Random Compiler for Fast Hamiltonian Simulation
Random Compiler for Fast Hamiltonian Simulation
复制标题
DOI：
10.1103/physrevlett.123.070503
复制
发表时间：
2019-08-14
影响因子：
8.6
通讯作者：
Campbell, Earl
中科院分区：
文献类型：
--
作者：
Campbell, Earl
量子系统的动力学可以使用量子计算机通过将幺正分解为一个和两个量子位门的量子电路来模拟。最成熟的方法是Trotter-Suzuki分解，对于该方法，电路大小的严格界限取决于系统哈密顿量中的项L的数量和哈密顿量λ中最大项的大小。因此，Trotter-Suzuki方法仅适用于稀疏哈密顿。Trotter-Suzuki是一个确定性编译器，但最近表明，随机编译提供更低的开销。在这里，我们提出并分析了一个随机编译器的哈密顿模拟门的概率是成比例的强度相应的一项在哈密顿。这种方法要求电路大小独立于L和λ，而是取决于λ，即哈密顿强度的绝对和（l（1）范数）。因此，它特别适合于与量子化学相关的电子结构哈密顿量。考虑到丙烷、二氧化碳和乙烷，我们观察到与标准Trotter-Suzuki相比，在精度为10（-3）的物理显著模拟时间内，速度提高了306倍至1591倍。在化学精度进行相位估计，我们报告说，节省是相似的。
The dynamics of a quantum system can be simulated using a quantum computer by breaking down the unitary into a quantum circuit of one and two qubit gates. The most established methods are the Trotter-Suzuki decompositions, for which rigorous bounds on the circuit size depend on the number of terms L in the system Hamiltonian and the size of the largest term in the Hamiltonian Lambda. Consequently, the Trotter-Suzuki method is only practical for sparse Hamiltonians. Trotter-Suzuki is a deterministic compiler but it was recently shown that randomized compiling offers lower overheads. Here we present and analyze a randomized compiler for Hamiltonian simulation where gate probabilities are proportional to the strength of a corresponding term in the Hamiltonian. This approach requires a circuit size independent of L and Lambda, but instead depending on lambda the absolute sum of Hamiltonian strengths (the l(1) norm). Therefore, it is especially suited to electronic structure Hamiltonians relevant to quantum chemistry. Considering propane, carbon dioxide, and ethane, we observe speed-ups compared to standard Trotter-Suzuki of between 306x and 1591x for physically significant simulation times at precision 10(-3). Performing phase estimation at chemical accuracy, we report that the savings are similar.