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On a classical computer, an operation A acting on one or several registers is always reversible. That is, there is an operation B such that applying A then B amounts to no operation at all (note that B is not allowed to depend on the content of the register(s) before applying A).
For simplicity, think of logical operations (OR, AND, XOR, …) acting on a single bit.
On a quantum computer, an operation A (measurements excluded) acting on one or several quantum registers is always reversible. That is, there is an operation B such that applying A then B amounts to no operation at all (note that B is not allowed to depend on the content of the register(s) before applying A).
How is a quantum operation mathematically modelled?
What is the complexity of the adder with carry discussed in the lectures? More precisely, how does the number of elementary calculations scale with the number of bits in the numbers to be added?
What is the complexity of the adder based on the Quantum Fourier Transform presented in the slides, assuming we use the most basic implementation of the Quantum Fourier Transform? Here, by complexity we mean the number of elementary quantum gates required to implement the operation.
Is the weighted adder proposed in the lecture exact? That is, does it store in the result register the exact weighted addition of the numbers to be added?