Solving quantum circuit compilation problem variants through genetic algorithms

The gate-based model is one of the leading quantum computing paradigms for representing quantum circuits. Within this paradigm, a quantum algorithm is expressed in terms of a set of quantum gates that are executed on the quantum hardware over time, subject to a number of constraints whose satisfaction must be guaranteed before running the circuit, to allow for feasible execution. The need to guarantee the previous feasibility condition gives rise to the Quantum Circuit Compilation Problem (QCCP). The QCCP has been demonstrated to be NP-Complete, and can be considered as a Planning and Scheduling problem. In this paper, we consider quantum compilation instances deriving from the general Quantum Approximation Optimization Algorithm (QAOA), applied to the MaxCut problem, devised to be executed on Noisy Intermediate Scale Quantum (NISQ) hardware architectures. More specifically, in addition to the basic QCCP version, we also tackle other variants of the same problem such as the QCCP-X (QCCP with crosstalk constraints), the QCCP-V (QCCP with variable qubit state initialization), as well as the QCCP-VX that includes both previous variants. All problem variants are solved using genetic algorithms. We perform an experimental study across a conventional set of instances taken from the literature, and show that the proposed genetic algorithm, termed GAvx, outperforms previous approaches in the literature.