Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits whose depth scales with the number of steps. When the circuit elements are limited to a subset of SU(4) --- or equivalently, when the Hamiltonian may be mapped onto free fermionic models --- several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.
翻译:在一个依赖时间的汉密尔顿式情况下, 单体进化是量子硬件模拟的一个关键组成部分。 合成相应的量子电路通常通过打破进化成小时间级步骤( 也称为 " 梯度化 " ) 来完成, 由此形成深度尺度与步骤数相加的电路。 当电路元素限于SU(4)的一个子集时 -- 或等效地, 当汉密尔顿人可以被绘制到自由的发酵模型时 -- -- 有几个身份可以合并和简化电路。 基于这一点, 我们提出了一个算法, 将Trotter步骤压缩成一个单一的量子门块。 这导致某些汉密尔顿人类别固定的深度进化。 我们明确展示了该算法如何对几个旋转模型起作用, 并演示其用于对立状态准备横田Ising模型 。