Alberto Carlini

Time-optimal quantum evolution

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.

Time Optimal Unitary Operations

Department of Physics, Keio University, Yokohama, Japan(Dated: January 15, 2007)Extending our previous work on time optimal quantum state evolution [A. Carlini, A. Hosoya, T.Koike and Y. Okudaira, Phys. Rev. Lett. 96, 060503 (2006)], we formulate a variational principle forfinding the time optimal realization of a target unitary operation, when the available Hamiltoniansare subject to certain constraints dictated either by experimental or by theoretical conditions. Sincethe time optimal unitary evolutions do not depend on the input quantum state this is of more directrelevance to quantum computation. We explicitly illustrate our method by considering the case ofa two-qubit system self-interacting via an anisotropic Heisenberg Hamiltonian and by deriving thetime optimal unitary evolution for three examples of target quantum gates, namely the swap ofqubits, the quantum Fourier transform and the entangler gate. We also briefly discuss the case inwhich certain unitary operations take negligible time.

Quantum learning and universal quantum matching machine

Suppose that three kinds of quantum systems are given in some unknown states

Speeding up and slowing down the relaxation of a qubit by optimal control

|f{〉}^{\ensuremath{\bigotimes}N},

Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain

|{g}_{1}{〉}^{\ensuremath{\bigotimes}K},

Generalized second law of black hole thermodynamics and quantum information theory

and

Time-optimal unitary operations in Ising chains: unequal couplings and fixed fidelity

|{g}_{2}{〉}^{\ensuremath{\bigotimes}K},

Quantum Probabilistic Subroutines and Problems in Number Theory

and we want to decide which template state

Time-optimal thermalization of single-mode Gaussian states

|{g}_{1}〉