What’s Qubit and Qubit States?
Below is the summary of the section 1.1–1.2 of book “Quantum Computation and Quantum Information”
Quantum bits, also known as qubit, is the fundamental concept of Quantum Computation. Just like bits, Qubit has states, which can be defined as:
Where a and b is a vector in a two-dimensional complex vector space, and |0> and |1> are known as computational basis states. For measurement, we get the probability of each state instead of exact states. That is, we get state |0> with probability |a|² and |1> with probability |b|², where |a|² + |b|² = 1. For example, for qubit:
,representing we have ½ probability of |0> and ½ probability of |1>.
We can rewrite equation 1 as:
, where /theta, /Phi and /gamma are real numbers. We can reduce equation 2 to below since it has no observable effect:
where /Phi and /theta representing unit three dimensional sphere — Bloch sphere. A visualizing of Qubit state can be seen as below:
Multiple qubits
The n qubits system states has format |x_1x_2,…,x_n>. Consider 2 qubits system, which can be defined as:
where |00>, |01>, |10>, |11> are four basis states. Like the one qubit system, multiple qubit system has similar priority that the output is along with the corresponding probability.