Quantum Optimal Control via Magnus Expansion and Non-Commutative Polynomial Optimization
arXiv:2001.06464
Abstract
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.
References in corpus (22)
- Simple pulses for elimination of leakage in weakly nonlinear qubits
- Time Optimal Control in Spin Systems
- Roads towards fault-tolerant universal quantum computation
- Quantum Computation as Geometry
- Bounding the set of quantum correlations
- Optimal control technique for Many Body Quantum Systems dynamics
- Chopped random-basis quantum optimization
- Second order gradient ascent pulse engineering
- Gravitational Radiation Detection with Laser Interferometry
- Analytic control methods for high fidelity unitary operations in a weakly nonlinear oscillator
- Effective Hamiltonian models of the cross-resonance gate
- Are there traps in quantum control landscapes?
- Time-optimal control of SU(2) quantum operations
- Robust control of quantum gates via sequential convex programming
- Semidefinite approximations of the matrix logarithm
- Single qubit gates in frequency-crowded transmon systems
- Sufficient conditions for the convergence of the Magnus expansion
- Sparse Noncommutative Polynomial Optimization
- The role of controllability in optimizing quantum dynamics
- Geometric analysis of minimum time trajectories for a two-level quantum system
- A Scheme of Cartan Decomposition for su(N)
- An oracle-based projection and rescaling algorithm for linear semi-infinite feasibility problems and its application to SDP and SOCP