Quantum Hamiltonian formalism with constraints

J. Scott Little

A. Carlini, Akio Hosoya, Tatsuhiko Koike +1 more

We present a general formalism based on the variational principle for finding the time-optimal quantum evolution of mixed states governed by a master equation, when the Hamiltonian and the Lindblad operators are subject to certain constraints. The problem may be reduced to solving first a fundamental equation, which can be written down once the constraints are specified, for the Hamiltonian and then solving the constraints and the master equation for the Lindblad and the density operators. As an application of our formalism, we study a simple one-qubit model, where the optimal Lindblad operators can be simulated by a tunable coupling with an ancillary qubit.

Ashok Kumar Kapoor, Prasanta Kumar Panigrahi, S. Sree Ranjani

A. Carlini, Akio Hosoya, Tatsuhiko Koike +1 more

We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to that for the brachistochrone in classical mechanics. We reduce the problem to a formal equation for the Hamiltonian which depends on certain constraint functions specifying the range of available Hamiltonians. For some simple examples of the constraints, we explicitly find the optimal solutions.

Ashok Kumar Kapoor, Prasanta Kumar Panigrahi, S. Sree Ranjani

Yoshimasa Nakano

Hamiltonian formalism for systems with both c-numbers and Grassmann numbers developed by Casalbuoni is re-investigated to be pointed out that the invariance properties of the canonical transformation work also in cases of general potential. Following the quantization procedures of Dirac and Faddeev, a form of Feynman path-integral with constraints for boson-fermion systems is presented.