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

Composite Dipolar Recoupling: Anisotropy Compensated Coherence Transfer in Solid-State NMR

The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state NMR spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fields. The compensation scheme is very simple to implement as a scaffold (comb) of compensating pulses in which the pulse sequence to be improved may be inserted. The degree of compensation can be adjusted and should be balanced as a compromise between efficiency and length of the overall pulse sequence. We show by numerical and experimental data that the presented compensation protocol significantly improves the efficiency of known dipolar recoupling solid-state NMR experiment

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

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

Orbits of quantum states and geometry of Bloch vectors for NN-level systems

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in R^{n^2-1} only for n=2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version, corrected eq.(3), to appear in J. Physics

Distributed Quantum Computation Based-on Small Quantum Registers

We describe and analyze an efficient register-based hybrid quantum computation scheme. Our scheme is based on probabilistic, heralded optical connection among local five-qubit quantum registers. We assume high fidelity local unitary operations within each register, but the error probability for initialization, measurement, and entanglement generation can be very high (~5%). We demonstrate that with a reasonable time overhead our scheme can achieve deterministic non-local coupling gates between arbitrary two registers with very high fidelity, limited only by the imperfections from the local unitary operation. We estimate the clock cycle and the effective error probability for implementation of quantum registers with ion-traps or nitrogen-vacancy (NV) centers. Our new scheme capitalizes on a new efficient two-level pumping scheme that in principle can create Bell pairs with arbitrarily high fidelity. We introduce a Markov chain model to study the stochastic process of entanglement pumping and map it to a deterministic process. Finally we discuss requirements for achieving fault-tolerant operation with our register-based hybrid scheme, and also present an alternative approach to fault-tolerant preparation of GHZ states.Comment: 22 Pages, 23 Figures and 1 Table (updated references