Comment by krastanov
2 days ago
The magnitude of an "amplitude" is basis dependent. A basis is a human invention, an arbitrary choice made by the human to describe nature. The choice of basis is not fundamental. So just choose a basis in which there are no vanishingly small amplitudes and your worry is addressed.
Any implementation of Shor will need vanishingly small amplitudes, as it forms a superposition of 2^256 classical states.
This is completely missing the point. There is nothing fundamental to an amplitude. The amplitudes are this small because you have chosen to work in a basis in which they are small. Go to the Hadamard basis and the amplitude value is exactly 1. After all, the initial state of Shor's algorithm (the superposition of all classical bitstrings) is the perfectly factorizable, completely not entangled state |+++++++>
When the amplitude has norm 1, there is only one nonzero amplitude. Changing basis does not affect the number of basis functions.
5 replies →
The initial state of Shor's algorithm just has the n-bit number to be factored. From there it creates the superposition in the next n steps.
Forget the talk about amplitudes. What I find hard to believe is that nature will let us compute reliably with hundreds of entangled qubits.
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1/sqrt(N)