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Qubit 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. 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. 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. Unlike a classical bit, measurement generally disturbs the qubit state and destroys quantum coherence. Any pure qubit state can be written as Pure states lie on the surface of the Bloch sphere, while the global phase has no observable physical effect.

Definition

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

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.^[3]

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.^[4]

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.^[4]

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.^[4]

Pure states lie on the surface of the Bloch sphere, while the global phase has no observable physical effect.^[4]

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.^[4]

Quantum operations

Quantum states evolve according to unitary transformations:

$| ψ ⟩ \to U | ψ ⟩,$

where $U$ is a unitary operator.^[4]

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.^[4]^[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.^[1]

Physical significance

The qubit:

is the basic carrier of quantum information
enables superposition and interference
forms the foundation of quantum computation and communication

Description

Qubit is a matter-scale concept used to organize how quantum theory describes atoms, particles, fields, condensed matter, plasma, or spacetime-related systems. In the Quantum Collection it is placed by scale so the reader can move from materials and molecules down to subatomic degrees of freedom.

Quantum context

At this scale, the relevant behavior is controlled by quantized states, interactions, conservation laws, and the way excitations or particles are observed. The concept is normally linked to measurable properties such as energy, momentum, charge, spin, spectra, scattering rates, or collective modes.

Role in the collection

This page provides a compact reference point for related pages in Book II. It should be read together with nearby matter-scale topics and the corresponding foundations in quantum mechanics.^[6]

Interpretation

For qubit, the quantum description is useful because it separates the allowed states, interactions, and measurable quantities from the classical picture. The same concept may appear differently in spectroscopy, scattering, condensed matter, field theory, or cosmology.

Related measurements

Typical measurements involve spectra, decay products, transition rates, transport behavior, correlation functions, or detector signatures. These observations provide the empirical link between the page topic and the wider Quantum Collection.

Additional context

A qubit is also the point where physical implementation and information theory meet. Real qubits must be initialized, controlled, measured, and protected from noise, so the abstract two-state model is normally paired with hardware-specific discussions of gates, coherence time, readout fidelity, and error correction.

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 == 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.<ref name="NielsenChuang2010" />
+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.<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>
 Upon measurement:

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Physics:Quantum Qubit: Difference between revisions

Latest revision as of 00:31, 24 May 2026

Definition

Comparison with a classical bit

Bloch sphere representation

Mixed states

Quantum operations

Physical realizations

Quantum registers

Physical significance

Description

Quantum context

Role in the collection

Interpretation

Related measurements

Additional context

See also

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