  One of the limitations to the quantum computing capability of a
continuous-variable system is determined by our ability to cool it to the
ground state, because pure logical states, in which we accurately encode
quantum information, are conventionally pure physical states that are
constructed from the ground state. In this work, we present an alternative
quantum computing formalism that encodes logical quantum information in mixed
physical states. We introduce a class of mixed-state protocols that are based
on a parity encoding, and propose an implementation of the universal logic
gates by using realistic hybrid interactions. When comparing with the
conventional pure-state protocols, our formalism could relax the necessity of,
and hence the systemic requirements of cooling. Additionally, the mixed-state
protocols are inherently resilient to a wider class of noise processes, and
reduce the fundamental energy consumption in initialisation. Our work broadens
the candidates of continuous-variable quantum computers.
