OE-4.4 Quantum Algorithms
You can describe the quantum Fourier transform and phase estimation, and explain what Shor's, Grover's, Deutsch's and Deutsch-Jozsa algorithms achieve and at what speed-up.
These four algorithms are the reason the field is funded, but their speed-ups differ in kind: Shor is exponential and breaks RSA, Grover is only quadratic and merely accelerates search. Deutsch and Deutsch-Jozsa are the teaching algorithms - contrived problems whose point is to show interference doing computational work. The quantum Fourier transform and phase estimation are the shared machinery underneath Shor, so learn them before, not after.
Work through these
The quantum Fourier transform
The quantum version of the transform from the previous topic, and the engine inside most of the algorithms with a real speedup. This is the item to understand properly if you understand only one.
Quantum phase estimation
Extracting an angle from a state, which is how the transform above gets used in practice. It is a building block rather than an application.
Deutsch's algorithm
The first algorithm that does something no classical method can do in one step. Small enough to follow completely, which is why it is taught first.
The Deutsch-Jozsa algorithm
The same idea generalised, and the first case where the advantage grows with the problem size. Follow the two versions together and the generalisation is clear.
Grover's search algorithm
Searching an unsorted collection faster than checking every entry. The speedup is real and it is quadratic rather than exponential, which is worth stating precisely.
Shor's factoring algorithm
The result that made governments interested, because it threatens the cryptography the next topic describes. It uses the phase estimation and transform items above, so it is a good check on both.
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