arXiv subjects

Navin Khaneja

Publications and source records attributed to Navin Khaneja.

At least 37 records · Page 2Linked to original sources

arXiv2012

Control of Inhomogeneous Ensembles on The Bloch Sphere

Finding control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of composite pulses for compensating for dispersion in system dynamics is widely known and applied. In this paper, we introduce new pulse elements for correcting pulse errors. These design methods are analytical and can be used to prove arbitrarily good robust performance. Furthermore, the time-to-compensation is superior to existing Fourier Synthesis Methods which is critical for minimizing errors due to relaxation effects.

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arXiv2011

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.

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arXiv2010

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.

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arXiv2010

Time Optimal Control of Coupled Qubits Under Non-Stationary Interactions

In this article, we give a complete characterization of all the unitary transformations that can be synthesized in a given time for a system of coupled spin-1/2 in presence of general time varying coupling tensor. Our treatment is quite general and our results help to characterize the reachable set at all times for a class of bilinear control systems with time varying drift and unbounded control amplitude. These results are of fundamental interest in geometric control theory and have applications to control of coupled spins in solid state NMR spectroscopy.

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arXiv2009

High-fidelity fast quantum transport with imperfect controls

Effective transport of quantum information is an essential element of quantum computation. We consider the problem of transporting a quantum state by using a moving potential well, while maintaining the encoded quantum information. In particular, we look at a set of cases where the input control defining the position of the potential well is subject to different types of distortion, each of which is motivated by experimental considerations. We show that even under these conditions, we are able to perfectly transfer the quantum information non-adiabatically over any given distance.

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arXiv2007

Optimal approach to quantum communication using dynamic programming

Reliable preparation of entanglement between distant systems is an outstanding problem in quantum information science and quantum communication. In practice, this has to be accomplished via noisy channels (such as optical fibers) that generally result in exponential attenuation of quantum signals at large distances. A special class of quantum error correction protocols--quantum repeater protocols--can be used to overcome such losses. In this work, we introduce a method for systematically optimizing existing protocols and developing new, more efficient protocols. Our approach makes use of a dynamic programming-based searching algorithm, the complexity of which scales only polynomially with the communication distance, letting us efficiently determine near-optimal solutions. We find significant improvements in both the speed and the final state fidelity for preparing long distance entangled states.

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arXiv2007

Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system

In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case where unitary transformations produced by evolutions of the coupling take much longer time as compared to the time required to produce unitary transformations on the first qubit but much shorter time as compared to the time to produce unitary transformations on the second qubit. We present a canonical decomposition of SU(4) in terms of the subgroup SU(2)xSU(2)xU(1), which is natural in understanding the time-optimal control problem of such a coupled qubit system with significantly different time scales. A typical setting involves dynamics of a coupled electron-nuclear spin system in pulsed electron paramagnetic resonance experiments at high fields. Using the proposed canonical decomposition, we give time-optimal control algorithms to synthesize various unitary transformations of interest in coherent spectroscopy and quantum information processing.

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arXiv2007

Triple oscillating field technique for accurate measurements of couplings in homonuclear spin systems

We present a new concept for homonuclear dipolar recoupling in magic-angle-spinning (MAS) solid-state NMR experiments which avoids the problem of dipolar truncation. This is accomplished through the introduction of a new NMR pulse sequence design principle: the triple oscillating field technique. We demonstrate this technique as an efficient means to accomplish broadband dipolar recoupling of homonuclear spins, while decoupling heteronuclear dipolar couplings and anisotropic chemicals shifts and retaining influence from isotropic chemical shifts. In this manner, it possible to synthesize Ising interactions in homonuclear spin networks and thereby avoid dipolar truncation - a serious problem essentially all previous homonuclear dipolar recoupling experiments suffer from. Combination of this recoupling concept with rotor assisted dipolar refocusing enables easy readout of internuclear distances through comparison with analytical Fresnel curves. This forms the basis for a new class of solid-state NMR experiments with potential for structure analysis of uniformly carbon labelled proteins through accurate measurement of {13}C-{13}C internuclear distances. The concept is demonstrated experimentally by measurement of C_alpha-C', C_β-C', and C_γ-C' internuclear distances in powder samples of the amino acids \textit{L}-alanine and \textit{L}-threonine.

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arXiv2007

Switched Control of Electron Nuclear Spin Systems

In this article, we study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static B_0 field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control on nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation on the nuclear spins, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations can be used to synthesize any unitary transformation on the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.

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arXiv2007

Fourier Synthesis Methods for Control of Inhomogeneous Quantum Systems

Finding control laws (pulse sequences) that can compensate for dispersions in parameters which govern the evolution of a quantum system is an important problem in the fields of coherent spectroscopy, imaging, and quantum information processing. The use of composite pulse techniques for such tasks has a long and widely known history. In this paper, we introduce the method of Fourier synthesis control law design for compensating dispersions in quantum system dynamics. We focus on system models arising in NMR spectroscopy and NMR imaging applications.

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arXiv2006

Quantum Gate Design Metric

What is the time-optimal way of realizing quantum operations? Here, we show how important instances of this problem can be related to the study of shortest paths on the surface of a sphere under a special metric. Specifically, we provide an efficient synthesis of a controlled NOT (CNOT) gate between qubits coupled indirectly via Ising-type couplings to a third spin. Our implementation of the CNOT gate is more than twice as fast as conventional approaches. The pulse sequences for efficient manipulation of our coupled spin system are obtained by explicit computation of geodesics on a sphere under the special metric. These methods are also used for the efficient synthesis of indirect couplings and of the Toffoli gate. We provide experimental realizations of the presented methods on a linear three-spin chain with Ising couplings.

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arXiv2005

Semidefinite Programming and Reachable Sets of Dissipative Bilinear Control Systems

In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems it is shown that the optimal solution and the reachable set can be found by solving a semidefinite program. In practice, solutions to these problems generate optimal methods for control of quantum mechanical phenomena in presence of dissipation. In the area of coherent spectroscopy, this translates into the maximum signal to noise ratio that can be obtained in a spectroscopy experiment.

math.OC↗

arXiv2005

Noncommuting vector fields, polynomial approximations and control of inhomogeneous quantum ensembles

Finding control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of composite pulses for compensating dispersion in system dynamics is widely known and applied. In this paper, we make explicit the key aspects of the dynamics that makes such a compensation possible. We highlight the role of Lie algebras and non-commutativity in the design of a compensating pulse sequence. Finally we investigate three common dispersions in NMR spectroscopy, the Larmor dispersion, rf-inhomogeneity and strength of couplings between the spins.

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arXiv2005

Relaxation Optimized Transfer of Spin Order in Ising Spin Chains

In this manuscript, we present relaxation optimized methods for transfer of bilinear spin correlations along Ising spin chains. These relaxation optimized methods can be used as a building block for transfer of polarization between distant spins on a spin chain. Compared to standard techniques, significant reduction in relaxation losses is achieved by these optimized methods when transverse relaxation rates are much larger than the longitudinal relaxation rates and comparable to couplings between spins. We derive an upper bound on the efficiency of transfer of spin order along a chain of spins in the presence of relaxation and show that this bound can be approached by relaxation optimized pulse sequences presented in the paper.

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arXiv2004

Efficient decoupling and recoupling in solid state NMR for quantum computation

A scheme for decoupling and selectively recoupling large networks of dipolar-coupled spins is proposed. The scheme relies on a combination of broadband, decoupling pulse sequences applied to all the nuclear spins with a band-selective pulse sequence for single spin rotations or recoupling. The evolution-time overhead required for selective coupling is independent of the number of spins, subject to time-scale constraints, for which we discuss the feasibility. This scheme may improve the scalability of solid-state-NMR quantum computing architectures.

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arXiv2004

Optimal Control of Quantum Dissipative Dynamics: Analytic solution for cooling the three level $Λ$ system

We study the problem of optimal control of dissipative quantum dynamics. Although under most circumstances dissipation leads to an increase in entropy (or a decrease in purity) of the system, there is an important class of problems for which dissipation with external control can decrease the entropy (or increase the purity) of the system. An important example is laser cooling. In such systems, there is an interplay of the Hamiltonian part of the dynamics, which is controllable and the dissipative part of the dynamics, which is uncontrollable. The strategy is to control the Hamiltonian portion of the evolution in such a way that the dissipation causes the purity of the system to increase rather than decrease. The goal of this paper is to find the strategy that leads to maximal purity at the final time. Under the assumption that Hamiltonian control is complete and arbitrarily fast, we provide a general framework by which to calculate optimal cooling strategies. These assumptions lead to a great simplification, in which the control problem can be reformulated in terms of the spectrum of eigenvalues of $ρ$, rather than $ρ$ itself. By combining this formulation with the Hamilton-Jacobi-Bellman theorem we are able to obtain an equation for the globaly optimal cooling strategy in terms of the spectrum of the density matrix. For the three-level $Λ$ system, we provide a complete analytic solution for the optimal cooling strategy. For this system it is found that the optimal strategy does not exploit system coherences and is a 'greedy' strategy, in which the purity is increased maximally at each instant.

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arXiv2003

Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation

A parameterization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parameterization we find the region of permissible vectors which represent a density operator. The inequalities which specify the region are shown to involve the Casimir invariants of the group. In particular cases, this allows the determination of degeneracies in the spectrum of the operator. The identification of the Casimir invariants also provides a method of constructing quantities which are invariant under {\it local} unitary operations. Several examples are given which illustrate the constraints provided by the positivity requirements and the utility of the coherence vector parameterization.

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arXiv2003

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.

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