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