8 research outputs found

### On optimum Hamiltonians for state transformations

For a prescribed pair of quantum states |psi_I> and |psi_F> we establish an
elementary derivation of the optimum Hamiltonian, under constraints on its
eigenvalues, that generates the unitary transformation |psi_I> --> |psi_F> in
the shortest duration. The derivation is geometric in character and does not
rely on variational calculus.Comment: 5 page

### Adiabatic passage and ensemble control of quantum systems

This paper considers population transfer between eigenstates of a finite
quantum ladder controlled by a classical electric field. Using an appropriate
change of variables, we show that this setting can be set in the framework of
adiabatic passage, which is known to facilitate ensemble control of quantum
systems. Building on this insight, we present a mathematical proof of
robustness for a control protocol -- chirped pulse -- practiced by
experimentalists to drive an ensemble of quantum systems from the ground state
to the most excited state. We then propose new adiabatic control protocols
using a single chirped and amplitude shaped pulse, to robustly perform any
permutation of eigenstate populations, on an ensemble of systems with badly
known coupling strengths. Such adiabatic control protocols are illustrated by
simulations achieving all 24 permutations for a 4-level ladder

### Implementing Quantum Gates using the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions

We demonstrate an implementation scheme for constructing quantum gates using
unitary evolutions of the one-dimensional spin-J ferromagnetic XXZ chain. We
present numerical results based on simulations of the chain using the
time-dependent DMRG method and techniques from optimal control theory. Using
only a few control parameters, we find that it is possible to implement one-
and two-qubit gates on a system of spin-3/2 XXZ chains, such as Not, Hadamard,
Pi-8, Phase, and C-Not, with fidelity levels exceeding 99%.Comment: Updated Acknowledgement

### Common polynomial Lyapunov functions for linear switched systems

In this paper, we consider linear switched systems. x( t) = A(u( t))x( t), x is an element of R-n, u is an element of U, {Au u is an element of U} compact, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ( UAS). Given a UAS system, it is always possible to build a common polynomial Lyapunov function. Our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given

### Geometric Control and Nonsmooth Analysis

The volume provides a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions. It is the 76th volume of the Series on Advances in Mathematics for Applied Sciences