arXiv subjects

N. Khaneja

Publications and source records attributed to N. Khaneja.

7 recordsLinked to original sources

arXiv2009

Optimal Control for Generating Quantum Gates in Open Dissipative Systems

Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control using relaxation parameters against time-optimal control is explored and exemplified in numerical and in algebraic terms: it is the method of choice to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes. In a standard model system generalising decoherence-free subspaces to more realistic scenarios, openGRAPE-derived controls realise a CNOT with fidelities beyond 95% instead of at most 15% for a standard Trotter expansion. As additional benefit it requires control fields orders of magnitude lower than the bang-bang decouplings in the latter.

quant-ph↗

arXiv2007

Elliptic functions and efficient control of Ising spin chains with unequal couplings

In this article, we study optimal control of dynamics in a linear chain of three spin 1/2, weakly coupled with unequal Ising couplings. We address the problem of time-optimal synthesis of multiple spin quantum coherences. We derive time-optimal pulse sequence for creating a desired spin order by computing geodesics on a sphere under a special metric. The solution to the geodesic equation is related to the nonlinear oscillator equation and the minimum time to create multiple spin order can be expressed in terms of an elliptic integral. These techniques are used for efficient creation of multiple spin coherences in Ising spin-chains with unequal couplings.

quant-ph↗

arXiv2007

Geodesics for Efficient Creation and Propagation of Order along Ising Spin Chains

Experiments in coherent nuclear and electron magnetic resonance, and optical spectroscopy correspond to control of quantum mechanical ensembles, guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and decoherence and to optimize the sensitivity of the experiments. Here we give efficient syntheses of various unitary transformations on Ising spin chains of arbitrary length. The efficient realization of the unitary transformations presented here is obtained by computing geodesics on a sphere under a special metric. We show that contrary to the conventional belief, it is possible to propagate a spin order along an Ising spin chain with coupling strength J (in units of Hz), significantly faster than 1/(2J) per step. The methods presented here are expected to be useful for immediate and future applications involving control of spin dynamics in coherent spectroscopy and quantum information processing.

quant-ph↗

arXiv2006

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.

quant-ph↗

arXiv2005

Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity

In this paper, we demonstrate that optimal control algorithms can be used to speed up the implementation of modules of quantum algorithms or quantum simulations in networks of coupled qubits. The gain is most prominent in realistic cases, where the qubits are not all mutually coupled. Thus the shortest times obtained depend on the coupling topology as well as on the characteristicratio of the time scales for local controls {\em vs} non-local ({\em i.e.} coupling) evolutions in the specific experimental setting. Relating these minimal times to the number of qubits gives the tightest known upper bounds to the actual time complexity of the quantum modules. As will be shown, time complexity is a more realistic measure of the experimental cost than the usual gate complexity. In the limit of fast local controls (as {\em e.g.} in NMR), time-optimised realisations are shown for the quantum Fourier transform (QFT) and the multiply controlled {\sc not}-gate ({\sc c$^{n-1}$not}) in various coupling topologies of $n$ qubits. The speed-ups are substantial: in a chain of six qubits the quantum Fourier transform so far obtained by optimal control is more than eight times faster than the standard decomposition into controlled phase, Hadamard and {\sc swap} gates, while the {\sc c$^{n-1}$not}-gate for completely coupled network of six qubits is nearly seven times faster.

quant-ph↗

arXiv2004

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.

quant-ph↗

arXiv2003

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.

quant-ph↗