Learn Quantum Computing

-by Akash Kumar Singh

I have been exploring quantum computing since my BS-MS days at IISER Tirupati and have amassed a wealth of resources throughout my journey. While I do not claim to have mastered everything, I am continually learning and progressing toward my goals. I believe in sharing knowledge and resources with others who are passionate about quantum computing and related subjects. Though to tell you the truth this is secretly my checklist that I want to complete some day. So below is a curated set of resources that I have compiled for those who wish to delve into this fascinating field. Before starting I must say that learning beforehand Linear Algebra, Group Theory, Ordinary and Partial differential equations can make your journey a lot easier but you can also learn it even after taking an introductory course of Quantum computing.
Though I am compiling list for broad area of Quantum computing but from now on I will try to be more focused on Quantum Algorithms and expand on that. Also if there is any typo, I apologies beforehand. And yes I am to open to all suggestions if any, just drop me an e-mail on akashkumar@students.iisertirupati.ac.in.
Last but not the least I want to dedicate this page to Late Dr. Sankaranarayanan Selvarajan, SQT,DIAT Pune who was a great source of inspiration for me.

Quantum Computing:

1. General advice by Prof. Aram Harrow for learning Quantum Information,MIT Physics. Link

I am not generally following everything he mentions here otherwise no point in writing it again but broadly I carry the gist of what Prof. Harrow wants to convey in this whole document and then trying to compile this according to my experience.

2. Quantum Computing Introduction by Prof. Apoorva Patel, IISC Physics (good mathematical rigour) Link

3. Classical and Quantum Algorithms.

To learn quantum algorithms at an introductory level, you may not need extensive knowledge of classical algorithms initially. However, to design quantum algorithms, understanding classical algorithms and complexity theory is essential. Interestingly, I have also included Quantum Information notes by Prof. Scott Aaronson, a computer scientist, because traditionally, CS majors design algorithms. And his CS perspective on Quantum Information Science as a whole is invaluable. I think in the future, designing algorithms will likely be the work of both CS and physics majors, especially quantum algorithms and hence will get best of both worlds.

  1. Discrete Maths/ Maths for Computer Science (Proofs Based), MIT. Link
  2. Intro to Theoretical Computer Science,Udacity Link
  3. MIT 18.404J Theory of Computation, Fall 2020 Link
  4. Advanced Data Structure, MIT Link
  5. Introduction to Algorithms, MIT Link
  6. Design and Analysis of Algorithms, MIT. Link
  7. Algorithmic Lower Bounds, MIT Link
  8. Quantum Computation and Information at CMU ,Dr.Ryan O'Donnell, CMU. Link
  9. Quantum Algorithms, Prof. Andrew Childs,UMD. Link
  10. Quantum Information 1, Prof. Scott Aaronson,UT Austin. Link
  11. Quantum Information 2, Prof. Scott Aaronson,UT Austin. Link
  12. Quantum Computational Complexity, Dr. John Watrous,IBM. Link
  13. Quantum Walks, Dr. Renato Portugal, Link
  14. Graph Theory, Prof. Soumen Maity, IISER Pune Link
  15. Quantum Simulation, QGSS 2023,IBM. Link
    (more helpful if done after QM, condensed matter theory and Numerical methods)
  16. Quantum Algorithms for Optimizers, Dr.Giacomo nannicini,USC. Link
  17. Quantum Algorithms for Scientific Computation, Prof.Lin Lin,UC Berkeley. Link
  18. Quantum Algorithm Zoo (Your one stop destination for latest Quantum Algorithms). Link
  19. Interesting Papers on Quantum Algorithms.
    1. Quantum algorithms papers Link
    2. Quantum algorithms: an overview Prof. Ashley Montanaro (Good overview of Quantum Algorithms use cases). Link
    3. Quantum algorithms: A survey of applications and end-to-end complexities by Dr. Alexander M. Dalzell et al. (detailed review of Quantum Algorithms and their applications). Link
    4. Quantum Algorithm Design: Techniques and Applications SHAO Changpeng et al. (You know to how to access this:) ) Link
    5. Quantum Computation as Geometry Michael A. Nielsen et al. Link

4. Quantum Machine Learning and Classical Machine Learning

Same with Quantum Machine Learning you need familiarity with “classical” machine learning first. This is already done to some extend in these texts but I am stilling putting a great resource for classical ML which is Andrew ng course on ML which can supplement it, It is paid though, knowledge is not easy to access sometime but you know what to do ☺.

  1. Machine Learning Specialization by Prof. Andrew Ng, Stanford Link
  2. Quantum Machine Learning QGSS 2021,IBM Link
  3. Quantum Machine Learning, Late. Dr. Peter wittek,UoT Link
  4. Quantum Algorithms for Data Analysis, Alessandro Luongo, CQT NUS Link
  5. Machine Learning with Quantum Computers, Dr.Maria Schuld, Xanadu This is an old copy which only covers supervised learning but I trust you to find the updated one your own which is more complete, I cannot share it here due to copyright issues. Search with the name written, it is correct. Link
  6. Quantum Machine Learning practical, Pennylane Link

5. Quantum Error Correction

  1. Arthur Pesah blogs on Quantum Error Correction, UCL(London) Link
    Go through his blogs on Classical and Quantum Error correction for Introduction to QEC and stabilizer theory.
  2. Quantum Error Correction,Prof. Gotessmann and Prof. Yoshida,Perimeter Institute Link
  3. Surviving as Quantum Computer in Classical World,Prof. Gotessmann,UMD Link
  4. Stabilizer Code and Quantum Error correction,Thesis, Prof. Daniel Gottesmann,UMD Link
  5. Quantum Error Correction, Prof. Daniel A. Lidar and Prof.Todd A. Brunn. Link
    Here too I think you can find the book on your own.

6. Quantum Information Theory and Classical Information theory

  1. Information and Coding Theory, Prof. Ranjan Bose. Link
  2. Elements of Information theory, Thomas Cover. Link
  3. From Classical to Quantum Shannon Theory Dr. Mark M.Wilde,Cornell university. Link

7. Classical and Post-Quantum Cryptography

Though lot of people think post-quantum cryptography involves quantum algorithms but I hate to break it to you that PQC are just Classical schemes that Quantum Computers can not break still I am mentioning two separate sets of videos for the curious ones. For classical/pre-quantum cryptography I may not have a great resource and so I am using a short-cut. Lot of Indian engineering majors will be familiar with this channel though☺.

  1. Introduction to Cryptography, Neso Academy Link
  2. Post-Quantum Cryptography, Prof. Tanja Lange,TUE Link

8. Experimental Quantum Computing:

I am not particularly experienced with experimental work, so please take this suggestion with a grain of salt. However, the knowledge mentioned here can be helpful for those interested in the experimental side of quantum computing (This part still need lot of work so open to suggestions, if any). I will be more inclined towards optical setups and a little bit towards superconducting for now. I recommend to do this after completing Quantum Mechanics section.

  1. Quantum Hardware Course (A great introduction to Quantum Hardware (optical setups) by Zaiku Group) Link
  2. Optics,MIT Link
  3. Non-Linear optics,Prof. K.Thyagarajan,IIT Delhi Link
  4. Quantum optics 1, Prof. Ivan H. Deutsch,UNM Link
  5. Quantum optics 2, Prof. Ivan H. Deutsch,UNM Link
  6. Quantum optics Dr. Gustavo Aroeira,Emory University Link
  7. Analog electronics, Prof. Shanthi Pavan,IIT Madras Link
  8. Digital electronics, Prof.S.Srinivasan,IIT Madras Link
  9. Digital Electronics, Neso Academy(Again a shortcut) Link
  10. Practical Electronics for inventors, Scherz Link
  11. Digital Signal processing, Prof. S.C Dutta Roy, IIT Delhi Link
  12. Control systems, Prof. C. S. Shankar Ram, IIT Madras Link
  13. This particular course of control system has lot of use in Quantum sensing and metrology too.

  14. FPGA Link

    FPGA-Based Embedded System Developers Guide,Prof. Bazil Raj,DIAT Pune.
    It is paid but you know what to do.

  15. FPGA project using Basys 3, Prof. mughal Link
    For practical and specific courses on superconducting qubits, I recommend starting with the IBM Qiskit Global Summer School 2020. Following that, explore Qiskit Metal.

  16. Qiskit Global Summer School 2020,IBM (refer to last section) Link
  17. Qiskit Metal Link
  18. Circuit QED — Lecture Notes Link
  19. A quantum engineer's guide to superconducting qubits Link

9. ZX-Calculus

I was confused where to put this in QEC or QM but this is such a crucial and innovative field that I think it deserves a section of its own. I have lot of resources for this but I will just put one to go stop for this that is ZX website. Also I suggest whoever interested in this to join discord group for help needed with ZX-Calculus. Link
You can find everything needed is on the website about ZX-Calculus except my MS thesis which is on use case of ZX calculus and which I need to publish, Good reminder phew!!

10. Miscellaneous

  1. Open Quantum Problems, IQOQI Vienna. Link
  2. Scott Aaronson blogs for general Quantum Computing stuff. Link
  3. Dr. James wooton blogs for Quantum Error Correction. Link
  4. For advance maths used Quantum Computing follow Zaiku Group by Bambordé Baldé. Link
  5. Quantiki:For latest updates on positions and Conferences related to Quantum. Link
  6. For latest updates on jobs, internships and conferences subscribe to ORNL QCI Digest. Link
  7. Learn Qiskit and Quantum computing from IBM (should have made a separate section for this:) ). Link
  8. CS50 Introduction to Programming using Python, Harvard (Good introduction to basic programming). Link
  9. Project Euler: If you love to code and like maths challenges (Not directly related to Quantum Computing). Link

Quantum Mechanics:

Quantum Mechanics at least at the level of 3rd year BS-MS student (at IISER) should be enough for Quantum Computing. For Computer Science majors, MIT's Quantum Mechanics 1 lectures should provide an adequate background. However, if you aim to converse with physicists or work on quantum hardware and optics, it is advisable to study all three levels of MIT's Quantum Mechanics courses.

  1. Quantum Physics 1,MIT Link
  2. Quantum Physics 2,MIT Link
  3. Quantum Physics 3,MIT Link
  4. Book: Quantum Mechanics by Cohen-Tonnoudji et al. Vol:1,2,3 Link
  5. Sakurai is a great resource too. Link

Quantum Communication(QKD)

  1. Security of Quantum Key Distribution, Dr. Ramona Wolf Link
  2. Applied Quantum Cryptography, Dr. Kollmitzer et al.
    Not fully accessible again you know what to do☺. Link
  3. If you still want more resources I suggest this YouTube channel "Q-Leap Edu Quantum Communications" Link

Quantum Metrology and Sensing

I was taught this course by Late. Dr. Sankaranarayanan Selvarajan at DIAT Pune using research papers and different other resources. So I do not have any one particular source to point too.
I will leave this section to some good suggestions from others…

General Physics:

This section is more inclined towards physics majors and those interested in theoretical physics, rather than solely focusing on quantum computing. It is aimed at the level of a senior BS-MS student or even a graduate student.

Common advice

  1. How to be a good Theorist, Nobel laureate Prof. Gerardus 't Hooft. Link
  2. Prof.David Tong: Lectures on Theoretical Physics. Link
    From here I will again compile a list according to my convenience though keeping in perspective both profs. core ideas.

Courses

  1. Waves and Oscillations, MIT Link
  2. Mathematical methods for Physicists By Prof. Samudra Roy,IIT KGP Link
  3. Mathematical methods for Physics and Engineering, GP Sir Link
  4. Classical mechanics,Prof. Charudatt Kadolkar,IIT Guwahati Link
  5. Special Relativity, Prof. Susskind, Stanford Link
  6. Electromagnetism,Prof. Manoj Harbola,IIT Kanpur Link
  7. Thermodynamics,MIT Link
  8. Fluid Mechanics,Prof. Subashisa Dutta, IIT Guwahati Link
  9. Nonlinear Dynamics and Chaos, Dr. Shane Ross Link
  10. **Include Quantum Mechanics Sequence mentioned above.
  11. Statistical Mechanics 1 Link
  12. Statistical Mechanics 2 Link
  13. Fundamentals of Semiconductor Devices,Prof.Digbijoy N. Nath,IISc Link
  14. Electronics,Prof. D.C. Dube,IIT Delhi Link
  15. Solid State Physics,Dr. Aman Kumar Das, IIT KGP Link
  16. Advanced Condensed Matter Physics,Prof. Sourabh Basu,IIT Guwahati Link
  17. Numerical/Computational Methods in Physics,Prof. Saurabh Basu,IIT Guwahati. Link
  18. Experimental methods in Physics 1,Prof. Amal Kumar Das,IIT KGP Link
  19. Experimental methods in Physics 2,Prof. Amal Kumar Das,IIT KGP Link
  20. AMO Physics 1,MIT Link
  21. AMO Physics 2,MIT Link
  22. Nuclear and Particle Physics,MIT Link
  23. General Astronomy,Spahn's Science Lectures Link
  24. Astronomy and Astrophysics - An Introductory Survey, A lecture series by Prof. G. Srinivasan Link
  25. General Relativity,Prof.Susskind,Stanford Link
  26. General Relativity, MIT Link
  27. Quantum Field Theory 1,MIT Link
  28. Quantum Field Theory 2,Prof. Sunil Mukhi,IISER Pune Link

Extras:

This is not needed compulsorily for theoretical physics but it will be helpful to know this if you are interested in Simulation and Quantum Simulations. This is good add on to the Quantum Simulation: QGSS, IBM that is mentioned above in Quantum Algorithms section and can be great background study before going on to that Summer School playlist.
  1. Computational Chemistry and Classical Molecular Dynamics,Prof. B.L. Tambe, IIT Bombay Link
  2. MIT 3.021J Introduction to Modeling and Simulation Link
  3. Density Functional Theory (O.Feia, 2023) Link

General Maths Needed for Graduate Level Theoretical Physics

There is not much need to go through all this maths if you are just in Quantum Computing except Quantum Algorithms and Theoretical Physics. Nevertheless It is still good to have at least knowledge until topics that mentioned here until Group Theory. I myself a rookie in pure maths so if there is any mistake please share your suggestion on the mail given above.

  1. Linear Algebra, Prof. Gilbert Strang et al, MIT Link
  2. Multivariable Calculus,Dr. S.K. Gupta,IIT Roorkee Link
  3. ODE and PDE,Prof.P.N.Aggarawal and Prof.D.N. Pandey, IIT Roorkee Link
  4. Fourier analysis,Prof. G.K. Srinivasan,IIT Bombay Link
  5. Probability and Statistics,Prof. of practice Joe Blitzstein,Harvard Link
  6. Calculus of Variations,Dr. Gajendra Purohit Link
  7. Real Analysis,Dr. Jaikrishnan,IIT Palakkad Link
  8. Complex Analysis,Dr. P.A.S. Sree Krishna,IIT Guwahati Link
  9. Abstract Group Theory, Prof. Krishna Hanumanthu,CMI (Intro Level) Link
  10. Topology,Prof. Indrava Roy, IMSc Link
  11. Representation Theory, Dr. Walter Mazorchuk Link
  12. Differential Geometry, Harish Seshadri, IISC Link
  13. Differential Geometry(Physics perspective),Prof. Sunil Mukhi, IISER Pune Link
  14. Functional Analysis, Dr.Casey Rodriguez, MIT Link
  15. Lie Algebra,Prof. R Venkatesh,IISC Bangalore. Link
  16. Measure Theory, Prof. Indrava Roy, IMSc Link
  17. Random Matrix Theory, Euler Bernhard, IPhT, Saclay (Useful in Quantum Algorithms and Quantum Walks) Link

Extras:

These are some extra maths course not directly needed for theoretical physics but can be helpful for Quantum Cryptography, Quantum Algorithms and Quantum Complexity research.
  1. Numerical Analysis (Advanced), Prof. S Baskar, IIT Bombay (It will be helpful for Quantum Algorithms for Differential equations followed by Lie Algebra) Link
  2. Applications of Lie Algebra in Differential equations, Dr.Peter J. olver (It will be helpful for Quantum Algorithms for Differential equations using symmetry analysis, you know how to downlaod this) Link
  3. Manifold Theory, James cook (It will be helpful for Quantum Algorithms for Differential equations) Link
  4. Harmonic Analysis, Boyu Li, University of Waterloo (It will be helpful for Quantum Algorithms for Differential equations but should be done after fourier analysis, group theory and topolgy atleast) Link
  5. Introduction to Galois Theory, Prof. Krishna Hanumanthu, CMI (Less necessary at first compare to above ones but it will be helpful for Quantum Algorithms for Differential equations) Link
  6. Stochastic Calculus, Prof. Joydeep Dutta et al. (It will be helpful prerequisite for Quantum Algorithms for Finance) Link
  7. Number Theory, Michael Penn (It will be helpful prerequisite for Post-Quantum Cryptography) Link
  8. Operations Research, Prof. Kusum Deep, IIT Roorkee (It will be helpful prerequisite for Quantum Algorithms for Optimization) Link
  9. Introduction to Combinatorics, Prof.N Narayanan, IIT Madras (It will be helpful prerequisite for Quantum Complexity Theory and analysis of Quantum Algorithms) Link
  10. Game Theory, Prof. K.S. Mallikarjuna, IIT Bombay (It will be helpful prerequisite for analysis of Algorithms) Link

I want to thank first of all Naman for making this wonderful idea into reality. I want to thank Yashovardhan, Naimish ,Shubham kumar, Shubham Chouhan,Rupayan for engaging in discussions on topics from physics to philosophy. The crux of those fruitful discussions is this page.
I hope this list will be useful to inspire someone around the world, sitting on the desk with his/her laptop wondering how he/she can solve the deepest questions this universe poses using Quantum Computing and beyond!!

Best of luck
-By a physics student curiously lost in the field Quantum Computing.