An accurate and efficient numerical electromagnetic model for superconducting qubits is essential for characterizing and minimizing design-dependent dielectric losses. The energy participationratio (EPR) is the commonly adopted metric used to evaluate these losses, but its calculation presents a severe multiscale computational challenge. Conventional finite element method (FEM) requires 3D volumetric meshing, leading to prohibitive computational costs and memory requirements when attempting to capture singular electric fields at nanometer-thin material interfaces. To address this bottleneck, we propose SesQ, a surface integral equation simulator tailored for the precise simulation of the EPR. By applying discretization on 2D surfaces, deriving a semi-analytical multilayer Green’s function, and employing a dedicated non-conformal boundary mesh refinement scheme, SesQ accurately resolves singular edge fields without an explosive growth in the number of unknowns. Validations with analytically solvable models demonstrate that SesQ accelerates capacitance extraction by roughly two orders of magnitude compared to commercial FEM tools. While achieving comparable accuracy for capacitance extraction, SesQ delivers superior precision for EPR calculation. Simulations of practical transmon qubits further reveal that FEM approaches tend to significantly underestimate the EPR. Finally, the high efficiency of SesQ enables rapid iteration in the layout optimization, as demonstrated by minimizing the EPR of the qubit pattern, establishing the simulator as a powerful tool for the automated design of low-loss superconducting quantum circuits.
One significant advantage of superconducting processors is their extensive design flexibility, which encompasses various types of qubits and interactions. Given the large number oftunable parameters of a processor, the ability to perform gradient optimization would be highly beneficial. Efficient backpropagation for gradient computation requires a tightly integrated software library, for which no open-source implementation is currently available. In this work, we introduce SuperGrad, a simulator that accelerates the design of superconducting quantum processors by incorporating gradient computation capabilities. SuperGrad offers a user-friendly interface for constructing Hamiltonians and computing both static and dynamic properties of composite systems. This differentiable simulation is valuable for a range of applications, including optimal control, design optimization, and experimental data fitting. In this paper, we demonstrate these applications through examples and code snippets.
Fluxonium qubits are recognized for their high coherence times and high operation fidelities, attributed to their unique design incorporating over 100 Josephson junctions per superconductingloop. However, this complexity poses significant fabrication challenges, particularly in achieving high yield and junction uniformity with traditional methods. Here, we introduce an overlap process for Josephson junction fabrication that achieves nearly 100% yield and maintains uniformity across a 2-inch wafer with less than 5% variation for the phase slip junction and less than 2% for the junction array. Our compact junction array design facilitates fluxonium qubits with energy relaxation times exceeding 1 millisecond at the flux frustration point, demonstrating consistency with state-of-the-art dielectric loss tangents and flux noise across multiple devices. This work suggests the scalability of high coherence fluxonium processors using CMOS-compatible processes, marking a significant step towards practical quantum computing.
In the quest for fault-tolerant quantum computation using superconducting processors, accurate performance assessment and continuous design optimization stands at the forefront. Tofacilitate both meticulous simulation and streamlined design optimization, we introduce a multi-level simulation framework that spans both Hamiltonian and quantum error correction levels, and is equipped with the capability to compute gradients efficiently. This toolset aids in design optimization, tailored to specific objectives like quantum memory performance. Within our framework, we investigate the often-neglected spatially correlated unitary errors, highlighting their significant impact on logical error rates. We exemplify our approach through the multi-path coupling scheme of fluxonium qubits.