| name | alternating-minimization-gate-synthesis |
| description | Alternating-minimization methodology for large-scale multimode entangling-gate synthesis in trapped-ion systems. Use when designing multi-tone control fields for entangling gates, optimizing spin-spin interactions while suppressing spin-motion entanglement, or scaling gate synthesis to large ion chains (N=100-1000). Activation: alternating minimization, gate synthesis, trapped-ion, multimode entangling, multi-tone control, spin-spin interaction, programmable interaction engineering, Mølmer-Sørensen gate, ion chain gate design, quantum gate compilation for trapped-ion |
Alternating-Minimization Gate Synthesis
Methodology from arXiv:2606.27266 for synthesizing large-scale multimode entangling gates in trapped-ion quantum processors.
Core Problem
As ion chains grow (N > 50), the density of collective motional modes makes gate synthesis a high-dimensional non-convex optimization problem with three competing requirements:
- Realize desired spin-spin interactions (J_{ij} target matrix)
- Suppress residual spin-motion entanglement (phase space closure)
- Limit experimental control resources (laser power, bandwidth, tone count)
Alternating-Minimization Strategy
The key insight: decompose the joint optimization into alternating sub-problems, each convex or tractable:
Step 1: Fix control amplitudes, optimize phases to minimize spin-motion residual
Step 2: Fix phases, optimize amplitudes to match target spin-spin couplings
Step 3: Iterate until convergence (typically 10-50 iterations)
This improves numerical stability vs. monolithic gradient descent and scales to N=1000.
Key Results
- All-to-all and nearest-neighbor interaction patterns synthesized for N=1000 ion chains
- Control resources do NOT exhibit rapid growth with system size
- Global laser control only required (no per-ion addressing for uniform targets)
- Extended to individual addressing: structured qLDPC target at N=512 demonstrated
