Quantum gate control · Chapter 03
What the simulations establish—and what they leave open
The project has moved from basic control tests to reusable two-qubit calibration. These are ongoing research results from simulation, not hardware demonstrations or a claim that reinforcement learning always beats numerical optimization.
A strong baseline changes the learning problem
The Walsh-basis reproduction includes single-qubit tests and fixed- and random-target two-qubit experiments. Early random-target residual policies could damage an already good analytical pulse. The current accept/reject design protects the retained solution and turns learning into a sequence of bounded calibration proposals.
That protection is important to interpreting the results: with exact fidelity feedback, retained performance cannot decrease by construction. A rising trajectory alone therefore does not establish that the learned proposals are better than other proposal strategies.
Generalization with frozen policies
Each noise condition uses 2,048 held-out target–noise pairs and its own trained controller. The plot starts at the analytical baseline (cycle zero); every subsequent point is a saved evaluation, not a fitted learning curve.
Ten cycles require 561 complete-pulse fidelity evaluations, including the initial reference. The target and detuning remain fixed within each task. These results demonstrate improvement on unseen samples from the training distribution; they do not show one controller transferring between the two noise distributions.
Frozen-policy calibration over ten cycles
View plot data
| Series | Calibration cycle (0 = analytical pulse) | Mean average gate fidelity |
|---|---|---|
| σδ = 5 × 10⁶ rad/s | 0 | 0.733751 |
| σδ = 5 × 10⁶ rad/s | 1 | 0.918987 |
| σδ = 5 × 10⁶ rad/s | 2 | 0.941751 |
| σδ = 5 × 10⁶ rad/s | 3 | 0.951121 |
| σδ = 5 × 10⁶ rad/s | 4 | 0.956065 |
| σδ = 5 × 10⁶ rad/s | 5 | 0.958967 |
| σδ = 5 × 10⁶ rad/s | 6 | 0.960801 |
| σδ = 5 × 10⁶ rad/s | 7 | 0.962021 |
| σδ = 5 × 10⁶ rad/s | 8 | 0.962905 |
| σδ = 5 × 10⁶ rad/s | 9 | 0.963551 |
| σδ = 5 × 10⁶ rad/s | 10 | 0.964093 |
| σδ = 10⁷ rad/s | 0 | 0.488384 |
| σδ = 10⁷ rad/s | 1 | 0.722086 |
| σδ = 10⁷ rad/s | 2 | 0.772601 |
| σδ = 10⁷ rad/s | 3 | 0.799891 |
| σδ = 10⁷ rad/s | 4 | 0.817488 |
| σδ = 10⁷ rad/s | 5 | 0.827919 |
| σδ = 10⁷ rad/s | 6 | 0.833975 |
| σδ = 10⁷ rad/s | 7 | 0.838083 |
| σδ = 10⁷ rad/s | 8 | 0.840908 |
| σδ = 10⁷ rad/s | 9 | 0.843017 |
| σδ = 10⁷ rad/s | 10 | 0.844632 |
| Detuning SD (rad/s) | Baseline | 1 cycle | 10 cycles | Final SD |
|---|---|---|---|---|
| 5 × 10⁶ | 0.733751 | 0.918987 | 0.964093 | 0.047095 |
| 10⁷ | 0.488384 | 0.722086 | 0.844632 | 0.146780 |
More informative feedback helps in a matched test
A separate reproduction compares feedback choices on the same 2,048 held-out tasks at detuning standard deviation 5 × 10⁶ rad/s.
Each controller uses 57 complete-pulse evaluations, but these counts do not include the extra hardware measurements needed to estimate projection features. This task set is different from the ten-cycle evaluation above, so the numbers should not be combined into a single improvement curve.
| Method | Mean fidelity | 10th percentile | Pulse evaluations |
|---|---|---|---|
| Analytical reference | 0.766964 | — | 1 |
| Fidelity-only RL | 0.930154 | 0.829266 | 57 |
| Projection-feedback RL | 0.976065 | 0.965282 | 57 |
The next questions are about evidence and cost
The reported comparisons use exact channel-derived feedback and one training seed. A useful next step is to test whether the advantage survives imperfect measurement, changing noise, and variation across training runs. Another is to compare learned proposals with alternatives under the same evaluation budget.
- Test noisy fidelity estimates: accept/reject decisions need not protect true fidelity when measurements are uncertain.
- Account for the measurement cost of projection feedback, not just the number of candidate pulses.
- Use budget-matched random and numerical-search baselines, and examine difficult lower-tail cases rather than means alone.
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