: Unlike some simpler methods, PMP is excellent at handling real-world constraints, such as limits on how strong an external electromagnetic field can be. Applications in Quantum Technology PMP is widely used across several modern quantum fields:
: PMP links state and co-state dynamics through a defined Hamiltonian function. In the quantum context, this often relates to the Liouville-von Neumann equation. Maximality Condition : For a control u raised to the * power : Unlike some simpler methods, PMP is excellent
, a tool used to determine the best possible control strategies without needing real-time feedback. Core Concepts of PMP in Quantum Systems PMP provides first-order necessary conditions Maximality Condition : For a control u raised
PMP says the optimal control switches between extreme values (bang-bang) unless singular. It generalizes the classical calculus of variations to
We define the (or Pontryagin Hamiltonian) for quantum control:
for a control law to be optimal. It generalizes the classical calculus of variations to systems with dynamical constraints and bounded control inputs. State & Co-state Dynamics