As superconducting quantum circuits scale to larger sizes, the problem of frequency crowding proves a formidable task. Here we present a solution for this problem in fixed-frequency qubit architectures. By systematically adjusting qubit frequencies post-fabrication, we show a nearly tenfold improvement in the precision of setting qubit frequencies. To assess scalability, we identify the types of “frequency collisions” that will impair a transmon qubit and cross-resonance gate architecture. Using statistical modeling, we compute the probability of evading all such conditions, as a function of qubit frequency precision. We find that, without post-fabrication tuning, the probability of finding a workable lattice quickly approaches 0. However, with the demonstrated precisions it is possible to find collision-free lattices with favorable yield. These techniques and models are currently employed in available quantum systems and will be indispensable as systems continue to scale to larger sizes.

随着超导量子电路扩展到更大尺寸，频率拥挤问题被证明是一项艰巨的任务。在这里，我们提出了固定频率量子位架构中这个问题的解决方案。通过在制造后系统地调整量子位频率，我们显示设置量子位频率的精度提高了近十倍。为了评估可扩展性，我们确定了会损害 transmon qubit 和交叉谐振门架构的“频率冲突”类型。使用统计建模，我们计算逃避所有这些条件的概率，作为量子位频率精度的函数。我们发现，如果没有制造后调整，找到可行晶格的概率很快接近 0。然而，通过证明的精度，可以找到具有良好产量的无碰撞晶格。