  Recently, several platforms were proposed and demonstrated a
proof-of-principle for finding the global minimum of the spin Hamiltonians such
as the Ising and XY models using gain-dissipative quantum and classical
systems. The implementation of dynamical adjustment of the gain and coupling
strengths has been established as a vital feedback mechanism for analog
Hamiltonian physical systems that aim to simulate spin Hamiltonians. Based on
the principle of operation of such simulators we develop a novel class of
gain-dissipative algorithms for global optimisation of NP-hard problems and
show its performance in comparison with the classical global optimisation
algorithms. These systems can be used to study the ground state and statistical
properties of spin systems and as a direct benchmark for the performance
testing of the gain-dissipative physical simulators. The estimates of the time
operation of the physical implementation of the gain-dissipative simulators for
large matrices show a possible speed-up of the several orders of magnitude in
comparison with classical computations.
