Deterministic teleportation of a quantum gate between two logical qubits

A quantum computer has the potential to efficiently solve problems that are intractable for classical computers. However, constructing a large-scale quantum processor is challenging because of the errors and noise that are inherent in real-world quantum systems. One approach to addressing this challenge is to utilize modularity-a strategy used frequently in nature and engineering to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations have motivated the development of a quantum modular architecture, in which separate quantum systems are connected into a quantum network via communication channels(1,2). In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate(3-5), but such teleportation has hitherto not been realized as a deterministic operation. Here we experimentally demonstrate the teleportation of a controlled-NOT (CNOT) gate, which we make deterministic by using real-time adaptive control. In addition, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between two logical qubits, encoding quantum information redundantly in the states of superconducting cavities(6). By using such an error-correctable encoding, our teleported gate achieves a process fidelity of 79 per cent. Teleported gates have implications for fault-tolerant quantum computation(3), and when realized within a network can have broad applications in quantum communication, metrology and simulations(1,2,7). Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits and, if integrated with quantum error-correction protocols, indicate a promising path towards fault-tolerant quantum computation using a modular architecture.