EAGER: BRAIDING: Multi-terminal Josephson circuits supporting nontrivial Chern topologies for anyonic qubits

非技术摘要：这个研究项目旨在利用量子力学的物理定律来创造一种新的超高速信息处理工具，即量子计算。研究人员将在相同的亚原子粒子中编码信息，这种粒子被称为非阿贝尔粒子，可以“记住”它们相互位置的历史以及它们是如何交换位置的。实用的量子信息处理硬件预计将允许读出编码信息，并将在几个领域提供变革性进展，包括设计新的功能材料和复杂的多维信息处理操作。该项目将开发的量子材料和设备对于实现科学和技术中非常精确的测量非常重要。此外，该项目对基础科学具有重要意义；例如，可以使用这些新的量子信息处理方法来模拟宇宙的宇宙学模型。在这个项目下，学生将接受关于先进科学方法、材料科学和纳米技术的广泛培训，以及应用科学方法进行批判性思维和解决问题。技术摘要：这项工作集中展示了多终端超导约瑟夫森电路和量子比特作为非阿贝尔粒子的编织平台和新的高维拓扑态的仿真器的优越潜力，以及它们在拓扑保护计算中的可能应用。涡旋是在放置在拓扑绝缘体上的超导纳米岛的二维阵列中产生的。据预测，这样的涡旋将携带非阿贝尔马约拉纳零模。所研究的量子比特装置是一种交叉电流迈松跨量子比特，它能够提供圆极化的超电流，允许涡旋-反涡旋对的圆形编织轨迹。在这个项目中，通过将两个量子比特耦合到具有超导纳米岛阵列的多终端超导结上，产生量子叠加洛伦兹力。其目标是实现二维编织轨迹的叠加，以便存储量子信息。在第一阶段，一个由超导纳米岛阵列装饰的二维多终端超导邻近结被用来稳定和允许涡旋和反涡旋的二维移位。Majorana态的宇称影响量子比特的激发能量，因此可以用量子比特谱测量。将涡流和反涡流相结合是为了简化编织算法，因为在给定的超流作用下作用在反涡流上的洛伦兹力与作用在涡流上的洛伦兹力是相反的。邻近阵列的二维性质，在Transmon量子比特中充当非线性电感，是允许漩涡和反漩涡同时出现在交界处并相互移动以实现编织操作的关键因素。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。

Nontechnical Abstract: This research project aims to exploit the physical laws of quantum mechanics to create a new tool for superfast information processing, known as quantum computation. Researchers will encode information in identical subatomic particles, known as non-Abelian particles, which can "remember" the history of their mutual positions and how they have exchanged positions. Practical quantum information processing hardware is expected to allow the encoded information to be read out and will provide transformative advances in several areas, including the design of new, functional materials and complex, multi-dimensional information-processing operations. The quantum materials and devices to be developed in this project are important for enabling very precise measurements in science and technology. Furthermore, the project has important implications for fundamental science; for example, cosmological models of the Universe could be mimicked using these new methods of quantum information processing. Under this project, students will receive extensive training in advanced scientific methods, materials science and nanotechnology and, also, in applying scientific methods for critical thinking and problem solving. Technical Abstract: This work focuses on demonstrating the superior potential of multi-terminal superconducting Josephson circuits and qubits as a braiding platform for non-Abelian particles and as emulators of novel higher-dimensional topological states and their possible use in applications for topologically protected computing. The vortices are created in two-dimensional arrays of superconducting nano-islands placed on a topological insulator. Such vortices are predicted to carry non-Abelian Majorana zero modes. The studied qubit device is a cross-current meissneron transmon qubit, which is able to supply a circularly polarized supercurrent allowing circular braiding trajectories of vortex-antivortex pairs. In this project, a quantum-superposition Lorentz force is generated by means of the two qubits coupled to a multi-terminal superconducting junction having the array of superconducting nano-islands. The goal is to achieve a superposition of two-dimensional braiding trajectories in order to store quantum information. At the first stage, a two-dimensional multi-terminal superconducting proximity junction, decorated with an array of superconducting nano-islands, is being used to stabilize and permit two-dimensional translocation of vortices and antivortices. The parity of the Majorana states affects the qubit excitation energy and thus can be measured by qubit spectroscopy. Combining vortices and antivortices serves the purpose of simplifying braiding algorithms, because the Lorentz force acting on antivortices under a given supercurrent is opposite to the Lorentz force acting on vortices. The two-dimensional nature of the proximity arrays, serving as nonlinear inductors in transmon qubits, is the key factor allowing vortices and antivortices to be present simultaneously in the junction and to move around each other to achieve braiding operations.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.