We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted maximum cut or the Ising Hamiltonian. Measuring the expectation of this operator on a variational quantum state yields the variational energy of the quantum system. The system is enforced to evolve towards the ground state of the problem Hamiltonian by optimizing a set of angles using normalized gradient descent. Experimentally, our algorithm outperforms the state-of-the-art quantum approximate optimization algorithm on random fully connected graphs and challenges D-Wave quantum annealers by producing better approximate solutions. Source code and data files are publicly available.

翻译：我们提出一种混合量子-经典算法，用于计算二元组合问题的近似解。我们采用浅层量子电路实现一个幺正且厄米的算子，该算子对加权最大割或伊辛哈密顿量进行块编码。在变分量子态上测量该算子的期望值，即可得到量子系统的变分能量。通过使用归一化梯度下降优化一组角度，迫使系统向问题哈密顿量的基态演化。实验结果表明，在随机全连接图上，我们的算法性能优于当前最先进的量子近似优化算法，并通过生成更优的近似解挑战了D-Wave量子退火器。源代码和数据文件已公开发布。