Native measurement-based quantum approximate optimization algorithm applied to the Max K -Cut problem

Abstract

Photonic quantum computers, programed within the framework of the measurement-based quantum computing (MBQC), and gate-based platforms are racing toward useful quantum advantage, and some algorithms have emerged as main candidates to reach this goal in the near term. The majority of these algorithms are only expressed in the gate-based model of computation, which is incompatible with photonic platforms. Methods to translate gate-based algorithms into the MBQC framework exist, but they are not always optimal in terms of resource cost. In our work, we propose an MBQC algorithm to run the quantum approximate optimization algorithm (QAOA). Furthermore, we apply the MBQC-QAOA algorithm to the Max $K$-Cut problem, for all values of $K$, expressing the cost Hamiltonian and its constraints in a form easily implementable in the MBQC model. We conclude by analyzing the resource cost of our algorithm, compared to the case of translating a gate-based QAOA algorithm into MBQC rules, and show up to a 30-fold improvement. With our work, we contribute to closing the gap between gate-based and MBQC near-term algorithms, a gap not reflecting the current status of the hardware development.