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Lots of beginners are starting to learn quantum computing. But there are also experienced people that have been working in this field for many years.

What are some topics that might be considered important for a beginner to learn thoroughly?

By beginner, I mean someone who didn't work in the field, and who does not have a Ph.D. in the field (for example, someone who has just been reading about Quantum Computing for the last 3-4 months).

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    $\begingroup$ I think it depends on what you mean by beginner, I have worked as a QSE; and I'm sure many people on this SE would still consider me a beginner(rightfully so). I find often times questions like "Design an experiment that can distinguish a mixed state from a superposition" or "Why doesn't Teleportation break the universal speed limit" probe someone's understanding of concepts quite well. But of course in some circles those questions would be elementary. All depends I guess. $\endgroup$
    – Bertrand Einstein IV
    Feb 8, 2021 at 19:16
  • $\begingroup$ @BertrandEinsteinIV This is wrong way to look at it. If your logic holds then even a noble prize winning physicist might say "well, I don't know much" and so he is also a beginner? By beginner I meant somehow who didn't work anywhere, who is not having PhD , who is just reading QC for last 3-4 months. $\endgroup$
    – user27286
    Feb 8, 2021 at 19:34
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    $\begingroup$ Well then you could more precisely define beginner. I for one don't have a Phd, I don't even have a bachelor's degree in Math/Physics/CS, I just read free stuff online. The questions I put in my initial comment tests a certain level of knowledge, if that is unsatisfactory; then you have a different standard of knowledge which is fine; you just have to tune your questions to what you mean by beginner accordingly. $\endgroup$
    – Bertrand Einstein IV
    Feb 8, 2021 at 19:52
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    $\begingroup$ yes one more vote and it will be gone. Sad that people don't like that question. $\endgroup$
    – user27286
    Feb 8, 2021 at 21:57
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    $\begingroup$ I have heard this type of question a few times so I wrote up a list of useful things to learn in QC that'll hopefully help you with some of the important things in the field for a beginner to learn. $\endgroup$
    – Rajiv Krishnakumar
    Mar 7, 2021 at 20:31

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Made Community Wiki

Much as there's no royal road to geometry, getting familiar with quantum computing usually takes a lot of hard work. I would consider anyone who can answer Bertrand's questions in the comments to be pretty knowledgeable, at least having completed the first parts of a good semester of an advanced undergraduate/graduate course or have otherwise engaged in many many hours of self-study.

But there are many good lecture series on-line. YMMV.

Nonetheless knowledge of some topics that may be at least important to have a cocktail-level conversation of quantum computing might start off and include:

  • Qubits, two state quantum systems
  • The representation of a qubit on the complex plane
  • Superposition and the difference between a qubit and a bit
  • The Born rule of measurement and post-measurement states, with side topics about interpretations such as Copenhagen and Many-Worlds
  • The difference between the computational basis and the Hadamard basis
  • The no-cloning theorem
  • The Bloch sphere and the representation of a qubit in three dimensions
  • Neat applications like the Elitzur-Vaidman bomb tester
  • Other applications of qubits in product states, such as quantum money (Wiesner's scheme) and/or quantum cryptography (the BB84 scheme)

Moving on:

  • Entanglement and the EPR paper
  • The Bell inequality and/or the CHSH game and/or the Mermin-Peres magic square
  • Neat applications like teleportation and superdense coding
  • Other applications of Bell pairs like the E91 quantum cryptography scheme
  • Perhaps the GHZ state and/or the W state

Further on to quantum algorithms you have the greatest hits like:

  • The Bernstein-Vazirani algorithm
  • The Deutsch-Jozsa algorithm
  • The BQP complexity class
  • Simon's algorithm
  • Hamiltonian simulation
  • Quantum error correction
  • The crown jewels of Shor's algorithm/Grover's algorithm

etc.

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    $\begingroup$ Like the answer. I dont know some stuff from here.... : ) $\endgroup$
    – user27286
    Feb 9, 2021 at 1:08

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