Finding ground state solutions of diagonal Hamiltonians is relevant for both theoretical as well as practical problems of interest in many domains such as finance, physics and computer science. These problems are typically very hard to tackle by classical computing and quantum computing could help in speeding up computations and efficiently tackling larger problems. Here we use imaginary time evolution through a new block encoding scheme to obtain the ground state of such problems and apply our method to MaxCut as an illustration. Our method, which for simplicity we call ITE-BE, requires no variational parameter optimization as all the parameters in the procedure are expressed as analytical functions of the couplings of the Hamiltonian. We demonstrate that our method can be successfully combined with other quantum algorithms such as quantum approximate optimization algorithm (QAOA). We find that the QAOA ansatz increases the post-selection success of ITE-BE, and shallow QAOA circuits, when boosted with ITE-BE, achieve better performance than deeper QAOA circuits. For the special case of the transverse initial state, we adapt our block encoding scheme to allow for a deterministic application of the first layer of the circuit.

翻译：对角哈密顿量的基态求解在金融、物理和计算机科学等多个领域具有重要的理论与实际意义。这类问题通常难以通过经典计算有效处理，而量子计算有望加速计算过程并高效处理更大规模的问题。本文通过一种新型块编码方案实现虚时演化，以此类问题的基态求解为目标，并以最大割问题为例展示方法应用。为简化表述，我们将本方法称为ITE-BE，其无需进行变分参数优化，因为流程中的所有参数均可表示为哈密顿量耦合系数的解析函数。我们证明了该方法可与量子近似优化算法等其他量子算法有效结合。研究发现：QAOA拟设能提升ITE-BE的后选择成功率；而经ITE-BE增强的浅层QAOA电路，其性能优于更深层的QAOA电路。针对横向初始态的特殊情形，我们调整了块编码方案以实现电路第一层的确定性应用。