Quantum error-correcting code for ternary logic
Physical Review A
Ternary quantum systems are being studied because they provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2×2)-dimensional and (3×3)-dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2×2)-dimensional as well as (3×3)-dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a special type of error called a quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine-qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization.
Majumdar, Ritajit; Basu, Saikat; Ghosh, Shibashis; and Sur-Kolay, Susmita, "Quantum error-correcting code for ternary logic" (2018). Journal Articles. 1391.