$d$级粒子数字量子模拟的连接性相关资源需求
On connectivity-dependent resource requirements for digital quantum simulation of $d$-level particles
摘要：
量子计算的主要目标是有效地模拟量子物理。在科学和技术上重要的量子哈密顿量包括自旋- $s$、振动、光子和其他玻色子自由度，即由$d$ -能级粒子（qudits）组成或近似的问题。最近，已经引入了几种将这些系统编码成一组量子位的方法，其中每种编码的效率都根据量子位和门计数进行了研究。在这里，我们建立在以前的结果，包括硬件连接的影响。为了研究Trottounts常用量子算子所需的SWAP门的数量，我们使用了分析参数和自动工具，这些工具可以在多个阶段优化时间表。我们研究了一元（或一热），灰色，标准二进制和块一元编码，与三个连接：线性阵列，梯形阵列，和正方形网格。在其他趋势中，我们发现，虽然梯形阵列导致实质性的效率超过线性阵列，正方形的优势，梯形阵列是不太明显。这些结果适用于硬件协同设计，并在选择有效的qudit编码为一组给定的近期量子硬件。此外，这项工作可能与其他量子算法的调度有关，其中矩阵取幂是一个子程序。
英文摘要：
A primary objective of quantum computation is to efficiently simulate quantum physics. Scientifically and technologically important quantum Hamiltonians include those with spin-$s$, vibrational, photonic, and other bosonic degrees of freedom, i.e. problems composed of or approximated by $d$-level particles (qudits). Recently, several methods for encoding these systems into a set of qubits have been introduced, where each encoding's efficiency was studied in terms of qubit and gate counts. Here, we build on previous results by including effects of hardware connectivity. To study the number of SWAP gates required to Trotterize commonly used quantum operators, we use both analytical arguments and automatic tools that optimize the schedule in multiple stages. We study the unary (or one-hot), Gray, standard binary, and block unary encodings, with three connectivities: linear array, ladder array, and square grid. Among other trends, we find that while the ladder array leads to substantial efficiencies over the linear array, the advantage of the square over the ladder array is less pronounced. These results are applicable in hardware co-design and in choosing efficient qudit encodings for a given set of near-term quantum hardware. Additionally, this work may be relevant to the scheduling of other quantum algorithms for which matrix exponentiation is a subroutine.
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