Efficient analytic construction of quantum circuits for MaxCut problems

For performing various algorithms on current and near-future quantum computers, it is crucial to find systematically efficent ways to construct quantum circuits. It is mathematically known that an arbitrary unitary for a multiple-qubit system can be represented as a combination of at most two-qubit unitaries. For the quantum imaginary-time evolution method[1, 2] for MaxCut problems, we derive the conditions imposed on the gate parameters, from which they can be calculated analytically. We demonstrate that the expected energy exhibits numerically stable behavior both in noiseless and noiseful simulations.
[1] Motta et al., Nat. Phys. 16, 231 (2020)
[2] Nishi, Kosugi, and Matsushita, arXiv:2005.12715