# Quantum Optimal Control via Magnus Expansion and Non-Commutative Polynomial Optimization

arXiv: https://arxiv.org/abs/2001.06464 · HTML: https://mlsanity.com/paper/2001.06464/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [Learning quantum Hamiltonians at any temperature in polynomial time with Chebyshev and bit complexity](https://mlsanity.com/paper/2402.05552/) (2024)

## Abstract (arXiv)

Quantum optimal control has numerous important applications ranging from pulse shaping in magnetic-resonance imagining to laser control of chemical reactions and quantum computing. Our objective is to address two major challenges that have limited the success of applications of quantum optimal control so far: non-commutativity inherent in quantum systems and non-convexity of quantum optimal control problems involving more than three quantum levels. Methodologically, we address the non-commutativity of the control Hamiltonian at different times by the use of Magnus expansion. To tackle the non-convexity, we employ non-commutative polynomial optimisation and non-commutative geometry. As a result, we present the first globally convergent methods for quantum optimal control.