We present techniques for performing two-qubit gates on Gottesman-Kitaev-Preskill (GKP) codes with finite energy, and find that operations designed for ideal infinite-energy codes create undesired entanglement when applied to physically realistic states. We demonstrate that this can be mitigated using recently developed local error-correction protocols, and evaluate the resulting performance. We also propose energy-conserving finite-energy gate implementations which largely avoid the need for further correction.

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• Quantum computation
• Quantum error correction
• Quantum information processing
• Quantum information theory