Aqutrit (orquantum trit) is a unit ofquantum information that is realized by a 3-level quantum system, that may be in asuperposition of three mutually orthogonalquantum states.^[1]

The qutrit is analogous to the classicalradix-3trit, just as thequbit, a quantum system described by a superposition of two orthogonal states, is analogous to the classical radix-2bit.

There is ongoing work to develop quantum computers using qutrits^[2][3][4] andqudits in general.^[5][6][7]

A qutrit has three orthonormalbasis states orvectors, often denoted${\displaystyle |0⟩}$,${\displaystyle |1⟩}$, and${\displaystyle |2⟩}$ in Dirac orbra–ket notation.These are used to describe the qutrit as asuperposition state vector in the form of a linear combination of the three orthonormal basis states:

${\displaystyle |\psi ⟩=\alpha |0⟩+\beta |1⟩+\gamma |2⟩}$,

where the coefficients are complexprobability amplitudes, such that the sum of their squares is unity (normalization):

${\displaystyle |\alpha {|}^2+|\beta {|}^2+|\gamma {|}^2=1}$

Thequbit's orthonormal basis states${\displaystyle \{|0⟩,|1⟩\}}$ span the two-dimensional complexHilbert space${\displaystyle H_2}$, corresponding to spin-up and spin-down of aspin-1/2 particle. Qutrits require a Hilbert space of higher dimension, namely the three-dimensional${\displaystyle H_3}$ spanned by the qutrit's basis${\displaystyle \{|0⟩,|1⟩,|2⟩\}}$,^[8] which can be realized by a three-level quantum system.

Ann-qutritregister can represent 3ⁿ different states simultaneously, i.e., a superposition state vector in 3ⁿ-dimensional complex Hilbert space.^[9]

Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust todecoherence under certain environmental interactions.^[10] In reality, manipulating qutrits directly might be tricky, and one way to do that is by using anentanglement with aqubit.^[11]

Thequantum logic gates operating on single qutrits are${\displaystyle 3\times 3}$unitary matrices and gates that act onregisters of${\displaystyle n}$ qutrits are${\displaystyle 3^n\times 3^n}$ unitary matrices (the elements of theunitary groups U(3) and U(3ⁿ) respectively).^[12]

The rotation operator gates^[a] forSU(3) are${\displaystyle \mathrm{Rot}({\mathrm{\Theta }}_1,{\mathrm{\Theta }}_2,\dots ,{\mathrm{\Theta }}_8)=\exp \left(-i\sum _{a=1}^8{\mathrm{\Theta }}_a\frac{{\lambda }_a}{2}\right)}$, where${\displaystyle {\lambda }_a}$ is thea'thGell-Mann matrix, and${\displaystyle {\mathrm{\Theta }}_a}$ is areal value. TheLie algebra of thematrix exponential is providedhere. The same rotation operators are used forgluon interactions, where the three basis states are thethree colors(${\displaystyle |0⟩=\text{red},|1⟩=\text{green},|2⟩=\text{blue}}$) of thestrong interaction.^[13][14][b]

The global phase shift gate for the qutrit^[c] is where thephase factor${\displaystyle e^{i\delta }}$ is called theglobal phase.

This phase gate performs the mapping${\displaystyle |\mathrm{\Psi }⟩\mapsto e^{i\delta }|\mathrm{\Psi }⟩}$ and together with the 8 rotation operators is capable of expressing any single-qutrit gate inU(3), as aseries circuit of at most 9 gates.

• Gell-Mann matrices
• Generalizations of Pauli matrices
• Mutually unbiased bases
• Quantum computing
• Radix economy
• Ternary computing

Look upqutrit in Wiktionary, the free dictionary.

• Zyga, Lisa (Feb 26, 2008)."Physicists Demonstrate Qubit-Qutrit Entanglement".Physorg.com. Archived fromthe original on Feb 29, 2008. RetrievedMar 3, 2008.

• Units of information
• Quantum information science
• Quantum computing
• Ternary computers

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• Short description is different from Wikidata