Boundary of Quantum Evolution under Decoherence

Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this letter, we establish physical limits on how closely can a quantum mechanical system be steered to a desired target state in the presence of relaxation. In particular, we explicitly compute the maximum coherence or polarization that can be transferred between coupled nuclear spins in the presence of very general decoherence mechanisms that include cross-correlated relaxation. We give analytical expressions for the control laws (pulse sequences) which achieve these physical limits and provide supporting experimental evidence. Exploitation of cross-correlation effects has recently led to the development of powerful methods in NMR spectroscopy to study very large biomolecules in solution. We demonstrate with experiments that the optimal pulse sequences provide significant gains over these state of the art methods, opening new avenues for spectroscopy of much larger proteins. Surprisingly, in spite of very large relaxation rates, optimal control can transfer coherence without any loss when cross-correlated relaxation rates are tuned to auto-correlated relaxation rates

Broadband Relaxation-Optimized Polarization Transfer in Magnetic Resonance

Many applications of magnetic resonance are limited by rapid loss of spin coherence caused by large transverse relaxation rates. In nuclear magnetic resonance (NMR) of large proteins, increased relaxation losses lead to poor sensitivity of experiments and increased measurement time. In this paper we develop broadband relaxation optimized pulse sequences (BB-CROP) which approach fundamental limits of coherence transfer efficiency in the presence of very general relaxation mechanisms that include cross-correlated relaxation. These broadband transfer schemes use new techniques of chemical shift refocusing (STAR echoes) that are tailored to specific trajectories of coupled spin evolution. We present simulations and experimental data indicating significant enhancement in the sensitivity of multi-dimensional NMR experiments of large molecules by use of these methods

Decompositions of unitary evolutions and entanglement dynamics of bipartite quantum systems

We describe a decomposition of the Lie group of unitary evolutions for a bipartite quantum system of arbitrary dimensions. The decomposition is based on a recursive procedure which systematically uses the Cartan classification of the symmetric spaces of the Lie group SO(n). The resulting factorization of unitary evolutions clearly displays the local and entangling character of each factor.Comment: 11 pages, revtex

Interaction cost of non-local gates

We introduce the interaction cost of a non-local gate as the minimal time of interaction required to perform the gate when assisting the process with fast local unitaries. This cost, of interest both in the areas of quantum control and quantum information, depends on the specific interaction, and allows to compare in an operationally meaningful manner any two non-local gates. In the case of a two-qubit system, an analytical expression for the interaction cost of any unitary operation given any coupling Hamiltonian is obtained. One gate may be more time-consuming than another for any possible interaction. This defines a partial order structure in the set of non-local gates, that compares their degree of non-locality. We analytically characterize this partial order in a region of the set of two-qubit gates.Comment: revtex, 4 pages, no pictures, typos corrected, small changes in nomenclatur

Targeting qubit states using open-loop control

We present an open-loop (bang-bang) scheme which drives an open two-level quantum system to any target state, while maintaining quantum coherence throughout the process. The control is illustrated by a realistic simulation for both adiabatic and thermal decoherence. In the thermal decoherence regime, the control achieved by the proposed scheme is qualitatively similar, at the ensemble level, to the control realized by the quantum feedback scheme of Wang, Wiseman, and Milburn [Phys. Rev. A 64, #063810 (2001)] for the spontaneous emission of a two-level atom. The performance of the open-loop scheme compares favorably against the quantum feedback scheme with respect to robustness, target fidelity and transition times.Comment: 27 pages, 7 figure

Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer

Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrated that computing these time optimal pulse sequences can be reduced to geometric problems that involve computing sub-Riemannian geodesics on Homogeneous spaces

Dipolar recoupling in solid state NMR by phase alternating pulse sequences

We describe some new developments in the methodology of making heteronuclear and homonuclear recoupling experiments in solid state NMR insensitive to rf-inhomogeneity by phase alternating the irradiation on the spin system every rotor period. By incorporating delays of half rotor periods in the pulse sequences, these phase alternating experiments can be made γ encoded. The proposed methodology is conceptually different from the standard methods of making recoupling experiments robust by the use of ramps and adiabatic pulses in the recoupling periods. We show how the concept of phase alternation can be incorporated in the design of homonuclear recoupling experiments that are both insensitive to chemical shift dispersion and rf-inhomogeneity.United States. Office of Naval Research (38A-1077404)United States. Air Force Office of Scientific Research (FA9550-05-1-0443)National Science Foundation (U.S.) (0724057)National Institute for Biomedical Imaging and Bioengineering (U.S.) (Grant EB003151)National Institute for Biomedical Imaging and Bioengineering (U.S.) (Grant EB002026

Entanglement Dynamics in 1D Quantum Cellular Automata

Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is required between arbitrarily distant pairs of lattice qubits. An alternative model of quantum computation based on quantum cellular automata (QCA) requires only homogeneous local interactions that can be implemented in parallel. This would be a huge simplification in an actual experiment. We find some minimal physical requirements for the construction of unitary QCA in a 1 dimensional Ising spin chain and demonstrate optimal pulse sequences for information transport and entanglement distribution. We also introduce the theory of non-unitary QCA and show by example that non-unitary rules can generate environment assisted entanglement.Comment: 12 pages, 8 figures, submitted to Physical Review