibly projects. I synced it with LMS on as of 8/29.

1.3 Iclicker

We may use the new version of iclicker for in-class quizzes.

1.4 My research

I do parallel geometry algorithms on large problems for CAD and GIS. See my home page. If this is interesting, talk to me. Maybe you can do something that leads to a jointly-authored paper.

1.5 Changes from last year

  1. New textbooks.

  2. More non-IBM material.

  3. No piazza.

  4. Class is in person.

1.6 Optional text

Quantum Computing for Computer Scientists 1st Edition

I used this last year. This is nice but is 20 years old, and so omits some things. However I'll refer to it a little.

I encourage you to read several books, and pick and choose.

2 Quantum Computing: An Applied Approach, chapter 1

  1. Quantum computer: uses properties of quantum mechanics to compute

    1. world is quantum.

    2. compare to classical computer.

  2. quantum properties

    1. superposition

    2. entanglement

  3. state: complete math description of state.

    1. a complex vector.

    2. classical analog: e.g., position of a particle.

  4. superposition: linear combo of states is a legal state.

    1. the weights are complex numbers.

    2. everything in quantum mechanics uses complex numbers.

    3. superposition does not work classically.

  5. measurement of a state $\Psi$:

    1. this discussion assumes some specific set of basis vectors.

    2. you can use different basis systems to represent the same vector, and rotate between them.

    3. $\Psi$ is a linear combo of the basis vectors.

    4. the measurement is also defined wrt that basis.

    5. it changes $\Psi$ state randomly to one of the basis vectors.

    6. the observed output of the measurement is that basis vector.

    7. the probability of $\Psi$ changing to a particular basis vector is the modulus squared of the weight of that basis vector.

    8. define $z^c$ to be the complex conjugate of $z$.

    9. if $\Psi= \alpha\psi_1+\beta\psi_2$, where $\alpha^2+\beta^2=1$ then the probability of $\Psi$ changing to $\psi_1$ is $\alpha^c\alpha$. (the Born rule)

    10. $\alpha^c\alpha$ is called the modulus squared.

    11. important: measuring changes the system.

    12. see the polarization example in the book

  6. A qubit $q$ is a quantum analog to a classical bit.

  7. the quantum analog to classical bits 0 and 1 are $|0\!\!>$ and $|1\!\!>$.

  8. q's state is a superposition (linear combo) of those two basis states:

    1. $q = a|0\!\!> + b|1\!\!>$ ,

    2. where the weights $a$ and $b$ are complex numbers, and $ | a | ^2 + | b | ^2 = 1$.

  9. Note the weird notation (Dirac notation). In $|0\!\!>$, $|$ is like a left bracket and $>$ like a right one.

  10. It is wrong to think that $q$ is really in one of the two states, but you don't know which one. This is the hidden variable theory. It has been proved experimentally to be false.

  11. $q$ is really in both states simultaneously.

    Alice laughed. "There's no use trying," she said: "one can't believe impossible things." "I daresay you haven't had much practice," said the Queen. "When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast." - Through the Looking-Glass, and What Alice Found There (1871), by Lewis Carroll (Charles Lutwidge Dodgson).

  12. You cannot observe its state, unless it is $|0\!\!>$ and $|1\!\!>$, in which case you observe $0$ or $1$. This is the classical case.

  13. Otherwise you observe it with a measurement operator that transforms it to either $|0\!\!>$ and $|1\!\!>$, with probabilities

    $| a | ^2$ and $| b | ^2$, respectively.

  14. $a$ and $b$ are complex.

  15. That measurement changes $q$; it no longer has its old value.

  16. You cannot reclaim the old value.

  17. There are many possible measurement operators available.

    1. You can choose which to apply to $q$.

    2. That prevents you from applying the others to $q$, because you don't have $q$ available any more.

    3. Heisenberg uncertainty: measuring, say, position, prevents you from accurately measuring momentum.

  18. $q$, that is, $q$ 's value, can be considered to be a vector of length two: $$\begin{pmatrix} a | 0\!\!> \\ b | 1\!\!> \end{pmatrix} $$ or simply $$\begin{pmatrix}a\\b\end{pmatrix}$$.

  19. You operate on $q$ with a matrix multiplication: $q_2 = M q$.

  20. Unless $M$ is a measurement operator, it is invertible, so you can go backwards.

  21. Examples of 1-qubit gates

    1. not

    2. square root of not

    3. rotation, phase shift

  22. No cloning: You cannot copy a qubit, but can move it.

  23. The life cycle of a qubit:

    1. Create a qubit with a classical value, 0 or 1.

    2. Operate on it with matrices, which rotate it to have complex weights.

    3. Measure it by randomly projecting it onto a basis vector.

  24. So far, not very powerful.

  25. a quantum state $\Psi$ usually has many qubits.

    compare to a classical byte with 8 classical bits.

  26. However the different qubits in $\Psi$$ might be entangled.

    1. This is very weird and powerful.

    2. Entanglement means that if you measure one qubit then what you observe restricts what would be observed when you measure the other qubit.

    3. Even if the two qubits are 1000 mi apart. This has been experimentally observed.

    4. However that does not let you communicate.

2.1 Entanglement

  1. Crazy counterintuitive idea that's the basis for quantum speedup.

  2. Classical metaphor for entanglement:

    1. Start with a piece of paper.

    2. Tear it into two halves.

    3. Put each half into an envelope, seal them, and mix them up, so that you can't tell which half is in which envelope.

    4. Address and mail one envelope to a friend in Australia, and the other to a friend in Greenland.

    5. When the Australian opens his envelope, he knows what the Greenlander will find in his.

    6. However that doesn't let the Australian send any info to the Greenlander, or vv.

  3. This has been demonstrated with real qubits transported 1000 miles apart.

  4. Entanglement means that if you measure one qubit then what you observe restricts what would be observed when you measure the other qubit.

  5. However that does not let you communicate.

  6. The preceding metaphor is wrong in that it has a hidden variable, the unobserved half-paper state. That does not happen in quantum physics. With qubits, the states are not fixed until one is observed. I'm trying to get the idea across.

2.2 Reversibility of Quantum Computation (p9)

#. All operators used in quantum computation other than for measurement must be reversible. - textbook.

  1. Contrast to classical operators like and and or.

3 Chapter 2: history

  1. Read it on your own, but here are some additions:

  2. The property list on p15 is controversial and seems designed to exclude D-Wave.

  3. Like for classical computation, the main ideas of quantum computing were proposed before actual machines could be built.

4 Chapter 3: Qubits, Operators and Measurement

  1. (from the text callout 3.1) qubit: a two-level quantum mechanical system.

  2. state at any given time is a vector in a 2-D complex Hilbert space.

4.1 Two qubit operators

  1. Now, let $q$ be a system with two qubits, i.e., a 2-vector of qubits.

  2. $q$ is now a linear combo of 4 basis values, $ | 00\!\!>$, $ | 01\!\!>$, $ | 10\!\!>$, $ | 11\!\!>$.

  3. $q = a_0 | 00\!\!> + a_1 | 01\!\!> + a_2 | 10\!\!> + a_3 | 11\!\!> $

  4. where $a_i$ are complex and $ \sum | a_i | ^2 = 1$.

  5. $q$ exists in all 4 states simultaneously.

  6. If $q$ is a vector with n component qubits, then it exists in $2^n$ states simultaneously.

  7. This is part of the reason that quantum computation is powerful.

  8. A measurement operator applied to $q$ will rotate it to a basis {00, 01, 10, 11}, so that it will be observed in one of those four cases, with probabilities $ | a_i | ^2$.

  9. You operate on $q$ by multiplying it by a 4x4 matrix operator.

  10. The matrices are all invertible (except for measurement matrices), and all leave $ | q | = 1$.

  11. You set the initial value of $q$ by setting its two qubits each to 0 or 1.

  12. How this is done depends on the particular hw.

  13. I.e., initially, $q_1 = \begin{pmatrix}a_1 | 0\!\!> \\b_1 | 1\!\!> \end{pmatrix}$ and $q_2 = \begin{pmatrix}a_2 | 0\!\!> \\b_2 | 1\!\!> \end{pmatrix}$, and so

    $$q = \begin{pmatrix} q_1 \\ q_2 \end{pmatrix} = \begin{pmatrix} a_1 a_2 | 00 \!\!> \\ a_1 b_2 | 01 \!\!> \\ a_2 b_1 | 10 \!\!> \\ b_1 b_2 | 11 \!\!> \end{pmatrix}$$.

  14. The combined state is the tensor product of the individual qubits.

  15. In this case, you could separate out the individual qubits again.

  16. However, sometimes after operating on the combo (i.e., multiplying by a matrix), you cannot any more separate out the result into a tensor product of individual qubits.

  17. For $n$ qubits, the tensor product is a vector with $2^n$ elements, one element for each possible value of each qubit.

  18. Each element of the tensor product has a complex weight.

  19. You transform a state by multiplying it by a matrix.

  20. The matrix is invertible.

  21. The transformation doesn't destroy information.

  22. When you measure a state, it collapses into one of the basis states. (aka component states)

  23. You don't need to bring in consciousness etc. The collapse happens because the measurement causes the state to interact with the outside world.

  24. The probability of collapsing into a particular state is the squared magnitude of its complex weight.

  25. For some sets of weights, particularly after a transformation, the combined state cannot be separated into a tensor product of individual qubits. In this case, the individual qubits are entangled.

  26. That is the next part of why quantum computation is powerful.

  27. Entanglement means that if you measure one qubit then what you observe restricts what would be observed when you measure the other qubit.

  28. However that does not let you communicate.

  29. The current limitations are that IBM does only a few qubits and that the operation is noisy.

5 Class 2

Chapter 3 and on. Feel free to read ahead.

6 Homework 1

is online, due Thurs.

7 Videos to watch for Thurs

  1. Watch A Beginner’s Guide to Quantum Computing, 18 min, by Dr. Talia Gershon, IBM Research.

  2. David Deutsch - Why is the Quantum so Strange? (8:43)

Quantum Homework 1, Mon 2021-08-30

Due 2021-09-02 4pm in gradescope.

  1. (5 points) Compute (5+2i)/(3+4i).

  2. (5 pts) Compute the eigenvalues of $\begin{vmatrix} 5&2\\3&4 \end{vmatrix}$.

  3. (5 pts) Considering complex numbers as points in the 2D plane, what is the geometric effect of multiplying a complex number by (.6-.8i) ?

  4. (5 pts) Let c = 1 + i. Convert it to polar coordinates, calculate its fifth power, and revert the answers to Cartesian coordinates.

  5. (5 pts) Find all the cube roots of c = 1 - i.

  6. (5 pts) Invert the Hadamard matrix $\frac{1}{\sqrt{2}} \begin{vmatrix} 1&1\\1&-1\end{vmatrix}$.

Total: 30