量子计算在一些复杂问题上的计算效率远超经典计算机，是现代量子信息技术中最具颠覆性的研究方向。超导量子计算基于固态器件、相干时间与门保真度指标较为领先、与半导体集成电路制造工艺兼容、设计灵活、外围电路可选的超导电子学器件丰富，是目前最有希望实现规模化扩展的量子计算方案。现有的基于 transmon 超导量子比特的多比特超导量子处理器架构主要包括近邻式耦合与总线式耦合两类。近邻式耦合可以实现的门保真度高，可扩展性好，但量子比特连通性受限；总线式耦合的量子比特具有全连通性，但无法直接规模化扩展。 针对这组矛盾，本文提出并研究了多模分组总线耦合的超导量子处理器架构：组内的量子比特通过总线形成局域全连通耦合；组与组之间共用若干个量子比特，形成类近邻耦合，通过态交换来传递相互作用。该架构的超导量子处理器能够以耦合组为单位进行规模化扩展。同时，组间共用的量子比特也形成了多模总线耦合。我们利用数值仿真，研究了多模总线耦合情况下的双比特量子门，发现多模耦合可以突破传统单模总线耦合架构中的门操作速度与门保真度之间的制约关系；研究了多模耦合下的 Purcell 效应，验证了多模耦合可以在维持原有耦合强度的前提下抑制耦合量子比特的 Purcell 耗散；研究了多模耦合的多个量子比特之间的串扰效应，提出了量子比特的频率区间划分所应该满足的原则；设计制备了多模分组总线耦合架构的超导量子处理器，并在低温测试中验证了多模耦合效应可以有效提升量子比特之间的虚光子耦合强度。 为了进一步提高超导量子处理器的器件性能，我们制备和测试了多批次的双角度蒸发铝约瑟夫森结，分析判断影响结成品率的主要因素与样品尺寸有关，并采用完整晶圆制样提升了结成品率。我们在低温下测试了铝、铌共面波导谐振器，判断红外噪声引起的准粒子耗散是主要的耗散因素。 本文还介绍了基于 transmon 的超导量子处理器的电路设计方法，包括电容的参数选择与仿真设计，以及共面波导传输线谐振器的设计。针对分组总线耦合芯片中总线谐振器数目多的特点，本文提出了多分支传输线网络谐振器模式的电路分析方法，相比于常用的电磁场数值计算方法，将计算效率提升了 3 个数量级以上，为规模化扩展的超导量子处理器的自动化设计提供了技术保障。
Quantum computation surpasses its classical counterpart in certain complex computational problems and manifests itself as the most revolutionary research field in modern quantum information technologies. Superconducting quantum computation (a) is based on solid-state devices, (b) can achieve relatively long coherence time and high gate fidelity, (c) is compatible with semiconductor integrated circuit fabrication technologies, (d) enjoys high design flexibility, (e) is supported by a wide variety of periphery superconducting electronics, therefore it is the most promising platform towards scalable quantum computation. State-of-art multi-qubit superconducting quantum processors based on transmon qubits are divided into two major categories of coupling architectures: nearest-neighbour coupling and bus coupling. Nearest-neighbour coupling has better scalability with high gate fidelity, while qubit connectivity is limited. Bus coupling is highlighted by its all-to-all connectivity, while its scalability is not yet obvious. As a remedy for their weaknesses, multimode grouped bus coupling architecture is proposed in this thesis. Qubits in each group are coupled by a bus coupler, achieving local all-to-all connectivity. Neighbouring groups are coupled by shared qubits, so that the groups can communicate by exchanging qubit states. Coupling groups can be duplicated for scaling-up of the processor. The shared qubits among neighbouring groups also couple to each other through multimode quantum bus. Numerical simulations demonstrate that, under multimode coupling scheme, two-qubit gate can be realized with enhanced gate speed and fidelity, and Purcell effect can be suppressed in coupling qubits without sacrificing coupling strength. Examination of crosstalk among multiple qubits further suggests the principles for allocation of qubits in frequency domain. Multimode grouped bus coupling superconducting quantum processors have been designed and fabricated. In proof-of-principle experiments on the proposed architecture, it is verified that multimode coupling can provide stronger virtual photon coupling strength as expected. For improvement of superconducting quantum processor device quality, aluminum Josephson junctions fabricated with double-angle shadow evaporation were tested under room temperature. It proved that enlarged sample size is the approach to higher yield. We performed cryogenic measurements of aluminum and niobium coplanar waveguide resonators and find that infrared-radiation-induced quasi-particle dissipation should be the major loss mechanism limiting device coherence. Regarding superconducting quantum processor design, simulations of various capacitors and transmission line resonators are discussed. Multi-branch transmission-line-network resonator equations are proposed for efficient analysis of quantum bus resonators in grouped bus coupling architectures. The equations promote design efficiency of complex resonators by more than three orders of magnitude compared to common electromagnetic simulation tools, opening up the possibility for application in future quantum design automation of scalable superconducting quantum processors.
