alternating-minimization-gate-synthesis

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:

1. Realize desired spin-spin interactions (J_{ij} target matrix)
2. Suppress residual spin-motion entanglement (phase space closure)
3. 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

Usage Pattern

Pattern 1: Uniform All-to-All Gates

When target J_{ij} = J (constant): use global multi-tone control. Amplitude per tone ~ O(1/N), total power scales linearly.

Pattern 2: Structured Targets (qLDPC)

When target J_{ij} follows a sparse graph (e.g., qLDPC Tanner graph): use individually addressed multi-tone control. Gate fidelity depends on graph degree and ion chain topology.

Pattern 3: Nearest-Neighbor

When target J_{ij} = delta(|i-j|,1): simpler synthesis with fewer tones required.

Implementation Steps

1. Define target interaction matrix J_{ij} for N qubits
2. Initialize control field with heuristic (e.g., from single-mode approximation)
3. Alternate optimization: a. Phase optimization: minimize sum_i |delta_i|^2 (phase space closure) b. Amplitude optimization: minimize sum_{i<j} |J_{ij}^actual - J_{ij}^target|^2
4. Verify: check residual spin-motion entanglement < epsilon threshold
5. Compile: convert control field to experimental pulse sequence

Error Handling

• Non-convergence: Increase tone count or relax target interaction pattern
• Mode crowding: For N > 500, use spectral filtering to avoid close mode pairs
• Calibration sensitivity: Add robustness regularization to optimization objective

References

• arXiv:2606.27266 - Large-scale multimode entangling-gate synthesis in trapped-ion systems