Qutrit
Units of information |
Information-theoretic |
---|
Data storage |
Quantum information |
A qutrit (or quantum trit) is a unit of
The qutrit is analogous to the classical
There is ongoing work to develop quantum computers using qutrits
Representation
A qutrit has three orthonormal basis states or vectors, often denoted , , and in Dirac or bra–ket notation. These are used to describe the qutrit as a superposition state vector in the form of a linear combination of the three orthonormal basis states:
- ,
where the coefficients are complex probability amplitudes, such that the sum of their squares is unity (normalization):
The qubit's orthonormal basis states span the two-dimensional complex Hilbert space , corresponding to spin-up and spin-down of a spin-1/2 particle. Qutrits require a Hilbert space of higher dimension, namely the three-dimensional spanned by the qutrit's basis ,[7] which can be realized by a three-level quantum system.
An n-qutrit register can represent 3n different states simultaneously, i.e., a superposition state vector in 3n-dimensional complex Hilbert space.[8]
Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust to
Qutrit quantum gates
The
The rotation operator gates
The global phase shift gate for the qutrit[c] is where the phase factor is called the global phase.
This phase gate performs the mapping and together with the 8 rotation operators is capable of expressing any single-qutrit gate in U(3), as a series circuit of at most 9 gates.
See also
- Gell-Mann matrices
- Generalizations of Pauli matrices
- Mutually unbiased bases
- Quantum computing
- Radix economy
- Ternary computing
Notes
- ^ This can be compared with the three rotation operator gates for qubits. We get eight linearly independent rotation operators by selecting appropriate . For example, we get the 1st rotation operator for SU(3) by setting and all others to zero.
- ^ Note: Quarks and gluons have color charge interactions in SU(3), not U(3), meaning there are no pure phase shift rotations allowed for gluons. If such rotations were allowed, it would mean that there would be a 9th gluon.[14]
- ^ Comparable with the global phase shift gate for qubits.
The global phase shift gate can also be understood as the 0th rotation operator, by taking the 0th Gell-Mann matrix to be the identity matrix, and summing from 0 instead of 1: and The unitary group U(3) is a 9-dimensional real Lie group.
References
- S2CID 110606655.
- S2CID 128064435.
- S2CID 221246177.
- PMID 36470858.
- ^ "Qudits: The Real Future of Quantum Computing?". IEEE Spectrum. 28 June 2017. Retrieved 2021-05-24.
- S2CID 254408561.
- S2CID 17645992.
- S2CID 27185877.
- S2CID 56567962.
- ^ B. P. Lanyon,1 T. J. Weinhold, N. K. Langford, J. L. O'Brien, K. J. Resch, A. Gilchrist, and A. G. White, Manipulating Biphotonic Qutrits, Phys. Rev. Lett. 100, 060504 (2008) (link)
- ISBN 978-1-84628-887-6.
- ISBN 978-3-527-40601-2.
- arXiv:hep-ph/0505265.
- ^ Ethan Siegel (Nov 18, 2020). "Why Are There Only 8 Gluons?". Forbes.
External links
- Zyga, Lisa (Feb 26, 2008). "Physicists Demonstrate Qubit-Qutrit Entanglement". Physorg.com. Archived from the originalon Feb 29, 2008. Retrieved Mar 3, 2008.