  A quantum computer has the potential to effciently solve problems that are
intractable for classical computers. Constructing a large-scale quantum
processor, however, is challenging due to errors and noise inherent in
real-world quantum systems. One approach to this challenge is to utilize
modularity--a pervasive strategy found throughout 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 motivate the development of a quantum
modular architecture, where separate quantum systems are combined via
communication channels into a quantum network. In this architecture, an
essential tool for universal quantum computation is the teleportation of an
entangling quantum gate, a technique originally proposed in 1999 which, until
now, has not been realized deterministically. Here, we experimentally
demonstrate a teleported controlled-NOT (CNOT) operation made deterministic by
utilizing real-time adaptive control. Additionally, we take a crucial step
towards implementing robust, error-correctable modules by enacting the gate
between logical qubits, encoding quantum information redundantly in the states
of superconducting cavities. Such teleported operations have significant
implications for fault-tolerant quantum computation, and when realized within a
network can have broad applications in quantum communication, metrology, and
simulations. Our results illustrate a compelling approach for implementing
multi-qubit operations on logical qubits within an error-protected quantum
modular architecture.
