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Wikipedia / Qutrit

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

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 qudits in general.

Representation

A qutrit has three orthonormal basis states or vectors 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:

  1. ,

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

The qubit span the two-dimensional complex Hilbert space, corresponding to spin-up and spin-down of a spin-1/2, 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.

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

Qutrit quantum gates

The quantum logic gates unitary matrices and gates that act on registers unitary matrices (the elements of the unitary groups U(3) and U(3n) respectively).

The rotation operator gates for SU(3) is the ath Gell-Mann matrix is a real value. The Lie algebra of the matrix exponential is provided here. The same rotation operators are used for gluon interactions, where the three basis states are the three colors of the strong interaction.

The global phase shift gate for the qutrit where the phase factor is called the global phase.

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.

Error corrected ternary quantum computing

Fault-tolerant implementation of a specific qutrit gate can be more or less challenging, depending on its place in the so-called Clifford hierarchy.

of ternary Pauli gates. Operators in the Pauli subgroup are in general the least expensive to implement. The multi-qutrit Pauli subgroup consists of arbitrary tensor products of single-qutrit Pauli operators.

A significantly larger group of Clifford gates consists of all the gates that stabilize the Pauli subgroup. As shown in , the following gates can be chosen as generators of the Clifford group

For any fixed set of qutrits the Clifford group is finite and therefore is not sufficient for universal quantum computation. Adding one single non-Clifford gate to a set of its generators, however, ensures quantum universality, but requires resource-consuming techniques such as magic state distillation.

numeric field).

See also

Notes

References