NSF-BSF: Efficiently Modeling Continuous Quantum Measurements of High-Dimensional Multi-Qubit Systems

现代计算机发展迅速，产生了史无前例的技术财富。这场技术革命提高了全球的生活水平，并已成为现代经济的基石。最近，计算能力的快速增长有所放缓，部分原因是硬件组件的尺寸缩小到了微观规模。在微观尺度上，硬件的行为符合量子力学定律，而量子力学定律与传统计算机的预期定律大相径庭。这些差异阻碍了使用现有硬件技术的持续增长，但也为新的可能性提供了可能性。目前正在努力开发一种硬件范例，利用量子力学的细微差别来加速计算。该项目通过解决超导量子电路的紧迫模拟问题，为这些量子计算工作做出了贡献，超导量子电路是可扩展量子技术的一个有前途的候选者。随着系统的规模，准确描述这样的量子电路的难度迅速增加，这使得硬件设计具有挑战性。如果成功，这项工作将提供数值方法和开源软件，大大简化常见场景的建模任务，这将有助于加快超导量子电路的未来发展。描述量子电路通常需要大量参数，这使得蛮力模拟具有挑战性。这种高维性的一个特别重要的例子发生在量子电路的标准测量协议期间。在这个协议中，行进的微波场与微波谐振器耦合，而微波谐振器又与具有多个能级的非线性振荡器耦合。当行场被收集时，量子系统根据测量的随机信号不断演化，产生复杂的动力学。这个项目将开发有效的方法来模拟这些连续的量子测量，使用几个设计阶段。在开发了多组件芯片上的微波放大和读出电路的全参考数值模型之后，我们将开发简化的半经典表示法，将高维压缩为更少的参数。这些简化将扩展已知的微波动力学的弱场相干稳态近似，以考虑非线性效应。这个项目将探索使用机器学习方法，特别是递归神经网络，来自动学习如何有效地压缩动力学。同时，本科生将通过演示、视频等方式与当地社区进行接触，以提高公众对量子力学的素养。该项目将提供开源软件、在线互动笔记和教程，作为其广泛推广工作的一部分。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Modern computers developed rapidly, leading to a historically unprecedented wealth of technology. This technological revolution has improved standards of living globally and has become a cornerstone of the modern economy. Recently, the rapid growth of computational power has slowed, in part because the size of hardware components has shrunk to microscopic scales. At microscopic scales, hardware behaves according to the laws of quantum mechanics, which are quite different from the laws expected for traditional computers. These differences have impeded continued growth using established hardware techniques, but also allow for new possibilities. Efforts are ongoing to develop a paradigm of hardware that leverages the nuances of quantum mechanics to accelerate computation. This project contributes to these quantum computing efforts by addressing a pressing simulation problem for superconducting quantum circuits, which are a promising candidate for scalable quantum technology. The difficulty in accurately describing such a quantum circuit grows rapidly with the size of the system, making hardware design challenging. If successful, this work will provide numerical methods and open source software that dramatically simplify this modeling task for common scenarios, which should help accelerate the future development of superconducting quantum circuits.Large numbers of parameters are generally required to describe quantum circuits, making brute force simulation challenging. A particularly important example of this high dimensionality occurs during the standard measurement protocol for quantum circuits. In this protocol, traveling microwave fields couple with microwave resonators, which in turn couple with nonlinear oscillators that have several energy levels. As the traveling field is collected, the quantum system continuously evolves in accordance with the measured stochastic signal, producing complicated dynamics. This project will develop efficient methods for simulating these continuous quantum measurements using several design phases. After developing a full reference numerical model for the microwave amplification and readout circuitry on a multi-component chip, we will develop simplified semi-classical representations that compress the high dimensionality into a smaller number of parameters. These simplifications will extend known weak-field coherent steady-state approximations of the microwave dynamics to account for nonlinear effects. This project will explore the use of machine learning methods, particularly recurrent neural networks, to automatically learn how to compress the dynamics efficiently. In parallel, undergraduates will perform outreach to the local community through demonstrations, videos, and more to raise public literacy of quantum mechanics. This project will deliver open-source software, online interactive notes, and tutorials as part of its broad outreach effort.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.