Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors

The paper addresses the challenge of realizing robust large-scale quantum information processors, where high-fidelity gates, strong connectivity, low crosstalk, and favorable quantum volume are required. Fixed-frequency transmon lattices are promising due to insensitivity to charge/flux noise and improving coherence times. However, frequency crowding threatens scalability, particularly for the cross-resonance (CR) two-qubit gate, whose performance depends sensitively on the detuning between control and target qubits. Incorrect detunings lead to frequency collisions that suppress the ZX interaction or introduce undesirable Hamiltonian terms (e.g., ZZ), degrading fidelity. Achieving precise qubit frequencies requires tight control over Josephson junction critical current and resistance. While junction resistance can be measured precisely and relates to critical current via the Ambegaokar–Baratoff relation, state-of-the-art as-fabricated resistance precision (~2%) translates to frequency imprecision (~1%), insufficient for large-scale lattices, which often require fractional frequency precision of ~0.25–0.5%. The authors introduce an adaptive post-fabrication trimming technique based on selective laser annealing to incrementally increase junction resistance and thereby tune qubit frequency. They demonstrate improved frequency precision limited by the residual imprecision of predicting frequency from resistance. To assess scalability, they develop a statistical yield model of frequency collisions vs. frequency precision across different lattice topologies (square, heavy-square, heavy-hexagon) and code distances, finding conventional fabrication leads to near-zero yields at scale, whereas the demonstrated tuning precision enables collision-free, error-correction-capable lattices (e.g., distance-3 and -5 heavy-hexagon) with favorable yield.

Chip fabrication: Test chips were fabricated with Nb microwave elements (~200 nm) on Si, each transmon coupled to a half-wave readout resonator and not directly to other qubits. All transmon capacitors and junctions were designed identically, with junctions patterned by electron beam lithography and realized via double-angle Al deposition and oxidation, targeting Ic ~30 nA and anharmonicity ~330 MHz. Of 36 qubits, 3 were damaged during packaging; 2 of the remaining were left un-tuned as controls, and 31 were used for tuning demonstrations.

Selective laser anneal (LASIQ) for resistance tuning: An integrated rework system measures and modifies the junction normal resistance Rn at room temperature via four-point probing on the transmon capacitor pads. A diode-pumped solid-state laser frequency-doubled to 532 nm provides anneal power (approximately 1.7–2.0 W) controlled by a waveplate and polarizing beam splitter with feedback from a silicon photodiode. A precision-timed shutter provides exposures of ~0.3–10 s per anneal. Beam alignment is performed via pattern recognition and a piezo-controlled mirror. The beam is shaped into a four-spot pattern and relayed to avoid direct junction illumination while heating the surrounding substrate uniformly (spot diameter ~4 μm). Calibration on 126 junctions established nonlinear relationships between laser power, exposure duration (total 2–80 s), and Rn shifts up to ~15%.

Adaptive tuning process: For each junction, a target Rn is selected based on a pre-established correlation f(Rn) derived from measured data. Since anneal only increases Rn, targets are chosen above initial Rn. Anneals are applied incrementally, with Rn measured after each pulse, using pre-calibrated power/duration steps to monotonically approach the target without overshoot. Junctions requiring larger shifts undergo repeated anneals. The control algorithm terminates when measured Rn is within 0.3% of the target. In a separate precision trial, >300 junctions were tuned to targets ranging from 0.4% to 14.5% above initial values and landed within the 0.3% margin, independent of target Rn. The expected translation of 0.3% Rn precision is ~0.15% in transmon frequency.

Frequency measurement and correlation: On a test vehicle with 31 identically fabricated transmons, qubit frequencies were measured in a dilution refrigerator using dispersive readout and Ramsey fringes, achieving <100 kHz precision. Post-anneal frequencies were remeasured; two qubits had reduced SNR and were measured via CW spectroscopy (~2 MHz precision). Room-temperature junction resistances were measured after warm-up.

Monte Carlo frequency-crowding model: Lattice topologies examined include square, heavy-square, and heavy-hexagon at code distances d=3, 5, and 7. Lattices are assigned frequency patterns of 3–5 setpoints (e.g., f1=5.00 GHz, f2=5.07 GHz, f3=5.14 GHz, etc.). Actual qubit frequencies are sampled from normal distributions centered at setpoints with standard deviation σf. Frequency collisions are counted according to seven dominant conditions (nearest- and next-nearest-neighbor degeneracies and forbidden regions), with bounds estimated from CR gate effective Hamiltonian models and typical gate parameters (e.g., type 1: |fi,01−fk,01|<17 MHz; type 2: |fi,02−2 fk,01|<4 MHz; type 3: |fi,01−fk,12|<30 MHz; types 5–7 bounds based on types 1 and 3; type 4 forbids control frequencies below target 12 transition or vice versa). For counting, the higher-frequency qubit in a pair is designated control to avoid unnecessary type-4 counts. For each σf, spacings between setpoints are swept to minimize collisions, then statistics are built over many repetitions (typically 1000; more for rare-event yield estimates). Outputs include mean number of collisions and fraction of collision-free trials (yield). A simplified yield model approximates the collision-free condition as requiring each qubit to lie within a fixed window ±Δf around its setpoint, yielding an expression of the form (Δf/σf)^N e^(−dx), from which Δf is fit for each lattice.

• As-fabricated frequency precision: For 31 identically fabricated transmons, σf = 132.3 MHz (2.3% of the median frequency). Junction resistance spread σRn = 365 Ω (4.6%). Fractional σf is exactly half of fractional σRn, consistent with Ambegaokar–Baratoff and transmon theory. The f–Rn correlation follows the expected inverse relation; residual scatter about the fit corresponds to 14.5 MHz (≈0.25% of median frequency), attributable to variations in Δ or C and/or small measurement systematics.
• Post-fabrication tuning: Using selective laser anneal, 31 qubits were tuned into two target resistance groups with medians 7.984 kΩ (N=16) and 8.798 kΩ (N=15), achieving σRn = 51 Ω (≈0.61%). The corresponding qubit frequency groups have medians 5.430 GHz and 5.7046 GHz. Overall post-tuning frequency imprecision is σf = 14.0 MHz (fractional ≈0.25%), nearly matching the 14.5 MHz residual prediction error from f(Rn). This represents a 9.5× reduction in σf compared to initial fabrication.
• Collision modeling and yields: Monte Carlo modeling across lattice types and sizes shows strong dependence of collision incidence on σf. • For d=5 at σf = 10 MHz: square (5-frequency) has ~5 mean collisions and ~0.8% yield; heavy-square (3-frequency) ~0.1 mean collisions and ~90% yield; heavy-hexagon (3-frequency) ~0.1 mean collisions and ~92% yield. • For d=5 targeting 10% yield: square requires σf < 8 MHz; heavy-square requires σf ≈ 16 MHz; heavy-hexagon requires σf ≈ 17 MHz. • With as-fabricated σf = 132.3 MHz: heavy-hexagon d=3 yields ~0.1% collision-free chips; other lattices/scales <0.1% yield. • With demonstrated σf = 14.0 MHz (this work): predicted yields (Table 2): heavy-hexagon d=3: 70% yield (mean collisions 0.4); heavy-square d=3: 67% (0.4); heavy-hexagon d=5: 33% (1.2); heavy-square d=5: 27% (1.5); heavy-hexagon d=7: 8% (2.7); heavy-square d=7: 6% (3.5); square lattices remain <0.1% yield at d=5 and d=7. • Fixed-window model fits yield Δf windows on the order of ~30 MHz for heavy-square/hexagon (e.g., heavy-hexagon d=5: Δf ≈ 29.91 MHz).
• Scaling outlook: The demonstrated σf ≈ 14 MHz supports practical yields up to ~100–200 qubits for heavy-hexagon lattices. Extrapolation indicates roughly a 2× further precision improvement (to ~6–8 MHz) is needed to sustain favorable yields approaching ~1000 qubits.

The study directly tackles frequency crowding in fixed-frequency transmon architectures by introducing an adaptive, localized, post-fabrication tuning method (LASIQ) that reduces qubit frequency spread from ~132 MHz to ~14 MHz. This precision aligns with the limit set by the ability to predict frequency from resistance, indicating the tuning process itself can be highly precise. By cataloging seven principal frequency collision mechanisms (including nearest- and next-nearest-neighbor degeneracies and weak ZX regions) and defining forbidden frequency windows, the authors connect frequency precision to two-qubit CR gate error susceptibility. Monte Carlo modeling across different lattice topologies shows that heavy-hexagon and heavy-square lattices using three carefully spaced frequency classes are significantly more robust to frequency imprecision than square lattices requiring five classes. With σf ≈ 14 MHz, collision-free distance-3 and distance-5 heavy-hexagon/square lattices are predicted at favorable yield, enabling practical error-correction experiments and high quantum volume operation. The results rationalize current hardware design choices (e.g., IBM’s heavy-hexagon systems) and quantify precision requirements for future scaling. Extrapolation suggests that to support ~1000-qubit collision-free lattices, an additional ~2× improvement in precision is necessary, motivating refinements in both tuning resolution and resistance-to-frequency prediction, and more precise, threshold-targeted collision definitions tied to gate error models.

This work demonstrates an adaptive laser-annealing technique (LASIQ) for post-fabrication tuning of Josephson junctions, achieving nearly an order-of-magnitude improvement in transmon frequency precision (σf ≈ 14 MHz) over conventional fabrication. The method aligns with the fundamental limit set by frequency prediction from measured junction resistance and enables arranging qubit frequencies to avoid frequency collisions that degrade cross-resonance gate performance. A comprehensive statistical model quantifies collision probabilities across lattice types and code distances, showing that three-frequency heavy-hexagon and heavy-square lattices attain substantially higher collision-free yields than five-frequency square lattices at realistic σf. The demonstrated precision enables fabrication of collision-free distance-3 and -5 heavy-hexagon lattices with favorable yield and is currently employed in operational systems. For next-generation systems scaling toward ~1000 qubits, the analysis indicates a need for roughly 2× further improvement in frequency precision and enhanced resistance-to-frequency prediction accuracy. Future work should refine tuning granularity, improve modeling of gate-error-based collision windows, and explore process improvements to reduce variability in superconducting gap and capacitance.

• The laser anneal increases junction resistance; tuning is one-sided, so targets must be above initial Rn.
• Frequency prediction from resistance has a residual imprecision (~14.5 MHz) due to device-to-device variations (e.g., superconducting gap Δ, capacitance C) and measurement systematics, which currently limits achievable σf.
• Collision bounds for next-nearest-neighbor interactions (types 5–7) are assumed based on nearest-neighbor models; precise thresholds tied to target error rates are not experimentally validated here.
• Gate errors are inferred from models and frequency windows rather than measured across large coupled lattices in this study.
• The test vehicle qubits are uncoupled; while suitable for frequency statistics, full-system behavior with buses and crosstalk is modeled rather than directly measured.
• Some measurements (two qubits) had reduced readout precision (~2 MHz) due to instrumentation changes, though this is small relative to σf.
• Potential long-term drift in Rn after anneal reported in literature did not limit this study but remains a consideration for long-term stability.