Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-\(\frac{1}{2}\) systems. Here, we instead consider encodings of d-level (i.e., qudit) quantum operators into multi-qubit operators, studying resource requirements for approximating operator exponentials by Trotterization. We primarily focus on spin-s and truncated bosonic operators in second quantization, observing desirable properties for approaches based on the Gray code, which to our knowledge has not been used in this context previously. After outlining a methodology for implementing an arbitrary encoding, we investigate the interplay between Hamming distances, sparsity patterns, bosonic truncation, and other properties of local operators. Finally, we obtain resource counts for five common Hamiltonian classes used in physics and chemistry, while modeling the possibility of converting between encodings within a Trotter step. The most efficient encoding choice is heavily dependent on the application and highly sensitive to d, although clear trends are present. These operation count reductions are relevant for running algorithms on near-term quantum hardware because the savings effectively decrease the required circuit depth. Results and procedures outlined in this work may be useful for simulating a broad class of Hamiltonians on qubit-based digital quantum computers.

量子系统的仿真有望成为量子计算最重要的应用之一，到目前为止，许多理论工作都集中在费米离子和自旋\（\ frac {1} {2} \）系统上。在这里，我们改为考虑将d级（即qudit）量子算符编码为多量子位算符，研究通过Trotterization近似算子指数所需的资源。我们主要专注于自旋小号并在第二次量化中使用截断的玻色子算符，观察基于格雷码的方法的理想特性，据我们所知，该特性以前并未在此上下文中使用。在概述了实现任意编码的方法之后，我们研究了汉明距离，稀疏模式，玻色截短和本地运算符的其他属性之间的相互作用。最后，我们获得了物理和化学中使用的五个常见汉密尔顿类的资源计数，同时对在Trotter步骤中进行编码之间转换的可能性进行了建模。最有效的编码选择在很大程度上取决于应用程序，并且对d高度敏感，尽管存在明显的趋势。这些操作计数的减少与在近期量子硬件上运行算法有关，因为这种节省有效地减少了所需的电路深度。这项工作中概述的结果和过程对于在基于量子位的数字量子计算机上模拟广泛的哈密顿量可能很有用。