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

Understand

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.