Quantum speed limits from symmetries in quantum control

Abstract In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control Hamiltonians and provide quantitative bounds that can be calculated without solving the controlled system dynamics. In particular we focus on two scenarios: On one hand, we provide bounds on the time that is needed for a control system to implement a given target unitary U and on the other hand we bound the time to implement the most difficult to reach evolution <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> <mml:mi>θ</mml:mi> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> of a target Hamiltonian H s . We apply our abstract bounds on physically relevant systems like coupled qubits, spin chains, globally controlled Rydberg atoms and NMR molecules and compare our results to the existing literature. We hope that our bounds can aid experimentalists to identify bottlenecks and design faster quantum control systems.