Physics:Quantum Qubit

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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]

Representation of a qubit state on the Bloch sphere.

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∈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⁡θ2|0⟩+eiϕsin⁡θ2|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=∑ipi|ψi⟩⟨ψi|.

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⟩→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 2n, 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

See also

Table of contents (185 articles)

Index

Full contents

9. Quantum optics and experiments (5) ↑ Back to index
14. Plasma and fusion physics (8) ↑ Back to index
Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.
Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.

References

  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. 
  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. Template:Creative Commons text attribution notice
  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. 
Author: Harold Foppele

Source attribution: Quantum qubit

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