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

量子系统的最优控制对于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非常大的相空间上最小化目标函数。为了克服这一挑战，目前的技术简单地搜索一个最佳的方案，严重截断搜索空间。然而，众所周知，这会忽略更快和更高保真的解决方案。该项目的目的是从理论上发展和实验上探索一种新的方法来设计量子系统的最优控制方案。 该项目的成功将使量子物理学家和工程师能够设计出比目前更好的最佳控制方案，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，他们将参与项目的各个方面，包括研究、合作和成果的传播。该方法基于一种计算指数大矩阵元素的新技术，而无需存储大量数据。该团队计划进一步开发这项技术，并将其调整到超大希尔伯特空间中的量子最优控制设置。当将原子或量子比特耦合到玻色子模式时，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。特别是在后者中，一个有前途的量子计算的硬件有效的方法是在玻色子模式的广阔空间中编码量子信息。在这样一个大的相空间内搜索可能被证明是至关重要的这种方法，和这个平台的多功能性可能被证明是至关重要的理解理论方案在现实setting.This奖项反映了NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的智力价值和更广泛的影响审查标准。

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.