Encoding a qubit in a trapped-ion mechanical oscillator.

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Sensing

Background:

• Stable quantum computer operation requires robust quantum error correction.
• Quantum error correction often relies on multiple physical qubits or higher-dimensional systems like harmonic oscillators.
• Previous proposals for encoding qubits in harmonic oscillators have been experimentally challenging.

Purpose of the Study:

• To experimentally demonstrate a powerful quantum error encoding scheme in a harmonic oscillator.
• To realize and control encoded qubits using a single trapped ion system.
• To explore applications in quantum error correction and quantum sensing.

Main Methods:

• Utilized a single trapped ⁴⁰Ca⁺ ion as a harmonic oscillator.
• Employed a superposition of displaced squeezed states for qubit encoding.
• Controlled and measured the mechanical oscillator via coupling to an ancillary internal-state qubit.

Main Results:

• Successfully prepared and reconstructed logical states with an average squared fidelity of 87.3 ± 0.7%.
• Demonstrated a universal logical single-qubit gate set with high process fidelities (approx. 97% for Pauli gates, 89% for continuous rotations).
• Achieved high fidelities for both discrete and continuous variable operations.

Conclusions:

• The demonstrated control method provides a viable route for continuous variable quantum error correction.
• This technique enables hybrid quantum information schemes combining discrete and continuous variables.
• The encoded states have direct applications in quantum sensing for simultaneous position and momentum measurements.