Revision as of 14:01, 17 May 2026

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A qubit (quantum bit) is the fundamental unit of quantum information. It is realized by a two-level quantum system and forms the quantum analogue of the classical bit.^[1]

Definition

A qubit is described by a state vector in a two-dimensional complex Hilbert space with orthonormal basis states $| 0 ⟩$ and $| 1 ⟩$ .^[2]^[3]

A general qubit state is

$| ψ ⟩ = α | 0 ⟩ + β | 1 ⟩,$

where $α, β \in ℂ$ satisfy the normalization condition

$| α |^{2} + | β |^{2} = 1.$

The coefficients $α$ and $β$ are probability amplitudes.^[4]

Comparison with a classical bit

A classical bit can take only one of two values, 0 or 1. A qubit, however, can exist in a coherent superposition of both basis states.^[1]

Upon measurement:

$| 0 ⟩$ is obtained with probability $| α |^{2}$
$| 1 ⟩$ is obtained with probability $| β |^{2}$

Unlike a classical bit, measurement generally disturbs the qubit state and destroys quantum coherence.^[1]

Bloch sphere representation

Any pure qubit state can be written as

$| ψ ⟩ = \cos \frac{θ}{2} | 0 ⟩ + e^{i ϕ} \sin \frac{θ}{2} | 1 ⟩ .$

This allows a geometric representation on the Bloch sphere, where $θ$ and $ϕ$ specify the state.^[1]

Pure states lie on the surface of the Bloch sphere, while the global phase has no observable physical effect.^[1]

Mixed states

A qubit may also be in a mixed state, described by a density matrix

$ρ = \sum_{i} p_{i} | ψ_{i} ⟩ ⟨ ψ_{i} | .$

Mixed states arise from statistical uncertainty or from interaction with an environment, and correspond to points inside the Bloch sphere.^[1]

Quantum operations

Quantum states evolve according to unitary transformations:

$| ψ ⟩ \to U | ψ ⟩,$

where $U$ is a unitary operator.^[1]

In quantum computing, these transformations are implemented as quantum gates. Examples include:

Pauli gates ( $X, Y, Z$ )
Hadamard gate
Controlled-NOT (CNOT) gate

These operations enable interference, superposition control, and the creation of entanglement.

Physical realizations

Qubits can be implemented in various physical systems, including:

electron spin
photon polarization
trapped ions
superconducting circuits
quantum dots

Different implementations are used depending on the application in quantum computing, communication, or sensing.^[1]^[5]

Quantum registers

A collection of qubits forms a quantum register. For $n$ qubits, the state space has dimension $2^{n}$ , allowing complex superpositions and correlations.^[2]

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 A '''qubit''' (quantum bit) is the fundamental unit of quantum information. It is realized by a two-level quantum system and forms the quantum analogue of the classical bit.<ref name="NielsenChuang2010">{{cite book |last1=Nielsen |first1=Michael A. |last2=Chuang |first2=Isaac L. |title=Quantum Computation and Quantum Information |publisher=Cambridge University Press |year=2010 |isbn=978-1-107-00217-3}}</ref>
-[[File:Bloch_sphere.png|thumb|400px|Representation of a qubit state on the Bloch sphere.]]
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+[[File:Bloch_sphere.png|thumb|280px|Quantum Qubit.]]
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 == Definition ==

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Physics:Quantum Qubit: Difference between revisions

Revision as of 14:01, 17 May 2026

Definition

Comparison with a classical bit

Bloch sphere representation

Mixed states

Quantum operations

Physical realizations

Quantum registers

Physical significance

See also

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