Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Structured Quantum Optimal Control under Bandwidth and Smoothness Constraints-An Inexact Proximal-ADMM Approach for Low-Complexity Pulse Synthesis

Ziwen Song

Abstract

Quantum optimal control is often judged by nominal fidelity alone, even though realistic pulse-design studies must also account for bandwidth, amplitude, and smoothness constraints. I study this structured-control regime with an inexact Proximal-ADMM framework that combines gate-infidelity minimization with $L_1$ sparsity, total-variation regularization, explicit band-limit projection, and box constraints in a single loop. The method is benchmarked against GRAPE, standard Krotov, and L-BFGS-B on a single-qubit $X$ gate, a leakage-prone qutrit task, and a two-qubit entangling gate. Across ten random seeds, Pareto scans, ablations, filtered-baseline fairness checks, significance analysis with false-discovery-rate correction, and robustness tests, the method is not a universal winner in either nominal fidelity or wall-clock cost. Its value is instead to expose and stabilize a low-complexity frontier of the fidelity-complexity landscape. After retuning the PADMM budgets and warm-start lengths, the qutrit and two-qubit structured fidelities rise to 0.6672 +- 0.0001 and 0.6342 +- 0.0003, respectively, while preserving markedly lower complexity than unconstrained quasi-Newton solutions. These values remain well below deployment-grade gate thresholds, so the contribution should still be read as a numerical framework for constrained pulse synthesis rather than as a finished route to immediately deployable high-fidelity gates. Training-time robust optimization yields only task-dependent gains, with the clearest effect appearing in qutrit drift robustness and amounting to a small absolute improvement. The results therefore position PADMM as a constraint-native framework for low-complexity frontier exploration, not as a replacement for unconstrained high-fidelity solvers.

Structured Quantum Optimal Control under Bandwidth and Smoothness Constraints-An Inexact Proximal-ADMM Approach for Low-Complexity Pulse Synthesis

Abstract

Quantum optimal control is often judged by nominal fidelity alone, even though realistic pulse-design studies must also account for bandwidth, amplitude, and smoothness constraints. I study this structured-control regime with an inexact Proximal-ADMM framework that combines gate-infidelity minimization with sparsity, total-variation regularization, explicit band-limit projection, and box constraints in a single loop. The method is benchmarked against GRAPE, standard Krotov, and L-BFGS-B on a single-qubit gate, a leakage-prone qutrit task, and a two-qubit entangling gate. Across ten random seeds, Pareto scans, ablations, filtered-baseline fairness checks, significance analysis with false-discovery-rate correction, and robustness tests, the method is not a universal winner in either nominal fidelity or wall-clock cost. Its value is instead to expose and stabilize a low-complexity frontier of the fidelity-complexity landscape. After retuning the PADMM budgets and warm-start lengths, the qutrit and two-qubit structured fidelities rise to 0.6672 +- 0.0001 and 0.6342 +- 0.0003, respectively, while preserving markedly lower complexity than unconstrained quasi-Newton solutions. These values remain well below deployment-grade gate thresholds, so the contribution should still be read as a numerical framework for constrained pulse synthesis rather than as a finished route to immediately deployable high-fidelity gates. Training-time robust optimization yields only task-dependent gains, with the clearest effect appearing in qutrit drift robustness and amounting to a small absolute improvement. The results therefore position PADMM as a constraint-native framework for low-complexity frontier exploration, not as a replacement for unconstrained high-fidelity solvers.
Paper Structure (14 sections, 18 equations, 8 figures, 12 tables)

This paper contains 14 sections, 18 equations, 8 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Model and method
  3. Discrete-time control model
  4. Structured pulse objective
  5. Variable splitting and inexact PADMM updates
  6. Warm-starting and robust training
  7. Numerical experiments
  8. Reproducibility protocol
  9. Main benchmark
  10. Pareto scans, ablations, and sensitivity
  11. Fairness checks against filtered baselines
  12. Post-training robustness and robust optimization
  13. Discussion
  14. Conclusion

Figures (8)

  • Figure 1: Main benchmark summary. Panels show ten-seed means for (a) nominal fidelity, (b) bandwidth excess, and (c) total variation across the five baseline methods. Error bars denote standard errors across seeds; full standard deviations are listed in the benchmark table.
  • Figure 2: Fidelity-complexity Pareto fronts. Panels show the qutrit and two-qubit tasks; pale points denote scanned PADMM configurations, the dark curve marks the non-dominated front, and colored symbols indicate baseline methods.
  • Figure 3: Constraint-component ablation of PADMM. Panels (a)-(c) correspond to the single-qubit, qutrit, and two-qubit tasks. Marker position encodes bandwidth excess and final fidelity, while marker area scales with total variation.
  • Figure 4: Selected PADMM sensitivity scans. Panels (a)-(c) correspond to the single-qubit, qutrit, and two-qubit tasks, while symbol color and shape indicate the hyperparameter family being varied.
  • Figure 5: Post-training robustness benchmark. Panels (a)-(c) correspond to the single-qubit, qutrit, and two-qubit tasks and show ten-seed mean fidelities under nominal dynamics, detuning, amplitude error, and control drift. Error bars denote standard errors across seeds.
  • ...and 3 more figures