Quantum Optimal Control via Magnus Expansion: The Non-Commutative Polynomial Optimization Problem
Jakub Mareček, Jiří Vala · arXiv (Cornell University) · 2020
Quantum optimal control has important applications in quantum computing. For example in transmon qubits, two-qubit gates are implemented by shaping a microwave pulse. More generally, one can replace the application of an entire quantum circuit with a control signal. Two major challenges 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. We present first globally convergent methods for quantum optimal control. 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. This makes it possible to revisit much of what is done in quantum computing.