Quantum Control Interpolation

---
name: quantum-control-interpolation
category: quantum-systems-engineering
description: Lie algebra-based quantum optimal control interpolation methodology for generating control pulses for arbitrary unitary operations in superconducting qubit systems.
source: arXiv 2606.02014
trigger: quantum control, Lie algebra, pulse generation, superconducting qubits, optimal control interpolation, unitary operations
---

# Lie Algebra-Based Quantum Optimal Control Interpolation

## Trigger Conditions
- Need to generate quantum control pulses for superconducting qubit systems
- Interpolating between pre-computed control solutions for new target operations
- Reducing computational cost of quantum optimal control for repeated operations
- Working with Trotter propagators or time-evolution operators

## Methodology Overview
Combines Lie group theory with feed-forward neural networks to generate quantum optimal control pulses for arbitrary unitary operations. Pre-computes control pulses via Lie group theory, then trains NNs to map target propagators to pulses efficiently.

## Core Steps
1. **Pre-compute control pulses** using Lie group theory for a set of basis unitary operations
2. **Map target propagators** to control parameters via neural network (feed-forward architecture)
3. **Train the NN** on the pre-computed dataset, learning the mapping from target unitary → optimal pulse sequence
4. **Interpolate** for new target operations by running them through the trained network
5. **Validate** pulse fidelities on the target quantum hardware/simulator

## Key Technical Details
- **Target systems**: 2-4 qubit superconducting systems
- **Neural architecture**: Feed-forward NN mapping target propagators to control pulses
- **Applications**: Trotter propagators for neutrino collective flavor oscillations, arbitrary single/multi-qubit gates
- **Advantage**: Once trained, pulse generation is near-instant vs. iterative optimal control methods

## Pitfalls
- Limited by the coverage of the pre-computed training set — extrapolation outside the training manifold may produce poor pulses
- Lie group pre-computation scales poorly with system size (curse of dimensionality)
- NN architecture must respect the geometry of the unitary group (consider using unitary-aware architectures)
- Hardware-specific pulse constraints (amplitude, bandwidth) may require additional post-processing

## Verification
- Check pulse fidelity against target unitary (>99% threshold)
- Validate on actual hardware/simulator with noise models
- Compare gate duration against quantum speed limit benchmarks