In this work we investigate the performance of greedy randomised search (GRS) techniques to the problem of compiling quantum circuits that solve instances of the Graph Coloring problem. Quantum computing uses quantum gates that manipulate multi-valued bits (qubits). A quantum circuit is composed of a number of qubits and a series of quantum gates that operate on those qubits, and whose execution realises a specific quantum algorithm. Current quantum computing technologies limit the qubit interaction distance allowing the execution of gates between adjacent qubits only. This has opened the way to the exploration of possible techniques aimed at guaranteeing nearest-neighbor (NN) compliance in any quantum circuit through the addition of a number of so-called swap gates between adjacent qubits. In addition, technological limitations (decoherence effect) impose that the overall duration (i.e., depth) of the quantum circuit realization be minimized. One core contribution of the paper is the application of an upgraded version of the greedy randomized search (GRS) technique originally introduced in the literature that synthesises NN-compliant quantum circuits realizations, starting from a set of benchmark instances of different size belonging to the Quantum Approximate Optimization Algorithm (QAOA) class tailored for the Graph Coloring problem. We propose a comparison between the presented method and the SABRE compiler, one of the best-performing compilation procedures present in Qiskit, an open-source SDK for quantum development, both from the CPU efficiency and from the solution quality standpoint.
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