As superconducting quantum processors increase in complexity, techniques to overcome constraints on frequency crowding are needed. The recently developed method of laser-annealing provides an effective post-fabrication method to adjust the frequency of superconducting qubits. Here, we present an automated laser-annealing apparatus based on conventional microscopy components and demonstrate preservation of highly coherent transmons. In addition, we perform noise spectroscopy to investigate the change in defect features, in particular, two-level system defects, after laser-annealing. Finally, we present a local heating model as well as demonstrate aging stability for laser-annealing on the wafer scale. Our work constitutes an important step toward both understanding the underlying physical mechanism and scaling up laser-annealing of superconducting qubits.

Superconducting quantum processors are a promising platform for realizing large-scale universal quantum computation.^{1} In comparison to other physical platforms,^{2–6} superconducting quantum processors are lithographically configurable, which allows a rich variety of qubit structures and feasible scalability, currently up to ∼100 qubits.^{7,8} Superconducting qubits require the Josephson junction (JJ), a nonlinear inductive element composed of two superconductors with a tunneling barrier in between.^{9,10} A capacitively shunted JJ forms the transmon qubit, a widely utilized superconducting qubit with advantages ranging from high coherence to simple coupling and readout.^{11,12} As quantum processors scale up further, precise fabrication of the JJ is required to avoid qubit frequency allocation problems that can lead to frequency collisions or slow entangling gates.^{13–15} However, the current state-of-the-art JJ fabrication methods exhibit $\u223c1%$ dispersion on a $1\u2009cm2$ chip.^{16} This does not satisfy the frequency constraints for a fixed-frequency multiqubit processor with even a few tens of qubits. One effective technique to circumvent this problem is post-fabrication laser-annealing, in which a laser beam is applied to the JJ in order to tune the qubit frequency.^{17,18} In this work, we build upon this technique and present a laser-annealing apparatus with conventional confocal microscopy components, allowing integration into various qubit preparation processes. We demonstrate that high coherence of fixed-frequency transmon qubits is maintained after frequency shifting by laser-annealing. Furthermore, we perform noise spectroscopy on one qubit in order to investigate the change in the two-level system (TLS) density after laser-annealing. Finally, we perform laser-annealing on 100 mm wafers with varying parameters and explain the results by using a local heating model as well as demonstrate that the effects of laser-annealing are preserved even after an extended period of JJ aging.

In order to facilitate integration into various qubit preparation processes, we present a laser-annealing apparatus based on confocal microscopy [schematically shown in Fig. 1(a)]. A continuous, collimated laser beam follows the optical path depicted by the green arrows and first passes through a shutter that serves as a switch and then a neutral density (ND) filter that adjusts the beam power. The beam is then expanded and focused onto the sample stage in order to minimize the beam spot. The motorized stage automatically positions the sample on the focal plane using image detection algorithms. Imaging is performed with a CMOS camera and a white light source (not shown). This automation enables laser-annealing of both individual chips as well as 100 mm wafers with 3000 JJ.

The sample under investigation is composed of four independent transmon qubits each at different frequencies and capacitively coupled to a coplanar waveguide resonator (RO). A representative qubit-RO pair is shown in Fig. 1(b). The qubit consists of a Nb coplanar capacitor that shunts an Al/Al-O_{x}/Al JJ [Fig. 1(c)]. The JJs are shadow evaporated using the Manhattan style technique with typical areas of $\u223c0.1\u2009\mu m2$. The JJ areas are varied to separate the frequencies of the four qubits. The qubits are driven and read out through the readout bus. Further details regarding the setup and fabrication are given in the supplemental material.

Across three samples, we directly expose the JJs of five transmon qubits at 40 mW and investigate the response in normal state resistance $RN$ at room temperature and the resulting shift in qubit frequency $fQ$ at ∼20 mK. We designate one qubit per chip as the control qubit which is not annealed during the laser-annealing step. We measure $RN$ using a lock-in two-point voltage probe with the probing needles electrically contacting the Nb capacitors. From $RN$, we utilize the Ambegaokar–Baratoff formula to calculate the critical current $IC$, nominally around 35 nA.^{19} Applying the transmon-regime approximation with $IC$, the predicted qubit frequency in the superconducting state is given by

where *h* is Planck's constant, *e* is the electron charge, $\Delta Al$ is the Al superconducting gap (=170 *μ*eV), and $EC$ is the charging energy of the transmon ($EC/h\u223c275\u2009MHz$).^{7} We expect laser-annealing to increase $RN$ and resultantly shift down $fQ$, while $\Delta Al$ and $EC$ remain constant. The qubit frequencies are measured using conventional two-tone spectroscopy and Ramsey sequences.^{7}

The normalized change in qubit frequency ($\Delta f/f0$) is plotted as a function of change in normal state resistance ($\Delta R/R0$) in Fig. 1(d), where *f*_{0} and *R*_{0} are the initial frequency and resistance. The prediction (gray dashed line) is given by $\Delta fQ/fQ,0=(\u22121/1.9)\Delta R/R0$. This is derived from Eq. (1) using $\Delta R/R0\u226a1$, which gives a slope of $(\u22121/2)/[1\u2212(e2RNEC)/(h\Delta Al)]\u2248(\u22121/1.9)$. Both unannealed (black cross) and laser-annealed (green circles) qubits follow the trend of the prediction, with a controlled frequency downshift for the laser-annealed qubits. The frequency shift of the four unannealed qubits, due to air reexposure during the laser-annealing step and frequency fluctuations across cryostat cooldowns, average to zero with a variation of $\xb10.3%$.^{20} The resistance drift of the unannealed qubits may be due to electrical contact variations across multiple resistance probings, while the discrepancies between prediction and measurement may be due to differences between the expected and actual values of $\Delta Al$ and $EC$.

We have so far demonstrated tunability of qubit frequency using laser-annealing. We now evaluate, for the five qubits shown in Fig. 1(d), the qubit relaxation ($T1$) and phase coherence ($T2$) times, which are highly sensitive to degradation in the material quality.^{21} To study the statistical features, we acquire the $T1$ [Fig. 2(a)] and $T2$ [Fig. 2(b)] of the transmons for ∼17 h before and after laser-annealing. Across the five qubits, the change in $T1$ ($T2$) is $8.5\xb138.1\u2009\mu s$ ($0.1\xb130.9\u2009\mu s$). Furthermore, the coherence means of laser-annealed qubits Q1_{L}–Q5_{L} (stars in green boxes) lie within or above three standard deviations of the means of Q1–Q5 (caps of white boxes), indicating no statistically significant decrease in coherence. On average, the $T1$ of Q1_{L}–Q5_{L} meets the current standards for high coherence times of ∼100 *μ*s.^{22} These results verify that our setup performs controlled frequency shifts while preserving high qubit coherence.

Several different noise sources can limit qubit coherence, such as dielectric loss, quasi-particle tunneling, and cosmic radiation.^{22–24} In particular, losses due to dielectrics at the interfaces of superconducting qubits can potentially induce energy relaxations.^{21} The source for dielectric losses can be modeled by an ensemble of two-level systems (TLSs) which are distributed in a broad microwave range with transition frequencies $fTLS$ and coupling *g* to the qubit.^{25,26} The qubit relaxation rate $\Gamma 1=1/T1$ increases, the closer $fQ$ is to $fTLS$. In particular, $\Gamma 1$ follows a Lorentzian profile with respect to qubit-TLS detuning $\Delta =fQ\u2212fTLS$: $\Gamma 1=(2\Gamma g2)/(\Gamma 2+\Delta 2)+\Gamma 1,Q$, where Γ is the sum of TLS and qubit energy relaxation and dephasing rates and $\Gamma 1,Q$ is the frequency-independent qubit energy relaxation rate.^{21,27} Hence, a spectral and temporal sweep of qubit *T*_{1}, or TLS spectroscopy, can probe the noise environment of a transmon qubit.^{28–31}

We perform TLS spectroscopy on Q5 before and after laser-annealing in order to detect changes in the TLS density. We do so by AC Stark shifting the qubit using an off-resonant tone of frequency $fQ\xb180\u2009MHz$.^{30} In contrast to Q1–Q4, Q5 has an additional coplanar waveguide (CPW) to drive the qubit, which is necessary since the frequency shift is proportional to the square of the tone amplitude; hence, higher delivered power is required in comparison to driving through the readout bus.^{32} With this configuration, we are able to reliably shift $fQ$ by ±33 MHz, measured by a Ramsey sequence. For fast acquisition, we measure the average excited state population $P|1\u27e9$ around $T1$.^{33}

TLS spectroscopy (160 h of continuous measurement) is shown both before [Fig. 3(a)] and after [Fig. 3(b)] laser-annealing. In Fig. 3(a), one consistent and several fluctuating (dark areas) TLS features are observed close to the initial qubit frequency $fQ$. Fitting to the Lorentzian, we find that the consistent feature is coupled to the qubit with *g *=* *76 kHz and lies 7.81 MHz away from $fQ$, which is more than three linewidths away from $fTLS$. The low coupling and large spectral distance make it unlikely for this single feature to solely limit the qubit coherence. In order to quantify the change in TLS densities, we sum the number of Lorentzian dips across all traces and divide by the total number of traces and the bandwidth of 66 MHz. We observe a small decrease from $0.10\xb10.03\u2009MHz\u22121$ to $0.09\xb10.03\u2009MHz\u22121$, before and after laser-annealing. This decrease in TLS density that we observe is consistent when we thermal cycle the cryostat twice before laser-annealing and twice after (see the supplemental material).^{34,35} Interestingly, we observe a statistically significant increase in both *T*_{1} (46.5 *μ*s to 95.0 *μ*s) and *T*_{2} (29.0 *μ*s to 49.8 *μ*s) after laser-annealing for Q5. We suggest that the increase in coherence may be due to the qubit frequency shifting into a different spectral environment with lower TLS density after laser-annealing. Additional studies with a wider spectral range as well as studies of other parasitic modes characteristic to the circuitry are needed to investigate this. However, the constancy of the TLS densities supports the observation that qubit coherence times are preserved after laser-annealing.

We now investigate the response of $RN$ to lasing parameters at the wafer-scale in order to understand the laser-annealing mechanism. This is enabled by the automated JJ image recognition of our setup, which positions and focuses the JJ with respect to the beam within 20 s.^{36} We utilize JJ test wafers with 3000 junctions similar to Ref. 16. Across multiple wafers, we study the effects of lasing power, spot displacement, and junction aging. Effects of lasing exposure time, repetition, and a summary of all parameters for each study are shown in the supplemental material.

Based on the previous studies of JJ thermal annealing, we hypothesize that laser-annealing locally heats the JJ and thickens the tunneling barrier, thereby increasing $RN$.^{37–39} We first verify local heating by measuring the normalized resistance change ($\Delta R/R0$) of JJs with three different areas with respect to lasing power [Fig. 4(a)]. Here, the spot directly exposes each JJ for 60 s. The normalized resistance change follows an exponentially plateauing function (red dashed line) that caps at $\Delta R/R0=1.8%$. This trend is similar to that of low temperature ($<150\u2009\xb0C$) thermal annealing of JJs demonstrated by Refs. 40–42. In order to understand the JJ temperature as a function of lasing power, we simulate the temperature (*T*) of a JJ directly illuminated by a Gaussian beam with a waist 0.81 *μ*m of varying power (*P*) using COMSOL Multiphysics. We observe a linear increase $T(P)=2.47P+20\u2009\xb0C$ that reaches ∼$120\u2009\xb0C$ at $P=40\u2009mW$. The resistance change at this simulated temperature is similar to the $\Delta R/R0$ observed in thermal annealing studies at this temperature regime.^{40–42} Extending this comparison, we expect a rapid increase in $RN$ for lasing powers exceeding 50 mW with our setup. These lasing powers correspond to JJ temperatures $>150\u2009\xb0C$ [as given by *T*(*P*)], at which accelerated growth of $RN$ has been observed.^{40–42}

Next, we investigate the heat absorption mechanism by studying the normalized resistance change with respect to laser spot displacement (*D*) from the JJ. Here, each JJ is exposed at 40 mW for 60 s. The displacement is measured from below the junction center, as shown in the inset of Fig. 4(b). We observe that the measured $\Delta R/R0$ is maximized at a displacement of 4 *μ*m, which corresponds to the extension length of the Al electrodes beneath the JJs. This is due to two competing effects: increased reflection from Al/Al-O_{x} as displacement is reduced and decreased heat transfer from the Si substrate as displacement is increased. We model the power loss from reflection by calculating the absorbed power with respect to displacement using Gaussian beam integration. We then multiply this with an exponentially decaying function $H(D)=A\u2009exp\u2009(\u2212D/D0)+B$ that models heat transfer, where *D*_{0} is a characteristic decay length for thermal conduction (see the supplemental material).^{43,44} We use this product function to fit the data (red dashed line). The reflection is minimized at $D>$ 4 *μ*m and *D*_{0} = 9.5 *μ*m, resulting in a maximum fitted $\Delta R/R0$ at *D *=* *5 *μ*m. The kink at *D* = 4 *μ*m is due to the increased absorption as the spot moves away from the Al electrode and onto the Si. It can also be seen that when the beam is placed more than 30 *μ*m away from the JJ, the change in resistance approaches that of unannealed JJs (gray dashed line). In other words, $RN$ is unaffected by a beam displaced more than 30 *μ*m. This demonstrates the locality of the laser heating on the sub-millimeter length scale.

Based on the measurements, we suggest that the laser beam locally heats the JJs through the Si substrate. Heat absorption has been proposed to thicken the JJ tunnel barrier in studies based on thermal annealing.^{37} Therefore, we measure the barrier thickness using high resolution transmission electron microscopy and fit the area-normalized $RN$ to the exponential of barrier thickness (see the supplemental material).^{45} From the fit, we estimate that a 30% change in $RN$ can originate from a ∼Å change in the tunnel barrier thickness. However, due to the non-uniformity of the barrier (dispersion $\u223c0.4\u2009nm)$, we are unable to detect the estimated increase in thickness (0.04 nm) caused by laser-annealing. This non-uniformity makes it unlikely for a simple barrier thickening model to fully explain the microscopic mechanism. Instead, consideration of other microscopic factors, such as barrier height and chemical composition changes at the Al/Al-O_{x} interface, is needed.^{39,46}

Finally, we study how robust laser-annealing is with respect to aging. JJ aging refers to the increase in $RN$ with exposure to air in time.^{37} While aging is currently unavoidable, it is important that the resistance difference between laser-annealed and unannealed JJs is conserved for an extended period of time. For superconducting qubits, this translates to maintaining frequency differences between different qubits, which is important for frequency allocation. We study the impact of aging on laser-annealing as follows. We prepare two wafers, one with newly fabricated JJs (wafer 1) and the other with 130 day aged JJs (wafer 2). Since aging exhibits exponentially plateauing behavior, the maximally aged JJs of wafer 2 serve to show the drift in $RN$ when aging effects are minimal.^{16} For each wafer, we probe the resistance of unannealed and laser-annealed JJs for a period of 30 days, stored in atmosphere. All four data groups are fit to an exponentially plateauing aging function, with the fit parameters given in the supplemental material. As can be seen in Fig. 4(c), aging effects are pronounced for wafer 1 (16%) in comparison to wafer 2 (7%). However, on average, the difference in resistance change between unannealed and laser-annealed JJs for each wafer is maintained even after 30 days of aging. This demonstrates that resistance differences induced by laser-annealing are preserved even after an extended period of aging.

In conclusion, we have constructed an automated laser-annealing apparatus using conventional microscopy components and demonstrated reliable frequency tuning of fixed-frequency transmon qubits. The high coherence of our transmons is preserved after laser-annealing. We have further performed TLS spectroscopy to investigate the change in defect features after laser-annealing. The coherence increase observed for this qubit may open possibilities toward treating defective qubits on multiqubit quantum processors using laser-annealing and TLS spectroscopy.

Furthermore, we have scaled up laser-annealing and studied the effects of lasing parameters at the wafer scale as well as demonstrated robustness against aging. With this, we have put forth a model of local heating through the Si substrate. Additional studies with a change or etching of substrate underneath the JJ can help verify this model.^{47–49} Further studies are needed to correlate normal-state resistance to JJ barrier thickness. This can be realized using different JJ geometries or different JJ materials. Efforts in this direction are necessary since a thorough understanding of each fabrication and treatment step is ultimately required as qubit coherence times are pushed higher into the millisecond regime.

See the supplementary material for the description on the laser-annealing automation and device fabrication, as well as for supplemental figures and tables referenced in the text.

The authors thank B. Marinelli for useful discussions regarding TLS. This work was funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05-CH11231 “High-Coherence Multilayer Superconducting Structures for Large Scale Qubit Integration and Photonic Transduction program (QIS-LBNL).” Comsol simulations were performed in the Molecular Graphics and Computation Facility at UC Berkeley, which was funded by the Kavli Institute and NIH S10OD023532. Focused ion beaming (FIB) for HRTEM was conducted at the Surface Analysis Lab at University of Utah by Brian Van Devener and Randy C. Polson.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Hyunseong Kim:** Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (lead); Software (equal); Supervision (equal); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). **John Mark Kreikebaum:** Data curation (supporting); Software (supporting). **D Frank Ogletree:** Formal analysis (supporting); Funding acquisition (supporting); Resources (equal); Writing – review & editing (supporting). **David I. Santiago:** Funding acquisition (supporting). **Irfan Siddiqi:** Funding acquisition (lead); Project administration (supporting); Resources (equal). **Christian Jünger:** Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (equal). **Alexis Morvan:** Conceptualization (lead); Formal analysis (supporting); Investigation (supporting); Project administration (supporting); Supervision (equal); Validation (equal); Visualization (supporting); Writing – review & editing (supporting). **Edward Simon Barnard:** Data curation (supporting); Investigation (supporting); Software (equal); Writing – review & editing (supporting). **William Peter Livingston:** Data curation (supporting); Formal analysis (supporting); Software (equal); Validation (equal); Writing – review & editing (supporting). **M. Virginia Altoé:** Data curation (supporting); Investigation (supporting). **Yosep Kim:** Formal analysis (supporting); Project administration (supporting); Supervision (equal); Visualization (supporting); Writing – review & editing (supporting). **Chengyu Song:** Data curation (supporting). **Larry Chen:** Data curation (supporting); Software (supporting).

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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_{x}-Al/Nb Josephson junctions. III. Annealing stability of AlO

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_{x}-Nb tunnel junctions

_{x}barriers in Al/AlO

_{x}/Al Josephson junctions