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== Comparison with a classical bit ==
== 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:
Upon measurement:

Latest revision as of 00:31, 24 May 2026

← Back to Quantum information and computing Book I
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Next : Entanglement →

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.

Quantum Qubit.

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∈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⁡θ2|0⟩+eiϕsin⁡θ2|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=∑ipi|ψi⟩⟨ψi|.

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⟩→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 2n, 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.

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.

See also

Table of contents (217 articles)

Index

Full contents

References

  1. ↑ 1.0 1.1 Yanofsky, Noson S.; Mannucci, Mirco A. (2013). Quantum Computing for Computer Scientists. Cambridge University Press. pp. 138–144. ISBN 978-0-521-87996-5. 
  2. ↑ 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. 
  3. ↑ Williams, Colin P. (2011). Explorations in Quantum Computing. Springer. pp. 9–13. ISBN 978-1-84628-887-6. 
  4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 4.6 Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information. Cambridge University Press. ISBN 978-1-107-00217-3. 
  5. ↑ Preskill, John (1998). Lecture Notes for Physics 229: Quantum Information and Computation. 
  6. ↑ "Quantum mechanics". https://en.wikipedia.org/wiki/Quantum_mechanics. 


Author: Harold Foppele


Source attribution: Physics:Quantum Qubit

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