In nature there is clear preference for coupling between pairs of entities. When there are more than two entities participating in an interaction, things tend to become problematic and “relationships” become frustrated. There are many social examples of polyamor relations and many historical books realted to triad relationships (e.g. the Divine Comedy of Dante). Similarly, in physics interactions appear in couples and many-body terms (where “many” stands more than two) introducing difficulties that need to be handled with care. These conflicts can be resolved with the introduction of chaperones that can help to disentangle the complicated many-body interactions. This is also happening in quantum computing. Mapping fermionic Hamiltonians into the qubit realization introduces undesired k-body interaction terms that can be disentangled using auxiliary qubits, called ancillas. The solution of this problem requires compromises or, more scientifically, approximations. In this work I provide a general overview of the already existing perturbative techniques for the reduction of k-local terms to 2-local terms. In addition, I evaluate new algorithms based on linear algebra and optimization techniques under the scope of natural and problematic relationships of humans and/or fermions.
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