ExpandQISE: Track 1: Analog quantum simulation of non-Markovian dynamics of multi-qubit systems

摘要：多量子比特系统用于各种量子技术，包括量子通信、量子传感、量子密码和量子模拟。由于任何量子系统都不能完全与环境隔离，因此引入开放量子系统来模拟量子系统的演化，同时考虑量子系统与环境之间的相互作用。根据这种相互作用的强度和类型，有两种类型的开放量子系统动力学-马尔可夫和非马尔可夫，其中非马尔可夫动力学更准确。在本研究中，项目组将推进和推动多量子位系统非马尔可夫动力学的模拟量子模拟研究。此外，这项研究将实施一个投资和奖励反馈循环，以激励K-12学生，吸引、留住和教育本科生、女性和代表性不足的少数民族学生，让他们接触到与量子相关的研究。此外，本项目通过加强现有课程和创建新课程，拓宽和加强目前本科阶段的量子物理课程。技术摘要：了解量子系统与其周围环境的动力学关系对于充分利用量子信息处理任务的潜力至关重要。然而，开放量子系统的非马尔可夫动力学建模面临两大挑战：(i)目前的研究使用修改的马尔可夫主方程来描述非马尔可夫动力学，这可能是不准确的。缺乏获得近似保正主方程的系统方法限制了目前技术在实践中的能力。本研究旨在发展模拟量子算法来研究基于量子态扩散（QSD）方程方法的多量子位系统的非马尔可夫动力学。特别地，本研究：(i)利用QSD方法获得了非马尔可夫主方程的广义形式；（ii）通过应用近似值优化和生成PPME；（iii）开发了一种系统的方法来推导复杂相互作用的克劳斯算子；（iv）设计了一种基于蒙特卡罗的量子模拟算法，该算法从随机量子轨迹开始，而不是从密度矩阵开始。该项目由多学科活动办公室（MPS/OMA）、计算与通信基金会（CCF）部门和技术前沿计划（TIP/TF）共同资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Non-technical Abstract: A multi-qubit system is used in various quantum technologies, including quantum communication, quantum sensing, quantum cryptography, and quantum simulation. Since any quantum system cannot be fully isolated from the environment, open quantum systems are introduced to model the evolution of a quantum system while considering the interactions between the quantum system and the environment. Depending on the strength and the type of this interaction, there are two types of open quantum systems dynamics - Markovian and non-Markovian, where the non-Markovian dynamics are more accurate. In this research, the project team will advance and promote the research on analog quantum simulation of non-Markovian dynamics of multi-qubit systems. In addition, this research will implement an investment and reward feedback loop for inspiring K-12 students and attracting, retaining, and educating undergraduate, female, and underrepresented minority students by exposing them to this quantum-related research. Further, this project broadens and strengthens the current quantum physics curriculum at the undergraduate level by enhancing existing courses and creating new ones.Technical Abstract: Understanding the dynamics of a quantum system in connection with its surrounding environment is crucial for harnessing the full potential of quantum information processing tasks. However, modeling the non-Markovian dynamics of open quantum systems faces two grand challenges: (i) current efforts use a modified Markovian master equation to describe the non-Markovian dynamics, which could be inaccurate. (ii) The lack of a systematic method for obtaining approximated positivity-preserving master equations (PPME) limits the capability of current techniques in practice. The research aims to develop analog quantum algorithms to study the non-Markovian dynamics of multi-qubit systems built on the quantum-state-diffusion (QSD) equation approach. Particularly, this research: (i) leverages the QSD approach to obtaining the generalized formalism of the non-Markovian master equation; (ii) optimizes and generates PPME with approximations applied; (iii) develops a systematic method to derive Kraus operators for complicated interactions; (iv) devises a Monte-Carlo-based quantum simulation algorithm initiated from the stochastic quantum trajectories, instead of the density matrix.This project is jointly funded by the Office of Multidisciplinary Activities (MPS/OMA), Computing and Communications Foundations (CCF) Division, and the Technology Frontiers Program (TIP/TF).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.