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 good 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，用于计算二进制组合问题的近似解。采用浅层量子电路实现一个块编码加权最大割或伊辛哈密顿量的幺正厄米算符。在该算符的变分量子态上测量期望值，可得到量子系统的变分能量。通过归一化梯度下降优化一组角度参数，系统被强制向问题哈密顿量的基态演化。实验结果表明，该算法在随机完全连接图上优于当前最先进的量子近似优化算法，并通过生成良好的近似解挑战D-Wave量子退火器。源代码与数据文件均已公开。