We explore the effectiveness of variational quantum circuits in simulating the ground states of quantum many-body Hamiltonians. We show that generic high-depth circuits, performing a sequence of layer unitaries of the same form, can accurately approximate the desired states. We demonstrate their universal success by using two Hamiltonian systems with very different properties: the transverse field Ising model and the Sachdev-Ye-Kitaev model. The energy landscape of the high-depth circuits has a proper structure for the gradient-based optimization, i.e. the presence of local extrema -- near any random initial points -- reaching the ground level energy. We further test the circuit's capability of replicating random quantum states by minimizing the Euclidean distance.
翻译:我们探索了可变量子电路在模拟量子多体汉密尔顿人的地面状态方面的有效性。 我们显示,通用高深度电路,进行一系列同一形态的分层单位,能够准确地接近预期状态。 我们通过使用两个具有非常不同特性的汉密尔顿系统,即横贯的Ising模型和Sachdev-Ye-Kitaev模型,展示了它们的普遍成功。 高深度电路的能源景观为基于坡度的优化提供了适当的结构, 即存在局部的极限体 -- -- 接近任何随机的初始点 -- -- 达到地面水平的能量。 我们进一步测试了电路复制随机量状态的能力, 最大限度地缩小了Euclidean距离。