Laskar Mostafizur Rahaman, Bhattacharya Atanu, Dasgputa Kalyan
IBM Research, Bangalore, India.
G. S. Sanyal School of Telecommunications, Indian Institute of Technology Kharagpur, Kharagpur, India.
Sci Rep. 2024 May 11;14(1):10831. doi: 10.1038/s41598-024-60605-6.
This study introduces a conceptually novel polynomial encoding algorithm for simulating potential energy operators encoded in diagonal unitary forms in a quantum computing machine. The current trend in quantum computational chemistry is effective experimentation to achieve high-precision quantum computational advantage. However, high computational gate complexity and fidelity loss are some of the impediments to the realization of this advantage in a real quantum hardware. In this study, we address the challenges of building a diagonal Hamiltonian operator having exponential functional form, and its implementation in the context of the time evolution problem (Hamiltonian simulation and encoding). Potential energy operators when represented in the first quantization form is an example of such types of operators. Through systematic decomposition and construction, we demonstrate the efficacy of the proposed polynomial encoding method in reducing gate complexity from to (for some ). This offers a solution with lower complexity in comparison to the conventional Hadamard basis encoding approach. The effectiveness of the proposed algorithm was validated with its implementation in the IBM quantum simulator and IBM quantum hardware. This study demonstrates the proposed approach by taking the example of the potential energy operator of the sodium iodide molecule (NaI) in the first quantization form. The numerical results demonstrate the potential applicability of the proposed method in quantum chemistry problems, while the analytical bound for error analysis and computational gate complexity discussed, throw light on issues regarding its implementation.
本研究介绍了一种概念上新颖的多项式编码算法，用于在量子计算机中模拟以对角酉形式编码的势能算符。量子计算化学的当前趋势是进行有效的实验以实现高精度的量子计算优势。然而，高计算门复杂度和保真度损失是在实际量子硬件中实现这一优势的一些障碍。在本研究中，我们解决了构建具有指数函数形式的对角哈密顿算符及其在时间演化问题（哈密顿模拟和编码）背景下的实现问题。以第一量子化形式表示的势能算符就是这类算符的一个例子。通过系统的分解和构建，我们证明了所提出的多项式编码方法在将门复杂度从 降低到 （对于某些 ）方面的有效性。与传统的哈达玛基编码方法相比，这提供了一种复杂度更低的解决方案。所提出算法的有效性通过在IBM量子模拟器和IBM量子硬件中的实现得到了验证。本研究以第一量子化形式的碘化钠分子（NaI）的势能算符为例展示了所提出的方法。数值结果证明了所提出方法在量子化学问题中的潜在适用性，而所讨论的误差分析和计算门复杂度的解析界限则揭示了其实现方面的问题。
