Superconducting quantum computers are expected to have a lot of identical qubits. Avoiding frequency collision is one of the most important challenges in fixed-frequency-transmon-qubit architectures, given that the spurious hybridization causes an error in quantum gates with smaller detuning between nearest and next-nearest neighboring qubits.
To achieve high-fidelity gates, the qubit frequencies should be well assigned in design and fabrication, and unavoidable fabrication errors are removed by the post-tuning process . In reference , they tune the critical current of a Josephson junction by irradiating laser pulses with feedback of the normal resistance under the assumption that the resistance and the qubit frequency have 1-to-1 correspondence. Thus, high-precision estimation of the qubit frequencies at room-temperature is getting in the heart of quality improvement of an entire system. However, there is another factor to deviate the qubit frequencies.
According to the formula (B1) in , the factors determining the qubit frequency are the capacitance of the electrodes and the junction inductance. We estimate the capacitance from the shape of the electrodes, and we can infer the inductance of the Josephson junction from two parameters: the superconducting gap Delta of the metal used for the junction and the normal-state resistance RN of the junction measurable at room temperature . Even If the normal-state resistance RN of the junction is controlled with laser annealing, superconducting gap fluctuation unmeasurable at room temperature may limit the accuracy of the qubit frequencies.
Here, we focus on whether we can accurately find qubit frequency using the same fabrication conditions and the junction resistanceRNin room temperature measurements. To clarify the relationship between theRNand the qubit frequency, we evaluated the fluctuation of the product of the critical current IC
obtained in low-temperature measurement and junction resistanceRNmeasured at room temperature. We experimentally obtained that ICRNvariation was almost less than 1%. For instance, we try to minimize the frequency variation below 0.5% (1.0% fluctuation for bothRNand ICRN) for all-working 64 qubits in our 8x8 lattice. We found that the variation was almost on the border of our criteria.
We found qubits having relatively largeICRNdeviation as exceptions. They show larger thickness variation in the oxidization layer in the Josephson junction (through TEM measurements) and show broader line widths observed at the qubits of g-e transition (shorter coherence time). We will discuss that reason and strategy for the improvement.
 J. B. Hertzberg, E. J. Zhang, S. Rosenblatt, E. Magesan, J. A. Smolin, J.-B. Yau, V. P. Adiga, M. Sandberg, M. Brink, and J. M. Chow et al., Laser-Annealing Josephson Junctions for Yielding Scaled-up Superconducting Quantum Processors, arXiv:2009.00781.
 Nicolas Didier, Analytical modeling of parametrically-modulated transmon qubits, Phys. Rev. A 97, 022330 (2018)
 Vinay Ambegaokar, Alexis Baratoff, Tunneling Between Superconductors, Phys. Rev. Lett. 10, 486 (1963)
Keywords: quantum, Josephson, superconducting gap