  Implementing a qubit quantum computer in continuous-variable systems
conventionally requires the engineering of specific interactions according to
the encoding basis states. In this work, we present a unified formalism to
conduct universal quantum computation with a fixed set of operations but
arbitrary encoding. By storing a qubit in the parity of two or four qumodes,
all computing processes can be implemented by basis state preparations,
continuous-variable exponential-swap operations, and swap-tests. Our formalism
inherits the advantages that the quantum information is decoupled from
collective noise, and logical qubits with different encodings can be brought to
interact without decoding. We also propose a possible implementation of the
required operations by using interactions that are available in a variety of
continuous-variable systems. Our work separates the `hardware' problem of
engineering quantum-computing-universal interactions, from the `software'
problem of designing encodings for specific purposes. The development of
quantum computer architecture could hence be simplified.
