The Rydberg blockade mechanism is the reason neutral-atom platforms can implement two-qubit entangling gates at all. When one atom is excited to a Rydberg state, its coupling to a neighboring atom shifts the energy of the joint two-photon excitation out of resonance. The neighboring atom cannot be excited simultaneously; it is "blocked." A CZ gate arises naturally from this interaction when you apply a Rydberg pi pulse to the control atom, attempt a 2pi rotation on the target atom (which is suppressed by the blockade), and return the control atom to the ground state. The net effect is a conditional phase flip on the control-target pair.
The theoretical fidelity of this gate depends on how well the blockade condition is satisfied. In practice, achieving high fidelity requires controlling the blockade interaction strength, which scales as 1/r^6 with interatomic distance, and separately controlling the laser pulse shape to minimize leakage to off-resonant intermediate levels. This post describes the engineering we have done on both fronts since our early 2026 baseline measurements.
Diagnosing the dominant error source
When we characterized our CZ gate using gate set tomography on a representative subset of qubit pairs in April 2026, the process matrix showed two distinct error contributions. The first was a phase error that appeared as a systematic rotation around the Z axis in the process matrix, consistent with a calibration offset in the blockade interaction strength. The second was a leakage component: population in states outside the computational subspace at the end of the gate sequence that could not be explained by decoherence alone.
Leakage in neutral-atom Rydberg gates typically traces to one of two places: off-resonant excitation of the intermediate level during the two-photon Rydberg excitation, or incomplete deexcitation leaving population in the Rydberg state. For our strontium-88 system, the two-photon Rydberg excitation pathway goes from 3P0 to 3D2 (at 2.6 microns) and then from 3D2 to the target Rydberg level. The 3D2 intermediate level is not infinitely far detuned for practical pulse durations, and population that transiently passes through it acquires a differential light shift because the 3D2 state has a different polarizability from both the ground and Rydberg states.
We confirmed the leakage attribution by measuring the gate process matrix at several different pulse bandwidths. Narrowing the bandwidth (longer pulses) systematically reduced the leakage contribution without affecting the phase error component, which was consistent with bandwidth-limited off-resonant excitation. Narrowing bandwidth too far introduced its own errors through increased sensitivity to laser frequency noise during the gate. The minimum leakage was found at a pulse duration 40% longer than our original operating point.
DRAG-inspired pulse shaping
The pulse duration fix addressed spectral selectivity but not the leading and trailing edge transients that produce off-resonant excitation during turn-on and turn-off. We implemented a DRAG-inspired pulse shaping protocol on the Rydberg excitation pulses. The original DRAG (Derivative Removal via Adiabatic Gate) technique was developed for superconducting qubit transmon systems to address leakage to the second excited level, but the underlying principle applies here: adding a quadrature component proportional to the derivative of the in-phase envelope shifts the leakage to a different frequency where it interferes destructively with the main excitation pathway.
The implementation required updating the waveform generation on our arbitrary waveform generator to support simultaneous in-phase and quadrature outputs at the Rydberg drive frequency, and calibrating the amplitude of the derivative component empirically. We swept the DRAG coefficient while measuring the leakage contribution using the process tomography and found a clear minimum at a coefficient value consistent with the theoretical prediction for our intermediate level detuning. The calibration is stable over days and is now tracked by our AI calibration loop as a monitored parameter.
Blockade radius calibration
The phase error component that appeared in the process matrix traced to an imprecise calibration of the blockade interaction strength for pairs at different interatomic distances. Our array has a nominal 3-micron site spacing, but the actual distances between loaded atom pairs vary by up to 50 nm due to the finite temperature of atoms in the trap and the discrete loading positions set by the tweezer geometry. For pairs at the design spacing, the blockade interaction strength is well-calibrated. For pairs that differ from nominal by 50 nm, the 1/r^6 scaling means the interaction is off by approximately 10% from the calibrated value. This propagates directly to a gate phase error.
The fix has two parts. First, we improved the precision of site-to-site spacing measurement using high-resolution fluorescence imaging on the cooling transition, which gives position determination to roughly 20 nm. Second, we use per-pair phase corrections stored in a calibration table that is updated at each calibration cycle by the AI calibration layer. Each pair in the 100-atom array that will participate in a two-qubit gate during a particular experimental session receives its own interaction time correction from this table, applied through a slight adjustment to the Rydberg pulse duration for that pair.
This per-pair correction table is one of the more operationally intensive parts of the calibration system. A naive approach would require direct CZ calibration for each pair, which is impractical at 100 qubits. Instead, we measure a sparse set of reference pairs covering a range of interatomic distances and use a physics-informed interpolation model to infer corrections for unmeasured pairs. The interpolation model uses the known 1/r^6 scaling with measured distances as the prior, and the sparse direct measurements as the observations. This reduces calibration overhead from O(N^2) pairs to O(N^0.5) reference pairs while maintaining sufficient accuracy for the correction.
Measured improvement
After implementing these changes and verifying the calibration procedure, we re-ran gate set tomography on the same representative pair subset used for the initial diagnosis. The leakage contribution to the process infidelity dropped from 0.9% to below 0.1%, consistent with the expected improvement from the pulse shaping and bandwidth change. The phase error component dropped from approximately 0.6% to 0.15%, attributed to the per-pair blockade correction. Total CZ process infidelity improved from the baseline by approximately 1.2 percentage points, based on our internal benchmarking data.
The remaining infidelity is now dominated by thermal motion in the trap ground state. Atoms at a finite temperature have a position distribution that adds uncertainty to the interatomic distance and therefore to the blockade interaction strength, in a way that cannot be corrected after the fact. The residual uncertainty limits the achievable fidelity unless the motional state of the atoms is controlled to a lower temperature. This is not a calibration problem; it requires sideband cooling to reduce the motional quantum number of atoms to near zero before two-qubit gate operations.
Sideband cooling: next steps
Resolved-sideband cooling in an optical tweezer has been demonstrated in several research groups for single and few atoms. The protocol requires driving the motional red sideband of the clock transition, which removes one motional quantum per photon scattered. For strontium-88 in an 813 nm tweezer at our typical trap frequencies (100-200 kHz radially), resolved-sideband cooling is accessible with the existing clock laser infrastructure. We are evaluating whether to implement it as a standard pre-gate cooling step for all two-qubit operations or only for selected pairs where higher fidelity is required.
The tradeoff is time overhead. A full sideband cooling sequence to the ground motional state takes approximately 1-2 ms per site, which adds to the experiment cycle time for all protocols involving two-qubit gates. For variational quantum eigensolver experiments with many two-qubit gate layers, this overhead may be acceptable. For shallow circuits, it may not be. We will report results from the sideband cooling implementation when we have characterized the fidelity improvement and the overhead cost on representative circuit types.