Time optimal quantum evolution of mixed states

Abstract

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.

Minimum-Time Selective Control of Homonuclear Spins

“…χ th is the theoretical value, and χ exp was experimentally constructed by QPT. The labels 1-16 in the x-and y-axes correspond to the operator basis (17).…”

Time-optimal transfer of coherence

“…The Hermitian operator Λ(s) and the real functions λ j (s) are Lagrange multipliers. The function α(s) gives the time cost and it relates the physical t and the parameter s times via t := α(s)ds [14].…”

“…The scheme was The QB is derived from an action principle which enforces the dynamical laws of quantum evolution (i.e., the Schrödinger equation or a master equation) and the constraints which the Hamiltonian of the physical system has to satisfy (e.g., a fixed total energy, the absence of certain qubit interactions etc..). The framework was designed for the time-optimal evolution of quantum states between fixed initial and final states [13]- [14], for the time-optimal generation of a certain unitary quantum gate [15], and for the situation (typical in experiments) where the target is reachable only in an approximate way (i.e., with a fidelity smaller than one [16]). …”

Genuine tripartite entanglement in quantum brachistochrone evolution of a three-qubit system

“…That is, it searches the shortest time interval T taken by a quantum system for evolving from an original state to a final one. This problem attracts a lot of attention [17,18,19]. For instance, Carlini et al [17] presented a general framework for finding the time-optimal evolution and the optimal Hamiltonian for quantum system with a given set of initial and final states.…”

“…Brody and Hook [18] established an elementary derivation of the optimum Hamiltonian, under constraints on its eigenvalues, that generates the unitary transformation |ψ I → |ψ F in the shortest duration. Carlini et al [19] investigated quantum brachistochrone evolution of mixed states.…”