Qutrit

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A qutrit (or quantum trit) is a unit of quantum information that is realized by a 3-level quantum system, that may be in a superposition of three mutually orthogonal quantum states. [1]

Contents

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

There is ongoing work to develop quantum computers using qutrits and qubits with multiple states. [2]

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 , [3] which can be realized by a three-level quantum system. However, not all three-level quantum systems are qutrits. [4]

An n-qutrit register can represents 3n different states simultaneously, i.e., a superposition state vector in 3n-dimensional complex Hilbert space. [5]

The quantum logic gates operating on single qutrits are unitary matrices and gates that act on registers of qutrits are unitary matrices (the elements of the unitary groups U(3) and U(3n) respectively). [6]

Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust to decoherence under certain environmental interactions. [7] In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement with a qubit. [8]

See also

Related Research Articles

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References

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  2. "Qudits: The Real Future of Quantum Computing?". IEEE Spectrum . Retrieved 2021-05-24.
  3. Byrd, Mark (1998). "Differential geometry on SU(3) with applications to three state systems". Journal of Mathematical Physics. 39 (11): 6125–6136. arXiv: math-ph/9807032 . doi:10.1063/1.532618. ISSN   0022-2488.
  4. "Quantum systems: three-level vs qutrit". Physics Stack Exchange. Retrieved 2018-07-25.
  5. Caves, Carlton M.; Milburn, Gerard J. (2000). "Qutrit entanglement". Optics Communications. 179 (1–6): 439–446. arXiv: quant-ph/9910001 . doi:10.1016/s0030-4018(99)00693-8. ISSN   0030-4018.
  6. Colin P. Williams (2011). Explorations in Quantum Computing. Springer. pp. 22–23. ISBN   978-1-84628-887-6.
  7. Melikidze, A.; Dobrovitski, V. V.; De Raedt, H. A.; Katsnelson, M. I.; Harmon, B. N. (2004). "Parity effects in spin decoherence". Physical Review B. 70 (1): 014435. arXiv: quant-ph/0212097 . Bibcode:2004PhRvB..70a4435M. doi:10.1103/PhysRevB.70.014435.
  8. 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)