Adventures in Computer Science by Vicente Moret-Bonillo

Author:Vicente Moret-Bonillo
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

We conclude, therefore, that a qubit is a vector of the vector space

According to quantum mechanics, V is a complex Hilbert space, where

is an orthonormal basis and the states are unitary vectors . A qubit can therefore be in any state (the coefficients designate amplitudes):

It is relatively easy to understand the basis states but not so easy to understand the intermediate states. Returning to the example of electron spin and analyzing an intermediate state, the qubit φ does not have a well-defined spin. Remember that the spin of an electron is a physical magnitude that is quantified, which is why the intermediate state φ does not have a defined spin.

We return now to the issue of information . The information contained in a qubit is obviously very small, so, to be able to represent greater amounts of information, we need n-qubit systems. If we want to describe the state of a system that consists not only of a qubit but of a set of n qubits, the laws of quantum mechanics tell us that we have to obtain the tensor product of the n single qubits.

To start with a simple example, suppose that n = 2 represents the spin of a system of two electrons. The spin of each electron can be in two states. When combined, four states for the two-qubit system are generated: |00〉, |01〉, |10〉 and |11〉.

For this two-qubit, the space dimension is 22 and the space basis is as follows:

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