382 research outputs found
Broadband Geodesic Pulses for Three Spin Systems: Time-Optimal Realization of Effective Trilinear Coupling Terms and Indirect SWAP Gates
Broadband implementations of time-optimal geodesic pulse elements are
introduced for the efficient creation of effective trilinear coupling terms for
spin systems consisting of three weakly coupled spins 1/2. Based on these pulse
elements, the time-optimal implementation of indirect SWAP operations is
demonstrated experimentally. The duration of indirect SWAP gates based on
broadband geodesic sequence is reduced by 42.3% compared to conventional
approaches.Comment: 22 pages, incl. 8 figure
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
Multiple-spin coherence transfer in linear Ising spin chains and beyond: numerically-optimized pulses and experiments
We study multiple-spin coherence transfers in linear Ising spin chains with
nearest neighbor couplings. These constitute a model for efficient information
transfers in future quantum computing devices and for many multi-dimensional
experiments for the assignment of complex spectra in nuclear magnetic resonance
spectroscopy. We complement prior analytic techniques for multiple-spin
coherence transfers with a systematic numerical study where we obtain strong
evidence that a certain analytically-motivated family of restricted controls is
sufficient for time-optimality. In the case of a linear three-spin system,
additional evidence suggests that prior analytic pulse sequences using this
family of restricted controls are time-optimal even for arbitrary local
controls. In addition, we compare the pulse sequences for linear Ising spin
chains to pulse sequences for more realistic spin systems with additional
long-range couplings between non-adjacent spins. We experimentally implement
the derived pulse sequences in three and four spin systems and demonstrate that
they are applicable in realistic settings under relaxation and experimental
imperfections-in particular-by deriving broadband pulse sequences which are
robust with respect to frequency offsets.Comment: 11 page
Thermal Equilibrium as an Initial State for Quantum Computation by NMR
We present a method of using a nuclear magnetic resonance computer to solve
the Deutsch-Jozsa problem in which: (1) the number of molecules in the NMR
sample is irrelevant to the number of qubits available to an NMR quantum
computer, and (2) the initial state is chosen to be the state of thermal
equilibrium, thereby avoiding the preparation of pseudopure states and the
resulting exponential loss of signal as the number of qubits increases. The
algorithm is described along with its experimental implementation using four
active qubits. As expected, measured spectra demonstrate a clear distinction
between constant and balanced functions.Comment: including 4 figure
Quantum pattern recognition with liquid-state nuclear magnetic resonance
A novel quantum pattern recognition scheme is presented, which combines the
idea of a classic Hopfield neural network with adiabatic quantum computation.
Both the input and the memorized patterns are represented by means of the
problem Hamiltonian. In contrast to classic neural networks, the algorithm can
return a quantum superposition of multiple recognized patterns. A proof of
principle for the algorithm for two qubits is provided using a liquid state NMR
quantum computer.Comment: updated version, Journal-ref adde
Time Optimal Control in Spin Systems
In this paper, we study the design of pulse sequences for NMR spectroscopy as
a problem of time optimal control of the unitary propagator. Radio frequency
pulses are used in coherent spectroscopy to implement a unitary transfer of
state. Pulse sequences that accomplish a desired transfer should be as short as
possible in order to minimize the effects of relaxation and to optimize the
sensitivity of the experiments. Here, we give an analytical characterization of
such time optimal pulse sequences applicable to coherence transfer experiments
in multiple-spin systems. We have adopted a general mathematical formulation,
and present many of our results in this setting, mindful of the fact that new
structures in optimal pulse design are constantly arising. Moreover, the
general proofs are no more difficult than the specific problems of current
interest. From a general control theory perspective, the problems we want to
study have the following character. Suppose we are given a controllable right
invariant system on a compact Lie group, what is the minimum time required to
steer the system from some initial point to a specified final point? In NMR
spectroscopy and quantum computing, this translates to, what is the minimum
time required to produce a unitary propagator? We also give an analytical
characterization of maximum achievable transfer in a given time for the two
spin system.Comment: 20 Pages, 3 figure
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.Comment: largely expanded version, superseedes v1: 10 pages, 5 figure
Heteronuclear Decoupling by Multiple Rotating Frame Technique
The paper describes the multiple rotating frame technique for designing
modulated rf-fields, that perform broadband heteronuclear decoupling in
solution NMR spectroscopy. The decoupling is understood by performing a
sequence of coordinate transformations, each of which demodulates a component
of the Rf-field to a static component, that progressively averages the chemical
shift and dipolar interaction. We show that by increasing the number of
modulations in the decoupling field, the ratio of dispersion in the chemical
shift to the strength of the rf-field is successively reduced in progressive
frames. The known decoupling methods like continuous wave decoupling, TPPM etc,
are special cases of this method and their performance improves by adding
additional modulations in the decoupling field. The technique is also expected
to find use in designing decoupling pulse sequences in Solid State NMR
spectroscopy and design of various excitation, inversion and mixing sequences.Comment: 18 pages , 5 figure
The Significance of the -Numerical Range and the Local -Numerical Range in Quantum Control and Quantum Information
This paper shows how C-numerical-range related new strucures may arise from
practical problems in quantum control--and vice versa, how an understanding of
these structures helps to tackle hot topics in quantum information.
We start out with an overview on the role of C-numerical ranges in current
research problems in quantum theory: the quantum mechanical task of maximising
the projection of a point on the unitary orbit of an initial state onto a
target state C relates to the C-numerical radius of A via maximising the trace
function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one
may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii)
in restricting the dynamics to {\em local} operations on each qubit, i.e. to
the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2).
Interestingly, the latter then leads to a novel entity, the {\em local}
C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither
star-shaped nor simply connected in contrast to the conventional C-numerical
range. This is shown in the accompanying paper (math-ph/0702005).
We present novel applications of the C-numerical range in quantum control
assisted by gradient flows on the local unitary group: (1) they serve as
powerful tools for deciding whether a quantum interaction can be inverted in
time (in a sense generalising Hahn's famous spin echo); (2) they allow for
optimising witnesses of quantum entanglement. We conclude by relating the
relative C-numerical range to problems of constrained quantum optimisation, for
which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200
Application of Optimal Control to CPMG Refocusing Pulse Design
We apply optimal control theory (OCT) to the design of refocusing pulses
suitable for the CPMG sequence that are robust over a wide range of B0 and B1
offsets. We also introduce a model, based on recent progress in the analysis of
unitary dynamics in the field of quantum information processing (QIP), that
describes the multiple refocusing dynamics of the CPMG sequence as a dephasing
Pauli channel. This model provides a compact characterization of the
consequences and severity of residual pulse errors. We illustrate the methods
by considering a specific example of designing and analyzing broadband OCT
refocusing pulses of length 10 t180 that are constrained by the maximum
instantaneous pulse power. We show that with this refocusing pulse, the CPMG
sequence can refocus over 98% of magnetization for resonance offsets up to 3.2
times the maximum RF amplitude, even in the presence of +/- 10% RF
inhomogeneity.Comment: 23 pages, 10 figures; Revised and reformatted version with new title
and significant changes to Introduction and Conclusions section
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