标题： 线性简化的QAOA参数和可转移性 显示英文标题

标题： Linearly simplified QAOA parameters and transferability

摘要： 量子近似优化算法（QAOA）提供了一种使用量子计算机解决组合优化问题的方法。 QAOA电路由成本哈密顿量的时间演化算子和状态混合算子组成，每个算子嵌入的变分参数被调整，使得成本函数的期望值最小化。 变分参数的优化是在经典设备上进行的，而成本函数则是以量子的方式进行测量。 为了便于经典优化，之前有几项工作研究了最优/初始参数的决策策略以及实例之间的相似性提取。 在我们当前的工作中，我们考虑了简化QAOA参数，这些参数在电路深度上呈线性形式。 这种简化，从与量子退火的类比中提出，使得参数空间从2p维大幅减少到4维，无论QAOA层的数量p是多少。此外，在缩减的参数空间中的成本景观在不同实例上具有一些稳定性。 这一事实表明，给定实例的最优参数集可以转移到其他实例。 在本文中，我们展示了针对随机伊辛模型和最大割问题实例获得的一些数值结果。 对于随机生成的源实例和目标实例，线性化参数的可迁移性得到了演示，并对其依赖于实例特征的情况进行了研究。 显示英文摘要

摘要： Quantum Approximate Optimization Algorithm (QAOA) provides a way to solve combinatorial optimization problems using quantum computers. QAOA circuits consist of time evolution operators by the cost Hamiltonian and of state mixing operators, and embedded variational parameter for each operator is tuned so that the expectation value of the cost function is minimized. The optimization of the variational parameters is taken place on classical devices while the cost function is measured in the sense of quantum. To facilitate the classical optimization, there are several previous works on making decision strategies for optimal/initial parameters and on extracting similarities among instances. In our current work, we consider simplified QAOA parameters that take linear forms along with the depth in the circuit. Such a simplification, which would be suggested from an analogy to quantum annealing, leads to a drastic reduction of the parameter space from 2p to 4 dimensions with the any number of QAOA layers p. In addition, cost landscapes in the reduced parameter space have some stability on differing instances. This fact suggests that an optimal parameter set for a given instance can be transferred to other instances. In this paper we present some numerical results that are obtained for instances of the random Ising model and of the max-cut problem. The transferability of linearized parameters is demonstrated for randomly generated source and destination instances, and its dependence on features of the instances are investigated.