construct an optimization algorithm by simulating the adiabatic evolution of Hamiltonian systems which can be used to approximate the MAX-CUT solution of an all-to-all connected graph. The approach is inspired by quantum adiabatic optimization for Ising systems [@Cit:Ising] with the following energy, $$\begin{aligned}
    E_{Ising}(s) = -\frac{1}{2}\displaystyle\sum_{i=1}^{N}\sum_{j=1}^{N}J_{ij}s_{i}s_{j},
    \label{eq:ising}\end{aligned}$$ where $s_i$ are the spins which can take values {-1,1} and $J_{ij}$ is the coupling coefficient. Finding the lowest energy state of the Ising system is computationally challenging (for a system with N spins, the potential number of states is $2^N$). Note that one can map the Ising problem to the MAX-CUT problem by setting $J_{ij}=-w_{ij}$, where $w_{ij}$ is the weight of the edge that connects nodes $i$ and $j$. It is easy to show that minimizing the energy in Eqn. \[eq:ising\] corresponds computing the solution of the MAX-CUT problem.

The approach outlined in [@Cit:quantum_net] relies on the adiabatic evolution of a network of nonlinear oscillators. This system exhibits a bifurcation (called “simulated bifurcation”) for each nonlinear oscillator. The two branches correspond to the $-1$ and $+1$ values for each spin. The authors exploit Graphical Processing Units (GPU) and Field Programmable Gate Array (FPGA) platforms to compute the solution of these Hamiltonian systems. 