  We demonstrate that a quantum annealer can be used to solve the NP-complete
problem of graph partitioning into subgraphs containing Hamiltonian cycles of
constrained length. We present a method to find a partition of a given directed
graph into Hamiltonian subgraphs with three or more vertices, called vertex
3-cycle cover. We formulate the problem as a quadratic unconstrained binary
optimisation and run it on a D-Wave Advantage quantum annealer. We test our
method on synthetic graphs constructed by adding a number of random edges to a
set of disjoint cycles. We show that the probability of solution is independent
of the cycle length, and a solution is found for graphs up to 4000 vertices and
5200 edges, close to the number of physical working qubits available on the
quantum annealer.
