Quantum error-correcting code for ternary logic

Abstract

Ternary quantum systems are being studied because these 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 $(2\times 2)$-dimensional as well as $(3\times 3)$-dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible $(2\times 2)$-dimensional as well as $(3\times 3)$-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 new type of error called 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.

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Cited by in corpus (10)

• High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
• Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
• Qudit Dynamical Decoupling on a Superconducting Quantum Processor
• Exploring Ququart Computation on a Transmon using Optimal Control
• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
• Realization of a fast triple-magic all-optical qutrit in strontium-88
• Randomised benchmarking for universal qudit gates
• Optimal Error Correcting Code For Ternary Quantum Systems
• Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
• Exploiting degeneracy to construct good ternary quantum error correcting code