  Modern quantum technologies using matter are designed as closed quantum
systems to isolate them from interactions with the environment. This design
paradigm greatly constrains the scalability and limits practical implementation
of such systems. Here, we introduce a novel computing paradigm, entropy
computing, that works by conditioning a quantum reservoir thereby enabling the
stabilization of a ground state. In this work, we experimentally demonstrate
the feasibility of entropy computing by building a hybrid photonic-electronic
computer that uses measurement-based feedback to solve non-convex optimization
problems. The system functions by using temporal photonic modes to create
qudits in order to encode probability amplitudes in the time-frequency degree
of freedom of a photon. This scheme, when coupled with electronic
interconnects, allows us to encode an arbitrary Hamiltonian into the system and
solve non-convex continuous variables and combinatorial optimization problems.
We show that the proposed entropy computing paradigm can act as a scalable and
versatile platform for tackling a large range of NP-hard optimization problems.
