Vibrational modes of trapped ions have traditionally served as quantum buses to mediate entanglement between internal qubits. However, with recent advances in quantum control, it has become possible to use these modes directly as quantum computational resources. Here, we propose a dual-rail encoding scheme in which two vibrational modes sharing a single phonon encode a qubit and show that such dual-rail qubits can serve as additional system qubits in trapped-ion quantum computing. The interaction between internal qubits and vibrational modes enables universal quantum computation on dual-rail qubits, and incorporating them into a hybrid system with internal qubits nearly doubles the number of available system qubits while preserving all-to-all connectivity. Additionally, we propose a method for implementing multiqubit controlled gates and discuss potential applications that can leverage the advantages of the hybrid system. Our scheme provides a practical framework for an internal qubit-bosonic qubit hybrid system in trapped-ion systems.

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• Quantum algorithms & computation
• Quantum information architectures & platforms
• Quantum information processing with continuous variables
• Quantum information with hybrid systems
• Quantum information with trapped ions