Quantum mechanics allows us to prepare super
positions of different physical configurations. In quantum computers, this means we are allowed
to make super positions of quantum digital codes and the amount of information necessary
to describe these super positions grows exponentially with the number of qubits. However, not all
of this information is accessible to us because the process of quantum measurement poses a fundamental limit. This can be illustrated with the example of a spin which is the simplest kind of quantum bit. Imagine we prepare a super position of spin up and spin down which means the spin is pointing horizontally. So its vertical component is zero. If we then try to measure this vertical component, quantum mechanics imposes that we must always find the spin in one of its basis states – either up or down. In other words, the act of measuring
a quantum object modifies its state. Moreover, the outcome of the measurement is probabilistic. We cannot predict with certainty in which direction the spin will be found, but we can assign a probably to it if we know what type of super position we have prepared. The probability to find the system in each one of the basis states is simply the square of the coefficient
of that state in the initial super position. The special case is when the system is already in one of the basis states. In that case, the outcome of the measurement is always well determined and the system remains in the state it was prepared in. This has very important implications for quantum computing. We know that with AND qubits, we need 2 to the power N numbers to fully describe the quantum state. But that information is not really
accessible because we’d destroy the quantum super position if we tried to measure it. So to use the power of quantum information, we need to develop quantum algorithms which explore the existence of huge amount of information stored in the quantum super position, but
at the end of the calculation, leave the system in one of the basis states which we are always
able to detect with certainty.