Compilation by stochastic Hamiltonian sparsification
Compilation by stochastic Hamiltonian sparsification
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DOI：
10.22331/q-2020-02-27-235
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发表时间：
2019-10
期刊：
影响因子：
6.4
通讯作者：
Yingkai Ouyang;D. R. White;E. Campbell
中科院分区：
文献类型：
--
作者：
Yingkai Ouyang;D. R. White;E. Campbell
量子化学模拟有望成为量子计算的主要应用。在量子模拟中，描述量子系统动力学的复杂哈密顿量被分解成其组成项，其中每一项在时间演化过程中的影响是单独计算的。对于许多物理系统，哈密顿量具有大量的项，限制了已建立的模拟方法的可扩展性。为了解决这一局限性，我们引入了一种新的方案，它用包含更少项的更稀疏的哈密顿量来逼近实际的哈密顿量。通过随机稀疏较弱的哈密顿项，我们受益于相对于确定性方法的误差的二次抑制。根据凸优化理论中的最优性条件，我们得到了较弱哈密顿项的一个合适的概率分布，并将其误差界与一些电子结构哈密顿量的其他概率分布作了比较。调整我们的近似哈密顿量的稀疏性允许我们的方案在最近的两个随机编译器之间进行内插：qDRIFT和随机化的一阶Trotter。因此，我们的方案是一种结合了随机旋转变换的优点和QDRIFT的效率的算法，并且对于中间门预算，其性能优于这两种先前的方法。
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme that approximates the actual Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochastically sparsifying weaker Hamiltonian terms, we benefit from a quadratic suppression of errors relative to deterministic approaches. Relying on optimality conditions from convex optimisation theory, we derive an appropriate probability distribution for the weaker Hamiltonian terms, and compare its error bounds with other probability ansatzes for some electronic structure Hamiltonians. Tuning the sparsity of our approximate Hamiltonians allows our scheme to interpolate between two recent random compilers: qDRIFT and randomized first order Trotter. Our scheme is thus an algorithm that combines the strengths of randomised Trotterisation with the efficiency of qDRIFT, and for intermediate gate budgets, outperforms both of these prior methods.