近日，澳大利亚墨尔本大学的Shaobo Zhang与澳大利亚联邦科学与工业研究组织的Akib Karim合作并取得一项新进展。他们实现了半导体材料在噪声量子处理器上的全能带结构计算。相关研究成果已于2024年12月9日在国际知名学术期刊《物理评论A》上发表。

在量子计算时代，量子化学是一项极具前景的应用，因为那些在传统模拟中需要指数级增长资源，才能实现的量子力学独特效应，在量子计算机上是可以控制的。费米子的自由度可以高效地编码到量子比特上，从而使得诸如量子运动方程方法等算法，能够找到量子系统的整个能谱。

在本文中，研究人员提出了简化量子运动方程方法，通过降低其广义特征方程的维度，使得所需测量次数相比传统的量子运动方程方法减少了一半，从而加快了算法速度，并减少了在实际器件上的噪声累积。特别是，研究人员分析了该方法在两种噪声模型下的性能，并使用IBM量子处理器，通过该方法计算了体积硅和砷化镓的激发能。

这一研究方法对均匀去极化误差具有完全的鲁棒性，并且研究人员证明了选择适当的原子轨道复杂度，可以提高该算法在实际噪声下的鲁棒性。研究人员还发现，由于精确值附近的波动，多次实验的平均值往往趋近于正确的能量值。该方法的这种噪声抗性可以在当前的量子器件上，用于解决量子化学问题。

附：英文原文

Title: Full band-structure calculation of semiconducting materials on a noisy quantum processor

Author: Shaobo Zhang, Akib Karim, Harry M. Quiney, Muhammad Usman

Issue&Volume: 2024/12/09

Abstract: Quantum chemistry is a promising application in the era of quantum computing since the unique effects of quantum mechanics that take exponential growing resources to simulate classically are controllable on quantum computers. Fermionic degrees of freedom can be encoded efficiently onto qubits and allow for algorithms such as the quantum equation-of-motion method to find the entire energy spectrum of a quantum system. In this paper, we propose the reduced quantum equation-of-motion method by reducing the dimensionality of its generalized eigenvalue equation, which results in half the measurements required compared to the quantum equation-of-motion method, leading to speed up the algorithm and less noise accumulation on real devices. In particular, we analyze the performance of our method on two noise models and calculate the excitation energies of a bulk silicon and gallium arsenide using our method on an IBM quantum processor. Our method is fully robust to the uniform depolarizing error, and we demonstrate that the selection of suitable atomic orbital complexity could increase the robustness of our algorithm under real noise. We also find that taking the average of multiple experiments tends toward the correct energies due to the fluctuations around the exact values. Such noise resilience of our approach could be used on current quantum devices to solve quantum chemistry problems.

DOI: 10.1103/PhysRevA.110.062415

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062415