论文标题
晶格旋转系统的数字量子模拟食谱
Recipes for the Digital Quantum Simulation of Lattice Spin Systems
论文作者
论文摘要
我们描述了在与局部相互作用的常规晶格上构造数字量子模拟算法的方法。除了诸如Trotter-Suzuki扩展和图形着色之类的工具外，我们还通过并行执行大量通勤项来讨论效率。我们为最重要的旋转系统和类别提供资源估计和量子电路元素。根据资源估计，我们指出了大门$ n $和仿真时间$ t $的总数，该数字以旋转1/2晶格站点的数量$ n $表示，目标准确性$ε$和模拟时间$ t $。我们提供电路构造，以实现仿真时间$ t^{（1）} \ propto nt^2/ε$和$ t^{（2q）} \ propto t^{1+η} n^η/ε^η$用于任意小$ $ $ $ $η= 1/2Q $的第一阶和更高订单和更高订单的扩展。我们还讨论了尚未充分探索的缩放门的潜在影响。
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the efficiency gained by parallel execution of an extensive number of commuting terms. We provide resource estimates and quantum circuit elements for the most important cases and classes of spin systems. As resource estimates we indicate the total number of gates $N$ and simulation time $T$, expressed in terms of the number $n$ of spin 1/2 lattice sites (qubits), target accuracy $ε$, and simulated time $t$. We provide circuit constructions that realize the simulation time $T^{(1)}\propto nt^2/ε$ and $T^{(2q)}\propto t^{1+η}n^η/ε^η$ for arbitrarily small $η=1/2q$ for the first-order and higher-order Trotter expansions. We also discuss the potential impact of scaled gates, which have not yet been fully explored.
