NSF-BSF: Fast Quantum Optimal Control on Exponentially Large Spaces

量子系统的最优控制对量子计算技术和基础实验的发展至关重要。寻找最优控制方案需要在一个巨大的相空间中最小化目标函数。为了克服这一挑战，目前的技术只是通过大量截断搜索空间来搜索最优方案。然而，众所周知，这忽略了更快和更高保真度的解决方案。本项目旨在理论发展和实验探索一种设计量子系统最优控制方案的新方法。该项目的成功将使量子物理学家和工程师能够设计出比现有方案更好的最优控制方案，从而增强现有量子技术的能力，并将推动高保真量子处理器的发展。从更广泛的意义上说，增强量子计算能力将影响我们解决比目前所有科学和工程领域更大问题的能力。此外，这项工作将为研究生提供培训，他们将参与项目的所有方面，包括研究、合作和成果的传播。该方法基于一种新的技术，用于计算指数大矩阵的元素，而不需要存储大量数据。该团队计划进一步发展这项技术，并将其调整为在巨大的希尔伯特空间中进行量子最优控制的设置。当原子或量子比特与玻色子模式耦合时，这种设置就会出现，并且在领先的量子技术平台中很常见，例如离子、腔qed和超导电路。在量子计算中，将量子信息编码在玻色子模式的广阔空间中是一种很有前途的硬件高效方法。在如此大的相空间内进行搜索可能对这种方法至关重要；这个平台的多功能性对于在现实环境中理解理论方案至关重要。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。

Optimal control of quantum systems is essential to the development of quantum computing technologies and fundamental experiments. Finding optimal control schemes requires minimizing an objective function over an overwhelmingly large phase space. To overcome this challenge, current techniques simply search for an optimal scheme by heavily truncating the search space. However, this is known to overlook faster and higher fidelity solutions. The aim of this project is to theoretically develop and experimentally explore a novel approach for designing optimal control schemes of quantum systems. The success of this project will allow quantum physicists and engineers to design optimal control schemes better than those available today, thus enhancing the capabilities of existing quantum technologies and will boost development of high-fidelity quantum processors. In a broader sense, enhancing quantum computation capabilities will affect our ability to solve larger problems than currently possible in all areas of science and engineering. In addition, the work will provide training to graduate students who will be involved in all aspects of the project, including research, collaboration and the dissemination of results.The approach is based on a novel technique for calculating elements of exponentially-large matrices without the need to store prohibitive quantities of data. The team plans to further develop this technique and adjust it to the settings of quantum optimal control in overwhelmingly large Hilbert spaces. Such settings arise when coupling an atom or qubit to a Bosonic mode, and are common in leading quantum technology platforms, such as Ions, Cavity-QED, and superconducting circuits. Specifically in the latter, a promising hardware-efficient approach for quantum computing is to encode the quantum information in the vast space of Bosonic modes. Searching within such a large phase space may prove to be crucial for this approach; and the versatility of this platform may prove crucial to understanding the theoretical scheme in a realistic setting.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.