What are tentpole topics in quantum computing?

Question

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).

Answer 1

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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.