Modular Bosonic Subsystem Codes

Area of Science:

• Quantum Information Science
• Continuous-Variable Quantum Computing
• Quantum Optics

Background:

• Quantum information science typically utilizes discrete quantum systems like qubits.
• Continuous-variable (CV) systems offer vast state spaces but are challenging to manipulate with qubit-based tools.
• Existing frameworks struggle to bridge the gap between discrete qubit and continuous-variable quantum information.

Purpose of the Study:

• To introduce a novel framework for decomposing bosonic modes into logical qubits and gauge modes.
• To enable the application of the established qubit toolkit within continuous-variable quantum information processing.
• To analyze the impact of this decomposition on specific quantum states and identify hidden structures.

Main Methods:

• Development of a theoretical framework for mode decomposition.
• Modular decomposition of the position basis.
• Application to Gottesman-Kitaev-Preskill (GKP) grid states.
• Identification and disentanglement of qubit cluster states within Gaussian CV cluster states.

Main Results:

• A method to represent a bosonic mode as a logical qubit and a gauge mode is established.
• Decomposition of GKP states shows potential for logical state damage via entanglement with the gauge mode.
• Qubit cluster states were identified and successfully disentangled from Gaussian CV cluster states.

Conclusions:

• The proposed framework successfully maps bosonic modes to qubit and gauge subsystems.
• Entanglement with the gauge mode presents a challenge for preserving logical qubit information in CV systems.
• This work provides new avenues for utilizing CV systems in quantum computation and information tasks.