Exploring the Quantum Frontier: Qubits, Bloch Sphere, and the Power of Entanglement

In a classical computer information is encoded using bits. A bit can be in either one of two states labeled as 0 or 1.

In a quantum computer the information is encoded in the form of quantum bits or Qubits.

Unlike the classical bit a qubit can be placed in both 0 and 1 states at the same time however, a qubit must split to to partially occupy these states. We say that such a qubit is in a superposition of states.

We can control the probability of measuring the qubit in one state or the other. It's important to understand that a qubit is not between 0 and 1 even if it is convenient to illustrate the superposition as so. Rather a qubit is in these two states with given proportions. We can represent a qubit by Bloch sphere.

Bloch Sphere

Here are the positions of the X, Y and Z axes of the Bloch sphere. In a Bloch sphere, a vector pointing upwards represents the state 0 of the system and a vector pointing downwards represents the state 1. The vector can also point in any direction other than 0 or 1 to represent a superposition of states. We can also vary a qubit state like so and represent the relative phase between 0 and 1.

Measuring qubits

To know a qubit's state, we must observe it or in other words, measure it. Even if there's an infinite number of possible states there are only two possible results for the measurement 0 or 1. If the qubit is already in the state 0 or 1 the measure will return the same value.

Entanglement

Quantum mechanics also allows us to describe entanglement as a phenomenon that defies our classical conception of the world. Accordingly, when two qubits are entangled, they are linked together, measuring one qubit determines the measure of the second no matter how far apart they are.

For example, if two qubits are entangled and in a superposition of 0 0 and 1 1.

It is impossible to say what the value of the first qubit measured will be. But once measured we know instantly the value of the second qubit.