# Qubit

A **qubit**, or quantum bit, is the basic unit of quantum information: a two-level quantum system whose state can exist in a superposition of the two basis states, used to encode data in quantum computing just as the bit encodes data in classical computing.<sup>[1](https://www.ibm.com/think/topics/qubit)</sup> The term is attributed to the American theoretical physicist Benjamin Schumacher.<sup>[1](https://www.ibm.com/think/topics/qubit)</sup> Qubits are generally, although not exclusively, created by manipulating and measuring quantum particles such as photons, electrons, trapped ions, superconducting circuits, and atoms.<sup>[1](https://www.ibm.com/think/topics/qubit)</sup>

| Key fact | Detail |
|---|---|
| Definition | A controllable two-level quantum system, the quantum analog of the classical bit<sup>[1](https://www.ibm.com/think/topics/qubit)</sup><sup> • </sup><sup>[2](https://quantum.cloud.ibm.com/docs/en/api/qiskit/dev/circuit)</sup> |
| State | Any superposition \( |\psi\rangle = \alpha|0\rangle + \beta|1\rangle \) with complex amplitudes satisfying \( |\alpha|^{2} + |\beta|^{2} = 1 \)<sup>[3](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)</sup> |
| Measurement | The Born rule: each classical outcome appears with probability equal to the absolute value squared of the corresponding state-vector entry<sup>[4](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/single-systems/quantum-information)</sup> |
| Geometry | A single isolated qubit state maps to a point on the Bloch sphere, a representation that works only for two-level systems<sup>[5](https://quantum.cloud.ibm.com/learning/en/courses/general-formulation-of-quantum-information/density-matrices/bloch-sphere)</sup> |
| No-cloning | An unknown quantum state cannot be perfectly copied, although standard basis states can be cloned with a controlled-NOT gate<sup>[6](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/quantum-circuits/limitations-on-quantum-information)</sup> |
| Entanglement | A property of multi-qubit systems, not of single qubits; entangled qubits cannot be described independently<sup>[7](https://learn.microsoft.com/en-us/azure/quantum/concepts-entanglement)</sup> |
| Noise | Real qubits interact with their environment, causing decoherence; general state changes are described by completely positive trace-preserving (CPTP) maps called quantum channels<sup>[8](https://quantum.cloud.ibm.com/learning/en/courses/tools-for-quantum-advantage/noise-and-errors)</sup> |

## Qubits versus bits

A classical bit holds one of two values, 0 or 1, typically represented by an electrical state in modern hardware. A qubit must obey the laws of quantum physics and be able to exist in a quantum superposition, a combination of the states \( |0\rangle \) and \( |1\rangle \).<sup>[1](https://www.ibm.com/think/topics/qubit)</sup> Formally, the state is written

\[ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle \]

where \( \alpha \) and \( \beta \) are complex numbers with \( |\alpha|^{2} + |\beta|^{2} = 1 \), and the basis states are the vectors \( (1, 0) \) and \( (0, 1) \) in a two-dimensional complex vector space.<sup>[3](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)</sup>

**Measurement is probabilistic.** When a qubit is measured, the observer does not see the state vector but a classical outcome: each classical state appears with probability equal to the absolute value squared of its entry in the state vector, the [Born rule](https://www.edgepedia.org/born-rule).<sup>[4](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/single-systems/quantum-information)</sup> Measuring the equal superposition \( |+\rangle = \tfrac{1}{\sqrt{2}}(|0\rangle + |1\rangle) \) yields 0 or 1, each with probability \( \tfrac{1}{2} \).<sup>[4](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/single-systems/quantum-information)</sup> After measurement the qubit collapses to the observed outcome and any previous superposition is lost.<sup>[9](https://quantum.cloud.ibm.com/learning/en/courses/use-a-qc-today/quantum-mechanics-basics)</sup>

A main difference between a superposition and a classical probability distribution is phase coherence, which allows the components of a superposition to interfere constructively or destructively.<sup>[10](https://quantum.cloud.ibm.com/learning/en/modules/quantum-mechanics/superposition-with-qiskit)</sup> Nothing is random about the superposition state itself: quantum gates rotate the state deterministically and reversibly, and randomness enters only at measurement.<sup>[10](https://quantum.cloud.ibm.com/learning/en/modules/quantum-mechanics/superposition-with-qiskit)</sup>

## The Bloch sphere

The state of a single isolated qubit can be visualized as a point on the [Bloch sphere](https://www.edgepedia.org/bloch-sphere), a sphere of radius 1. Up to a global phase, every state can be written

\[ |\psi\rangle = \cos\!\left(\tfrac{\theta}{2}\right)|0\rangle + e^{i\phi}\sin\!\left(\tfrac{\theta}{2}\right)|1\rangle \]

with polar angle \( \theta \in [0, \pi] \) set by the relative amplitudes and azimuthal angle \( \phi \in [0, 2\pi) \) set by the relative phase.<sup>[5](https://quantum.cloud.ibm.com/learning/en/courses/general-formulation-of-quantum-information/density-matrices/bloch-sphere)</sup><sup> • </sup><sup>[10](https://quantum.cloud.ibm.com/learning/en/modules/quantum-mechanics/superposition-with-qiskit)</sup> All single-qubit gates can be viewed as rotations of this vector; the X gate is a \( \pi \) rotation around the x axis (a bit flip taking \( |0\rangle \) to \( |1\rangle \)), and the [Hadamard gate](https://www.edgepedia.org/hadamard-gate) maps \( |0\rangle \) to the equal superposition \( |+\rangle \).<sup>[10](https://quantum.cloud.ibm.com/learning/en/modules/quantum-mechanics/superposition-with-qiskit)</sup><sup> • </sup><sup>[3](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)</sup> The Bloch sphere representation works only for qubits; once a system has three or more classical states the analogous picture no longer corresponds to a sphere.<sup>[5](https://quantum.cloud.ibm.com/learning/en/courses/general-formulation-of-quantum-information/density-matrices/bloch-sphere)</sup>

## Gates and circuits

Quantum computation is described with the circuit model: qubits are manipulated by gates, drawn as symbols in a circuit diagram with inputs on the left and outputs on the right, the name "gate" being mostly historical.<sup>[3](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)</sup> [Single-qubit gates](https://www.edgepedia.org/single-qubit-gates) are unitary, represented by matrices \( U \) satisfying \( U^{\dagger}U = UU^{\dagger} = I \), so the output state is \( |\psi'\rangle = U|\psi\rangle \).<sup>[3](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)</sup> The Pauli gates are

\[ X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \quad Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}, \quad Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \]

with X acting as the quantum NOT, or bit flip.<sup>[3](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)</sup> Two-qubit gates such as the controlled-NOT can entangle qubits, and circuit depth, the number of gate layers, is an important factor for obtaining useful results on noisy quantum hardware.<sup>[3](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)</sup>

## Entanglement and multiple qubits

**Entanglement links qubits irreducibly.** Two qubits A and B in the state \( \tfrac{1}{\sqrt{2}}(|0_A 0_B\rangle + |1_A 1_B\rangle) \) cannot be described independently; only the global system has a definite description.<sup>[7](https://learn.microsoft.com/en-us/azure/quantum/concepts-entanglement)</sup> Measuring both qubits in the computational basis yields only \( |00\rangle \) or \( |11\rangle \), each with probability \( \tfrac{1}{2} \), and either outcome determines the other's; this perfect correlation alone is classically reproducible, but the entangled state can violate Bell inequalities under suitable measurement choices, and entanglement is a key resource for quantum teleportation, quantum cryptography, and quantum computing.<sup>[7](https://learn.microsoft.com/en-us/azure/quantum/concepts-entanglement)</sup><sup> • </sup><sup>[17](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup> Entanglement is a property of multi-qubit systems; a single qubit cannot be entangled.<sup>[7](https://learn.microsoft.com/en-us/azure/quantum/concepts-entanglement)</sup> The four maximally entangled two-qubit states are the Bell states \( |\phi^{+}\rangle \), \( |\phi^{-}\rangle \), \( |\psi^{+}\rangle \), and \( |\psi^{-}\rangle \).<sup>[7](https://learn.microsoft.com/en-us/azure/quantum/concepts-entanglement)</sup>

When one qubit of an entangled pair is ignored, its state must be described by a density matrix rather than a state vector. For any of the four Bell states, the reduced state of each qubit alone is the completely mixed state \( \tfrac{1}{2}I \), the only description consistent with the impossibility of faster-than-light communication.<sup>[11](https://quantum.cloud.ibm.com/learning/en/courses/general-formulation-of-quantum-information/density-matrices/multiple-systems)</sup> Density matrices in general represent a broader class of states than state vectors, including noisy states and probabilistic mixtures, and they describe classical information as a special case within the same mathematical framework.<sup>[12](https://quantum.cloud.ibm.com/learning/en/courses/general-formulation-of-quantum-information/density-matrices/introduction)</sup>

## Fundamental limitations

The no-cloning theorem states that it is impossible to create a perfect copy of an unknown quantum state: no fixed state \( |\phi\rangle \) and unitary operation \( U \) can satisfy \( U(|\psi\rangle \otimes |\phi\rangle) = |\psi\rangle \otimes |\psi\rangle \) for every \( |\psi\rangle \).<sup>[6](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/quantum-circuits/limitations-on-quantum-information)</sup> The theorem concerns arbitrary unknown states; a standard basis state \( |0\rangle \) or \( |1\rangle \) can be cloned with a controlled-NOT gate, though the same operation fails for \( |+\rangle \).<sup>[6](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/quantum-circuits/limitations-on-quantum-information)</sup> The theorem also does not address approximate cloning, for which limited-accuracy methods exist.<sup>[6](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/quantum-circuits/limitations-on-quantum-information)</sup> A related result is that quantum information cannot be transmitted using classical communication alone.<sup>[13](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/entanglement-in-action/quantum-teleportation)</sup>

These limits shape how qubits are used. [Quantum teleportation](https://www.edgepedia.org/quantum-teleportation) transmits a qubit from a sender to a receiver using a shared entangled state, one e-bit, together with two bits of classical communication; what is teleported is the quantum information, not matter.<sup>[13](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/entanglement-in-action/quantum-teleportation)</sup> Because unknown qubits cannot be copied, quantum error correction cannot rely on duplicating data; instead, information from one logical qubit is encoded redundantly across the basis states of several physical qubits.<sup>[14](https://www.nist.gov/system/files/documents/2017/05/09/dkthesis.pdf)</sup>

## Noise and decoherence

Unitary, reversible evolution describes ideal qubits, but real qubits interact with their environment, and any such interaction can collapse the qubit state just as a measurement does, causing decoherence; qubits in a quantum computer must therefore be highly insulated from the environment while remaining controllable.<sup>[15](https://www.nist.gov/system/files/documents/2017/05/09/hume2010thesis.pdf)</sup> The most general physically allowed transformation of a qubit state is a [quantum channel](https://www.edgepedia.org/quantum-channel), a linear map on density matrices that is completely positive and trace-preserving (CPTP): it must not produce negative probabilities even when the system is entangled with something else, and probabilities must sum to 1.<sup>[8](https://quantum.cloud.ibm.com/learning/en/courses/tools-for-quantum-advantage/noise-and-errors)</sup> Quantum channels include unitary evolution, measurements, decoherence, amplitude damping (energy loss), and dephasing (loss of phase information), and can be written in Kraus form \( \Phi(\rho) = \sum_{k} A_k \rho A_k^{\dagger} \) with \( \sum_{k} A_k^{\dagger} A_k = I \).<sup>[8](https://quantum.cloud.ibm.com/learning/en/courses/tools-for-quantum-advantage/noise-and-errors)</sup> For example, a single-qubit [depolarizing channel](https://www.edgepedia.org/depolarizing-channel) \( \mathcal{E}(\rho) = (1-p)\rho + \tfrac{p}{3}(X\rho X + Y\rho Y + Z\rho Z) \) with strength \( p = 0.15 \) maps a state to \( 0.8\,\rho + 0.1\,I \).<sup>[16](https://quantum.cloud.ibm.com/learning/en/courses/tools-for-quantum-advantage/error-mitigation)</sup>

## Physical realizations

Any physical system with two distinguishable quantum states can in principle serve as a qubit, and candidate systems include photons, electrons, trapped ions, superconducting circuits, and atoms.<sup>[1](https://www.ibm.com/think/topics/qubit)</sup> In hardware descriptions a qubit is a controllable two-level quantum system, such as a transmon or the electronic state of a trapped ion.<sup>[2](https://quantum.cloud.ibm.com/docs/en/api/qiskit/dev/circuit)</sup> Experimental platforms must meet requirements for qubit initialization, measurement, coherence, and interaction, requirements formulated in the DiVincenzo criteria.<sup>[15](https://www.nist.gov/system/files/documents/2017/05/09/hume2010thesis.pdf)</sup> Because physical qubits are subject to decoherence, error-correction schemes encode one logical qubit into the joint state of many physical qubits.<sup>[14](https://www.nist.gov/system/files/documents/2017/05/09/dkthesis.pdf)</sup>

## References

1. [What is a qubit? IBM](https://www.ibm.com/think/topics/qubit)
2. [Qiskit circuit documentation, IBM Quantum](https://quantum.cloud.ibm.com/docs/en/api/qiskit/dev/circuit)
3. [Bits, gates, and circuits, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)
4. [Quantum information, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/single-systems/quantum-information)
5. [Bloch sphere, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/general-formulation-of-quantum-information/density-matrices/bloch-sphere)
6. [Limitations on quantum information, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/quantum-circuits/limitations-on-quantum-information)
7. [Entanglement and correlations, Azure Quantum, Microsoft Learn](https://learn.microsoft.com/en-us/azure/quantum/concepts-entanglement)
8. [Noise and errors, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/tools-for-quantum-advantage/noise-and-errors)
9. [Quantum mechanics basics, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/use-a-qc-today/quantum-mechanics-basics)
10. [Superposition with Qiskit, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/modules/quantum-mechanics/superposition-with-qiskit)
11. [Multiple systems and reduced states, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/general-formulation-of-quantum-information/density-matrices/multiple-systems)
12. [Density matrices: introduction, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/general-formulation-of-quantum-information/density-matrices/introduction)
13. [Quantum teleportation, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/entanglement-in-action/quantum-teleportation)
14. [A decoherence-free quantum memory (thesis), NIST](https://www.nist.gov/system/files/documents/2017/05/09/dkthesis.pdf)
15. [Thesis on trapped-ion qubit requirements, NIST](https://www.nist.gov/system/files/documents/2017/05/09/hume2010thesis.pdf)
16. [Error mitigation, IBM Quantum Learning](https://quantum.cloud.ibm.com/learning/en/courses/tools-for-quantum-advantage/error-mitigation)
17. [Nobel Prize in Physics 2022](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Quantum physics › Quantum information science › Quantum communication and information theory › Quantum information theory › Quantum channels and capacity › Quantum channels: overview and formalism*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*

License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license