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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]

Physical significance

The qubit:

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

Table of contents (136 articles)

Index

Core theory

Foundations
Conceptual and interpretations
Mathematical structure and systems
Atomic and spectroscopy
Wavefunctions and modes
Quantum dynamics and evolution
Measurement and information
Quantum information and computing

Matter (by scale)

Matter (by scale)

Applications and extensions

Quantum optics and experiments
Open quantum systems
Quantum field theory
Statistical mechanics and kinetic theory
Condensed matter and solid-state physics
Plasma and fusion physics
Timeline
Advanced and frontier topics

Methods and tools

Methods and tools

Full contents

1. Foundations (7)↑

2. Conceptual and interpretations (10)↑

3. Mathematical structure and systems (11)↑

4. Atomic and spectroscopy (11)↑

Physics:Quantum Atomic structure and spectroscopy
Physics:Quantum Hydrogen atom
Physics:Quantum Multi-electron atoms
Physics:Quantum Fine structure
Physics:Quantum Hyperfine structure
Physics:Quantum Isotopic shift
Physics:Quantum Zeeman effect
Physics:Quantum Stark effect
Physics:Quantum Spectral lines and series
Physics:Quantum Selection rules
Physics:Quantum Fermi's golden rule

5. Wavefunctions and modes (8)↑

Physics:Quantum Wavefunction
Physics:Quantum Superposition principle
Physics:Quantum Eigenstates and eigenvalues
Physics:Quantum Boundary conditions and quantization
Physics:Quantum Standing waves and modes
Physics:Quantum Normal modes and field quantization
Physics:Number of independent spatial modes in a spherical volume
Physics:Quantum Density of states

6. Quantum dynamics and evolution (9)↑

7. Measurement and information (6)↑

8. Quantum information and computing (6)↑

9. Quantum optics and experiments (4)↑

Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
Physics:Quantum optics beam splitter experiments
Physics:Quantum Ultra fast lasers
Physics:Quantum Experimental quantum physics

Template:Quantum optics operators

10. Open quantum systems (7)↑

11. Quantum field theory (18)↑

12. Statistical mechanics and kinetic theory (9)↑

13. Condensed matter and solid-state physics (7)↑

14. Plasma and fusion physics (8)↑

Physics:Quantum Fusion reactions and Lawson criterion
Physics:Quantum Plasma (fusion context)
Physics:Quantum Magnetic confinement fusion
Physics:Quantum Inertial confinement fusion
Physics:Quantum Plasma instabilities and turbulence
Physics:Quantum Tokamak core plasma
Physics:Quantum Tokamak edge physics and recycling asymmetries
Physics:Quantum Stellarator

15. Timeline (8)↑

16. Advanced and frontier topics (6)↑

References

↑ ^1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 ^1.6 ^1.7 Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information. Cambridge University Press. ISBN 978-1-107-00217-3.
↑ ^2.0 ^2.1 Yanofsky, Noson S.; Mannucci, Mirco A. (2013). Quantum Computing for Computer Scientists. Cambridge University Press. pp. 138–144. ISBN 978-0-521-87996-5.
↑ Seskir, Zeki C.; Migdał, Piotr; Weidner, Carrie; Anupam, Aditya; Case, Nicky; Davis, Noah; Decaroli, Chiara; Ercan, İlke et al. (2022). "Quantum games and interactive tools for quantum technologies outreach and education". Optical Engineering 61 (8). doi:10.1117/1.OE.61.8.081809. Bibcode: 2022OptEn..61h1809S. This article incorporates text from this source, which is available under the CC BY 4.0 license.
↑ Williams, Colin P. (2011). Explorations in Quantum Computing. Springer. pp. 9–13. ISBN 978-1-84628-887-6.
↑ Preskill, John (1998). Lecture Notes for Physics 229: Quantum Information and Computation.

Author: Harold Foppele

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[NielsenChuang2010-1] 1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 ^1.6 ^1.7 Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information. Cambridge University Press. ISBN 978-1-107-00217-3.

[YanofskyMannucci2013-2] 2.0 ^2.1 Yanofsky, Noson S.; Mannucci, Mirco A. (2013). Quantum Computing for Computer Scientists. Cambridge University Press. pp. 138–144. ISBN 978-0-521-87996-5.

[3] Seskir, Zeki C.; Migdał, Piotr; Weidner, Carrie; Anupam, Aditya; Case, Nicky; Davis, Noah; Decaroli, Chiara; Ercan, İlke et al. (2022). "Quantum games and interactive tools for quantum technologies outreach and education". Optical Engineering 61 (8). doi:10.1117/1.OE.61.8.081809. Bibcode: 2022OptEn..61h1809S. This article incorporates text from this source, which is available under the CC BY 4.0 license.

[Williams2011-4] Williams, Colin P. (2011). Explorations in Quantum Computing. Springer. pp. 9–13. ISBN 978-1-84628-887-6.

[5] Preskill, John (1998). Lecture Notes for Physics 229: Quantum Information and Computation.

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Definition

Comparison with a classical bit

Bloch sphere representation

Mixed states

Quantum operations

Physical realizations

Quantum registers

Physical significance

See also

Table of contents (136 articles)

Index

Full contents

References

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Physics:Quantum Qubit

Definition

Comparison with a classical bit

Bloch sphere representation

Mixed states

Quantum operations

Physical realizations

Quantum registers

Physical significance

See also

Table of contents (136 articles)

Index

Full contents

References

Navigation

Wiki tools

Page tools

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