基于可扩展超导量子线路的量子模拟

量子计算基于量子力学原理实现量子信息的处理，以在特定问题上实现超越 经典计算的量子优势为远景目标。量子计算实验方向在近二十年中出现了多种技术路线并开始迅速发展，超导量子线路是其中最具可扩展优势的平台之一。超导量子线路的实验基于线路量子电动力学的理论和微纳加工技术设计和制造量子芯片，能实现量子比特阵列的大规模扩展。近年来，更多的国内外科研团队开始参与超导量子线路的研究，使得多比特扩展的实验技术迅速发展。实验最多能控制的物理比特数量已经从10¹迈入了10²量级。

基于超导量子线路的实验平台，本论文针对量子系统的实验调控与相应模型的量子模拟问题展开了研究。我们首先从单个超导量子比特开始，研究了二能级系统的含时调控。实验通过绝热捷径方案缩短了二能级系统含时调控的演化时间， 实现了系统在参数空间沿绝热捷径的演化，并研究了所对应的一维链模型在动量空间中的拓扑性质。

在进一步引入比特的更高能级后，我们在实验中实现了多能级闭合回路耦合系统的量子模拟。通过系统哈密顿量的连续演化与量子门结合的混合方法，实验在原本不具有回路耦合的超导比特中等效实现了闭合回路耦合系统，观测了受相位调控的手征演化，并展示了绝热捷径方案用于区分系统手征性的应用。在扩展至两比特的四能级系统中，实验也实现了相似的耦合机制与手征演化。

在多比特系统的实验中，我们通过改良样品结构和多次的样品迭代成功实现了基于一维链结构的36比特芯片，并将二能级系统中含时调控量子模型的方法应用于多比特系统中。实验将比特的第一激发态作为格点中的单粒子态，通过控制比特和耦合器的频率模拟了无相互作用单粒子系统的拓扑泵浦。在此基础上，我们通过更高能级非谐性引入哈伯德相互作用，在不同的势能调制参数区间中分别 实现了双粒子束缚态的拓扑泵浦、相互作用粒子的共振隧穿、以及双粒子的边界态泵浦，进一步探讨了相互作用粒子的拓扑泵浦。我们的实验研究分别对参数含时调控的二能级、多能级、以及多比特系统进行了探索。实验通过含时调控与更高能级的激发态，实现了相互作用系统的量子模拟，这些方法和技术在未来还可以被进一步应用于二维阵列多比特系统的实验中。

Quantum computation implements information processing based on the principles of quantum mechanics, with the long-term goal of surpassing classical computing in specific problems. Over the past two decades, various physical realizations have emerged and rapidly developed, where the superconducting circuit is one of the most scalable platform. The experiments develop qubit chips based on the circuit quantum electrodynamics theory and microfabrication technology, which enable the development of a large-scale qubit array. In recent years, more research teams have participated in this researches, leading to rapid developments and the increased qubit number from the level of 10¹ to 10².

In this thesis, we focus on the experimental quantum control and relevant models of quantum simulation in superconducting circuits. Starting from the time-dependent control of two-level system, we realized adiabatic evolution using the shortcut to adiabaticity method and explored the topological properties in parameter space. 

Then we introduced higher energy levels and simulated the closed-contour coupling in multi-level systems. The experiments effectively constructed a three-level system with such coupling by the hybrid digital-analog method. We observed phase-controlled chiral dynamics, then demonstrated separation of chiral enantiomers, and finally discussed the similar dynamics in four-level system of two qubits. 

In the experiment of multi-qubit system, we developed the chip comprising a one-dimensional array of 36 qubits, and introduced the previously used time-dependent control. By periodically modulating the qubit and coupler frequencies, we simulated the topological pumping of noninteracting particles, where the first-excited state of each qubit acts as a single-particle state on the lattice site. Moreover, we demonstrated the related phenomena for the topological pumping of interacting particles, including the bound states evolution, resonant tunneling, and edge-state transport. Our researches experimentally explored the time-dependent control of two-level, multi-level, and multi-qubit system. We simulated the interacting system by introducing the higher excited states. These methods can further be applied in future experiments with two-dimensional array of qubits.

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