# Clarification on what we can consider a qubit to be

• I
In summary, a qubit in a 2 level quantum system can be represented by a pair of states, such as |0> and |1>, or by the superposition of these states, such as α|0> + β|1>. Both the individual states and the superposition are considered to be qubits, and they form a useful pair in anti-commuting observables.

In a 2 level quantum system, should I consider the states

$$|0>$$

and

$$|1|>$$

to be qubits by themselves?

Or is only the SUPERPOSITION of these two states,

$$\alpha |0> + \beta |1>$$

considered to be a qubit?

Nevermind, they have to be qubits as well. If we consider our superposition to be a qubit, then we can set ## \alpha = 1 ## and ## \beta = 0 ## and that should be an appropriate qubit state.

In a 2 level quantum system, should I consider [...] to be qubits by themselves?
The qubit is the 2-state system, just like a classical bit is a binary variable. The states are not qubits, but the qauntum analogues of the classical values.

You should consider the pair to form a qubit. On their own they're not very useful.

Another useful way to think about what a qubit is is as an anti-commuting pair of observables, such as the observable ##|0\rangle##-vs-##|1\rangle## paired with the observable ##\frac{1}{\sqrt{2}} \left( |0\rangle + |1\rangle \right)##-vs-##\frac{1}{\sqrt{2}} \left( |0\rangle - |1\rangle \right)##.

## 1. What is a qubit?

A qubit, short for quantum bit, is the basic unit of information in quantum computing. It is the quantum mechanical equivalent of a classical bit, and can represent a 0, 1, or a superposition of both states simultaneously.

## 2. How is a qubit different from a classical bit?

A classical bit can only represent one of two states (0 or 1) at a time, while a qubit can represent both states simultaneously in a superposition. This allows for more complex and powerful computations to be performed in quantum computing.

## 3. What physical systems can be used to implement a qubit?

There are multiple physical systems that can be used to implement a qubit, such as photons, ions, and superconducting circuits. Each system has its own advantages and challenges, and the choice depends on the specific application and requirements.

## 4. How is information stored and manipulated in a qubit?

Information is stored in the state of a qubit, which can be manipulated using quantum gates such as the Hadamard gate, CNOT gate, and others. These gates can change the state of a qubit and perform operations on it, similar to how logic gates work in classical computing.

## 5. Can a qubit be in more than two states simultaneously?

Yes, a qubit can be in a superposition of multiple states simultaneously. This is one of the key properties of qubits that allows for more complex and powerful computations in quantum computing.