On optimum Hamiltonians for state transformations. (English) Zbl 1085.81022
J. Phys. A, Math. Gen. 39, No. 11, L167-L170 (2006); corrigendum ibid. 40, No. 35, 10949 (2007).
Summary: For a prescribed pair of quantum states \(|\psi_{I}\rangle\) and \(|\psi_{F}\rangle\) we establish an elementary derivation of the optimum Hamiltonian, under constraints on its eigenvalues, that generates the unitary transformation \(|\psi_{I}\rangle \rightarrow |\psi_{F}\rangle\) in the shortest duration. The derivation is geometric in character and does not rely on variational calculus.
MSC:
81P68 | Quantum computation |
49S05 | Variational principles of physics |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |