We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to $4$. The central idea behind our approach is to collect mutually commuting Hamiltonian terms into groups that satisfy one of several symmetries identified in this work which allow an inexpensive simulation of the entire group of terms. We further show that the cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings. We further specifically discuss these optimizations for the case of fermionic dynamics and provide extensive numerical simulations for qDRIFT of our grouping strategy to 6 and 4-qubit Heisenberg models, $LiH$, $H_2$ and observe a factor of 1.8-3.2 reduction in the number of non-Clifford gates. This suggests Trotter-based simulation of chemistry in second quantization may be even more practical than previously believed.
翻译:我们为编集在Trotter、qDRIFT和非Clifford操作中出现的量子模拟电路提供了一种新的方法,这种电路在Trotter、qDRIFT和多产品公式中出现,可以将非Clifford操作的数量减少高达4美元的系数。我们的方法的核心思想是将相互通勤的汉密尔顿术语收集成能够满足这项工作中确定的若干对称的组合之一,从而能够对整个术语组进行廉价的模拟。我们进一步表明,在某些情况下,通过将汉密尔顿语术语部分分配给若干组,提供一种可以将术语贪婪地分配给适当组的多时古典算法,可以降低成本。我们进一步具体讨论这些优化,并为我们的组合战略中的qDRIFT提供广泛的数字模拟,即6和4Q-qubit Heisenberg模型, $LiH$,2美元,并观察到非Cliford门数量减少1.8-3的因素。这说明,第二次二次二次二次二次二次二次二次磁化中基于Troter的化学模拟可能比以前认为的要更实际。