Qubit-efficient encoding schemes for binary optimisation problems

We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where problem consisting $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number qubits. The underlying encoding scheme allows systematic increase in correlations among the captured by state progressively increasing qubits involved. first examine simplest limit all are neglected, i.e. when only describe statistically independent variables. apply this minimal to find approximate solutions general instance comprised 64 using 7 Next, we show how two-body between incorporated it improve quality solutions. give an example 42-variable Max-Cut 8 exploit specific topology problem. whether these cases optimized efficiently given limited resources available state-of-the-art platforms. Lastly, present framework extending expressibility probability distribution any multi-body correlations.