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CNT (carbon nanotube) yarns stretched in tension as mechanical springs are used to drive both electrical and mechanical loads in order to demonstrate the CNT yarns' potential for high power density, their potential for metered energy release, and their application to power practical systems. The energy-storing properties of the CNT yarn are characterized, and the design, operation, and characterization of three demonstration systems that store energy in stretched CNT yarns and release it to drive an electrical or mechanical load are presented. When loaded in tension, the yarn stores energy with an energy per unit length of up to 13.4 mJ/m and an energy density of up to 7720 kJ/m 3 or 6.7 kJ/kg. The CNT spring-driven demonstration systems include a mechanical slingshot and two mechanically-driven electric power supplies. The slingshot releases energy stored in a stretched CNT spring rapidly to launch a projectile, with up to 56% power extraction efficiency. The first electric power supply converts stored mechanical energy into electric power using an escapement-based power regulation mechanism and piezoelectric energy conversion. The second electric power supply uses an electromagnetic conversion system to convert energy stored in the CNT spring to electric output power without regulating the rate of energy release from the spring. The devices demonstrate that CNT yarn can be used to drive mechanical and electrical loads using both quick-release devices that provide high power, and slow-release, escapement-metered systems.

Decoherence-free subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multi-qubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians built-in, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.

We report on the experimental simulation of spin squeezing using a liquid-state nuclear magnetic resonance (NMR) quantum information processor. This was done by identifying the energy levels within the symmetric subspace of a system of n spin-1/2 nuclei with the energy levels of the simulated spin-(n/2) system. The results obtained for our simulations of spin-1 and spin-3/2 systems are consistent with earlier theoretical studies of spin squeezing, and illustrate interesting relations between the degree of squeezing and the strength of the correlations among the underlying spin-1/2 particles. PACS: 03.65.Bz; 03.67.-a; 03.67.Lx

Errors in the control of quantum systems may be classified as unitary, decoherent and incoherent. Unitary errors are systematic, and result in a density matrix that differs from the desired one by a unitary operation. Decoherent errors correspond to general completely positive superoperators, and can only be corrected using methods such as quantum error correction. Incoherent errors can also be described, on average, by completely positive superoperators, but can nevertheless be corrected by the application of a locally unitary operation that ``refocuses'' them. They are due to reproducible spatial or temporal variations in the system's Hamiltonian, so that information on the variations is encoded in the system's spatiotemporal state and can be used to correct them. In this paper liquid-state nuclear magnetic resonance (NMR) is used to demonstrate that such refocusing effects can be built directly into the control fields, where the incoherence arises from spatial inhomogeneities in the quantizing static magnetic field as well as the radio-frequency control fields themselves. Using perturbation theory, it is further shown that the eigenvalue spectrum of the completely positive superoperator exhibits a characteristic spread that contains information on the Hamiltonians' underlying distribution., 14 pages, 6 figures

This paper outlines the various applications of metric matrix embedding that I have made in the course of my career to date. This ongoing saga starts with my PhD work on protein folding by distance geometry, highlights the structure calculations done during postdoctoral work with Kurt Wuthrich (1982–84), and then goes on to protein homology modeling, the computer-aided analysis of NMR spectra, and NMR relaxation theory using the Lindblad formalism. It closes with a brief discussion of NMR-based quantum computing and how it is changing the face of NMR spectroscopy. Copyright © 2003 John Wiley & Sons, Ltd.

Nuclear magnetic resonance (NMR) is a direct macroscopic manifestation of the quantum mechanics of the intrinsic angular momentum of atomic nuclei. It is best known for its extraordinary range of applications, which include molecular structure determination, medical imaging, and measurements of flow and diffusion rates. Most recently, liquid-state NMR spectroscopy has been found to provide a powerful experimental tool for the development and evaluation of the coherent control techniques needed for quantum information processing. This burgeoning new interdisciplinary field has the potential to achieve cryptographic, communications, and computational feats far beyond what is possible with known classical physics. Indeed, NMR has made the demonstration of many of these feats sufficiently simple to be carried out by high school summer interns working in our laboratory (see the last two authors). In this paper the basic principles of quantum information processing by NMR spectroscopy are described, along with ...

We introduce a nonsymmetric real matrix which contains all the information that the usual Hermitian density matrix does, and which has exactly the same tensor product structure. The properties of this matrix are analyzed in detail in the case of multi-qubit (e.g., spin = 1/2) systems, where the transformation between the real and Hermitian density matrices is given explicitly as an operator sum, and used to convert the essential equations of the density matrix formalism into the real domain. PACS: 03.65.Ca; 03.67-a; 33.25.+k; 02.10.Xm

We experimentally explore the reduction of decoherence via concatenating quantum error correction (QEC) with decoupling in liquid-state NMR quantum information processing. Decoupling provides an efficient means of suppressing decoherence from noise sources with long correlation times, and then QEC can be used more profitably for the remaining noise sources. PACS: 03.67.Lx, 03.65.Bz

Control over spin dynamics has been obtained in NMR via coherent averaging, which is implemented through a sequence of RF pulses, and via quantum codes which can protect against incoherent evolution. Here, we discuss the design and implementation of quantum codes to protect against coherent evolution. A detailed example is given of a quantum code for protecting two data qubits from evolution under a weak coupling (Ising) term in the Hamiltonian, using an ``isolated'' ancilla which does not evolve on the experimental time scale. The code is realized in a three-spin system by liquid-state NMR spectroscopy on 13C-labelled alanine, and tested for two initial states. It is also shown that for coherent evolution and isolated ancillae, codes exist that do not require the ancillae to initially be in a (pseudo-)pure state. Finally, it is shown that even with non-isolated ancillae quantum codes exist which can protect against evolution under weak coupling. An example is presented for a six qubit code that protects two data spins to first order., Reformatted single spaced with figures incorporated into text (18 pages, 6 figures, PDF only, submitted to J. Chem. Phys.)

This paper surveys our recent research on quantum information processing by nuclear magnetic resonance (NMR) spectroscopy. We begin with a geometric introduction to the NMR of an ensemble of indistinguishable spins, and then show how this geometric interpretation is contained within an algebra of multispin product operators. This algebra is used throughout the rest of the paper to demonstrate that it provides a facile framework within which to study quantum information processing more generally. The implementation of quantum algorithms by NMR depends upon the availability of special kinds of mixed states, called pseudo-pure states, and we consider a number of different methods for preparing these states, along with analyses of how they scale with the number of spins. The quantum-mechanical nature of processes involving such macroscopic pseudo-pure states also is a matter of debate, and in order to discuss this issue in concrete terms we present the results of NMR experiments which constitute a macroscopic analogue Hardy's paradox. Finally, a detailed product operator description is given of recent NMR experiments which demonstrate a three-bit quantum error correcting code, using field gradients to implement a precisely-known decoherence model.

The implementation of small prototype quantum computers has been studied through ensemble quantum computing via NMR measurements. In such laboratory studies it is convenient to have access to a wide array of logic gates. Here a systematic approach to reduce the logic gate to an NMR pulse sequence is introduced. This approach views the truth table for a quantum logic operation as a permutation matrix that corresponds to a propagator for an NMR transition. This propagator is then used as the starting point for the derivation of a pulse sequence. Pulse sequences for all the permutations of a four level system are reported along with implementations of representative examples on a two spin-1/2 system, 13C-labeled chloroform.

Logic gates such as the controlled-NOT (c-NOT) and Toffoli gates play a key role in quantum information processing (QIP) and quantum computing. A natural extension of such gates would necessarily operate on one quantum bit (qubit) conditional on the state of the remaining qubits in the system. We show that such selective gates, termed $(\mathrm{controlled}{)}^{n}\ensuremath{-}\mathrm{NOT}$ gates, or ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates, are convenient in nuclear magnetic resonance (NMR) implementations of QIP and are straightforward to implement. NMR pulse sequences for these gates can be built using classical methods as well as insights from geometric algebra. These methods yield equivalent NMR pulse sequences for the generation of ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates for any number of control spins. In this work, a catalog of ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates for systems of as many as 16 spins is provided along with an experimental implementation of a ${\mathrm{c}}^{3}\ensuremath{-}\mathrm{N}\mathrm{O}\mathrm{T}$ gate on a four spin system, ${}^{13}\mathrm{C}$ alanine.

We present experimental results which demonstrate that nuclear magnetic resonance spectroscopy is capable of efficiently emulating many of the capabilities of quantum computers, including unitary evolution and coherent superpositions, but without attendant wave-function collapse. Specifically, we have: (1) Implemented the quantum XOR gate in two different ways, one using Pound-Overhauser double resonance, and the other using a spin-coherence double resonance pulse sequence; (2) Demonstrated that the square root of the Pound-Overhauser XOR corresponds to a conditional rotation, thus obtaining a universal set of gates; (3) Devised a spin-coherence implementation of the Toffoli gate, and confirmed that it transforms the equilibrium state of a four-spin system as expected; (4) Used standard gradient-pulse techniques in NMR to equalize all but one of the populations in a two-spin system, so obtaining the pseudo-pure state that corresponds to |00>; (5) Validated that one can identify which basic pseudo-pure state is present by transforming it into one-spin superpositions, whose associated spectra jointly characterize the state; (6) Applied the spin-coherence XOR gate to a one-spin superposition to create an entangled state, and confirmed its existence by detecting the associated double-quantum coherence via gradient-echo methods., Comment: LaTeX + epsfig + amsmath packages, 27 pages, 12 figures, to appear in Physica D; revision updates list of authors and references

This paper presents a new distance geometry algorithm for calculating atomic coordinates from estimates of the interatomic distances, which maintains the positions of the atoms in a known rigid substructure. Given an M × 3 matrix of coordinates X for the rigid substructure, this problem consists of finding the N × 3 matrix Y which yields the global minimum of the so-called STRAIN, i.e., $$\mathop {\min }\limits_Y \left\| {\left[ {\begin{array}{*{20}c} {XX^T } \\ {YX^T } \\ \end{array} \begin{array}{*{20}c} {XY^T } \\ {YY^T } \\ \end{array} } \right] - \left[ {\begin{array}{*{20}c} A \\ {B^T } \\ \end{array} \begin{array}{*{20}c} B \\ C \\ \end{array} } \right]} \right\|_F^2 ,$$ where $$A = XX^{\text{{\rm T}}} $$ , and B, C are matrices of inner products calculated from the estimated distances. The vanishing of the gradient of the STRAIN is shown to be equivalent to a system of only six nonlinear equations in six unknowns for the inertial tensor associated with the solution Y. The entire solution space is characterized in terms of the geometry of the intersection curves between the unit sphere and certain variable ellipsoids. Upon deriving tight bilateral bounds on the moments of inertia of any possible solution, we construct a search procedure that reliably locates the global minimum. The effectiveness of this method is demonstrated on realistic simulated and chemical test problems.

This work presents a study of the tensile mechanical properties of millimeter-long fibers comprising carbon nanotubes (CNTs). These CNT fibers are made of aligned, loosely packed parallel networks of CNTs that are grown in and harvested from CNT forests without drawing or spinning. Unlike typical CNT yarn, the present fibers contain a large fraction of CNTs that span the fibers' entire gauge length. The fibers are densified after growth and network formation to study how increasing the degree of interaction among CNTs in a network by various methods influences and limits the mechanical behavior of macroscopic CNT materials, particularly for the case in which the continuity of a large fraction of CNTs across the gauge length prevents failure purely by slip. Densification is carried out using various combinations of capillary-driven densification, mechanical pressure, and twisting. All methods of densification increase the fiber density and modify the nanoscale order of the CNTs. The highest strength and stiffness values (1.8 and 88.7 N tex(-1), respectively) are observed for capillary-densified fibers, whereas the highest toughness values (94 J g(-1)) and maximum reversible energy density (1.35 kJ kg(-1) or 677 kJ m(-3)) are observed for fibers densified by mechanical pressure. The results suggest that the path to higher performance CNT materials may lie not only in the use of continuous and long CNTs but also in controlling their density and nanoscale ordering through modification of the as-grown networks, such as by capillary-driven densification.

Geometric algebra is an elegant and practical merger of classical vector algebra with Hamilton's quaternions. In this paper we show how it can be used to solve the local deformation problem introduced by Gō and Scheraga in 1970. As a special case, this enables us to characterize the torsion angles in cyclic molecules that are consistent with the ring closure constraint.

A new computational method for simultaneously estimating all the proton-proton coupling constants in a molecule from COSY spectra [Yang, J.-X. and Havel, T.F. (1994) J. Biomol. NMR, 4, 807-826] is applied to experimental data from two polypeptides. The first of these is a cyclic hexapeptide denoted as VDA (-D-Ala1-Phe2-Trp3-Lys(Z)4-Val5-Phe6-), in deuterated DMSO, while the second is a 39-residue protein, called decorsin, in aqueous solution. The effect of different data processing strategies and different initial parameter values on the accuracy of the coupling constants was explored. In the case of VDA, most of the coupling constants did not depend strongly on the initial values chosen for the optimization or on how the data were processed. This, together with our previous experience using simulated data, implies strongly that these values are accurate estimates of the coupling constants. They also differ by an average of only 0.36 Hz from the values of the 14 coupling constants that could be measured independently by established methods. In the case of decorsin, many of the coupling constants exhibited a moderate dependence on their initial values and a strong dependence on how the data were processed. With the most successful data processing strategy, the amide-alpha coupling constants differed by an average of 1.11 Hz from the 21 values that could be measured by established methods, while two thirds of the three-bond coupling constants fell within 1.0 Hz of the ranges obtained by applying the Karplus relation to an independently computed ensemble of distance geometry structures. The averages of the coupling constants over multiple optimizations using random initial values were computed in order to obtain the best possible estimates of the coupling constants. Most clearly incorrect averages can be identified by large standard deviations in the coupling constants or the associated line widths and chemical shifts, and can be explained by strong coupling and/or overlap with the water signal, the diagonal peaks or other cross peaks.

Two-dimensional NMR spectra are rectangular arrays of real numbers, which are commonly regarded as digitized images to be analyzed visually. If one treats them instead as mathematical matrices, linear algebra techniques can also be used to extract valuable information from them. This matrix approach is greatly facilitated by means of a physically significant decomposition of these spectra into a product of matrices--namely, S = PAPT. Here, P denotes a matrix whose columns contain the digitized contours of each individual peak or multiple in the one-dimensional spectrum, PT is its transpose, and A is an interaction matrix specific to the experiment in question. The practical applications of this decomposition are considered in detail for two important types of two-dimensional NMR spectra, double quantum-filtered correlated spectroscopy and nuclear Overhauser effect spectroscopy, both in the weak-coupling approximation. The elements of A are the signed intensities of the cross-peaks in a double quantum-filtered correlated spectrum, or the integrated cross-peak intensities in the case of a nuclear Overhauser effect spectrum. This decomposition not only permits these spectra to be efficiently simulated but also permits the corresponding inverse problems to be given an elegant mathematical formulation to which standard numerical methods are applicable. Finally, the extension of this decomposition to the case of strong coupling is given.

A few years ago, lattice model studies indicated that compactness could induce polymer chains to develop protein-like secondary structures. Subsequent off-lattice studies have found the amounts of induced structure to be relatively small. Here we use distance geometry to generate random conformations of compact poly-alanine chains of various chain lengths. The poly-alanine chains are subjected only to compactness and excluded volume constraints; no other energies or conformational propensities are included in the chain generation procedure. We find that compactness leads to considerable stabilization of secondary structure, but the absolute amount of secondary structure depends strongly on the criteria used to define helices and sheets. By loose criteria, much secondary structure arises from compactness, but by strict criteria, little does. The stabilization free energy of secondary structure provided by compactness, however, appears to be independent of criteria. Since real helices and sheets in proteins can be identified by strict criteria, we introduced small energy perturbations to compact poly-alanine chains using the AMBER force field. Small refinements produced good α-helices. For β-sheets, however, larger refinements are necessary. Compactness appears to impart stability, but not much structural specificity, to secondary structures in proteins. Compactness acts more like diffusion as a force, a result of ensemble statistics, than like pair interactions such as hydrogen bonding.

Geometric algebra is an elegant and practical merger of classical vector algebra with Hamilton's quaternions. As part of our ongoing studies of its many potential applications to the theory of molecular conformation, we show how geometric algebra can be used to characterize the solutions to the classical problem of computing the optimum alignment of rigid structures. Using this characterization, we derive a new iterative algorithm for finding optimum alignments, which we can show is both globally and quadratically convergent.

As part of our on-going development of a method, based upon distance geometry calculations, for predicting the structures of proteins from the known structures of their homologues, we have predicted the structure of the 176 residue Flavodoxin from Escherichia coli. This prediction was based upon the crystal structures of the homologous Flavodoxins from Anacystis nidulans, Chondrus crispus, Desulfovibrio vulgaris and Clostridium beijerinckii, whose sequence identities with Escherichia coli were 44%, 33%, 23% and 16%, respectively. A total of 13,043 distance constraints among the alpha-carbons of the Escherichia coli structure were derived from the sequence alignments with the known structures, together with 8,893 distance constraints among backbone and sidechain atoms of adjacent residues, 978 between the alpha-carbons and selected atoms of the flavin mononucleotide cofactor, 116 constraints to enforce conserved hydrogen bonds, and 452 constraints on the torsion angles in conserved residues. An en...

A method is proposed for defining a probability distribution on an ensemble of protein conformations from a 2D NOE spectrum, while at the same time back-calculating the experimental spectrum from the ensemble. This enables one to assess the relative quality and significance of the conformations, and to test the consistency of the ensemble as a whole with the experimental spectrum. The method eliminates the need to integrate the cross-peak intensities and is surprisingly insensitive to random noise in the spectrum. In this communication, these advantages are demonstrated by applying the method to simulated data, for which the correct result is already known.

As part of our on-going development of a method, based upon distance geometry calculations, for predicting the structures of proteins from the known structures of their homologues, we have predicted the structure of the 176 residue Flavodoxin from Escherichia coli. This prediction was based upon the crystal structures of the homologous Flavodoxins from Anacystis nidulans, Chondrus crispus, Desulfovibrio vulgaris and Clostridium beijerinckii, whose sequence identities with Escherichia coli were 44%, 33%, 23% and 16%, respectively. A total of 13,043 distance constraints among the alpha-carbons of the Escherichia coli structure were derived from the sequence alignments with the known structures, together with 8,893 distance constraints among backbone and sidechain atoms of adjacent residues, 978 between the alpha-carbons and selected atoms of the flavin mononucleotide cofactor, 116 constraints to enforce conserved hydrogen bonds, and 452 constraints on the torsion angles in conserved residues. An en...

PERSPECTIVES AND OVERVIEW 167 THE STRUCTURAL INTERPRETATION OF NMR DATA 1 69 The Resonance A ssignment Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Geometric Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Distance Geometry Algorithms ......... 177 Refinement of N M R Structures . . . . . . . . 180

A high-precision solution structure of the elastase inhibitor eglin c was determined by NMR and distance geometry calculations. A large set of 947 nuclear Overhauser (NOE) distance constraints was identified, 417 of which were quantified from two-dimensional NOE spectra at short mixing times. In addition, a large number of homonuclear 1H-1H and heteronuclear 1H-15N vicinal coupling constants were used, and constraints on 42 chi 1 and 38 phi angles were obtained. Structure calculations were carried out using the distance geometry program DG-II. These calculations had a high convergence rate, in that 66 out of 75 calculations converged with maximum residual NOE violations ranging from 0.17 A to 0.47 A. The spread of the structures was characterized with average root mean square deviations () between the structures and a mean structure. To calculate the unbiased toward any single structure, a new procedure was used for structure alignment. A canonical structure was calculated from the mean distances, and all structures were aligned relative to that. Furthermore, an angular order parameter S was defined and used to characterize the spread of structures in torsion angle space. To obtain an accurate estimate of the precision of the structure, the number of calculations was increased until the and the angular order parameters stabilized. This was achieved after approximately 40 calculations. The structure consists of a well-defined core whose backbone deviates from the canonical structure ca. 0.4 A, a disordered N-terminal heptapeptide whose backbone deviates by 0.8-12 A, and a proteinase-binding loop whose backbone deviates up to 3.0 A. Analysis of the angular order parameters and inspection of the structures indicates that a hinge-bending motion of the binding loop may occur in solution. Secondary structures were analyzed by comparison of dihedral angle patterns. The high precision of the structure allows one to identify subtle differences with four crystal structures of eglin c determined in complexes with proteinases.

A modeling study of the potential for storing energy in the elastic deformation of springs comprised of carbon nanotubes (CNTs) is presented. Analytic models were generated to estimate the ideal achievable energy density in CNTs subject to axial tension, compression, bending and torsion, taking into account limiting mechanisms such as the strength of individual CNTs, the onset of buckling, and the packing density limitations of CNT groupings. The stored energy density in CNT springs is predicted to be highest under tensile loading, with maximum values more than three orders of magnitude greater than the energy density of steel springs, and approximately eight times greater than the energy density of lithium-ion batteries. Densely packed bundles of precisely aligned, small diameter single-walled carbon nanotubes are identified as the best structure for high performance springs. The conceptual design and modeling of a portable electric power source that stores energy in a CNT spring are presented as tools for studying the potential performance of a system for generating electricity from the CNTs' stored mechanical energy.

Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences. The distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. The observation and control of incoherence in small Hilbert spaces is well known. Here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. As expected, it is more difficult to separate incoherence and decoherence over such processes. However, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. This result is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation., 15 pages, 6 figures

There is a growing need for small, lightweight, reliable, highly efficient and fully rechargeable portable power sources. The focus of this project is the design and modeling of a system in which energy is stored in the elastic deformation of carbon nanotube (CNT)-based springs. The CNTs are coupled to a MEMS electric generator. When the CNT deformation is released, the stored energy actuates the generator, which then converts the energy into electricity. The MEMS generator may be operated in reverse, as a motor, in order to wind the CNT springs and recharge the system. Alternatively, the stored elastic energy may be used to supply a mechanical load directly. This project is motivated by recent research into the mechanical properties of CNTs. The CNTs have a high stiffness, low defect density, and a consequently high yield strain that enables them to store elastic energy with significantly greater energy density than typical spring materials such as high-carbon steel. Models suggest that CNTs can be reversibly stretched by up to 15% [1]; lower strains of up to 6% have been demonstrated experimen-tally to date [2-3].This type of system offers several important potential advantages. First, due to CNTs’ high strength, high flexibility, and low defect density, they can store energy at very high energy density. Con-sidering just the CNT-based spring itself, the energy density of an array of CNTs stretched to a reversible 15% strain is about 1500 W-hr/kg, about ten times the energy density of Li-ion batteries. The energy density of the final system will be lower because of the finite conversion efficiency of the generator and the weight of both the supporting structure and the generator hardware. In addition, because energy storage in the CNT system is based on stretching chemical bonds rather than breaking and reforming chemical bonds as in batteries, the CNT-MEMS generator sys-tem has the potential to operate at higher power densities, un-der harsher conditions, to deeper discharge levels, and through a greater number of charge-discharge cycles than a chemical bat-tery.The system architecture consists of a CNT-based energy storage element, an energy release rate mechanism, and a MEMS gen-erator. This project is examining and modeling different varia-tions on this system architecture that incorporate different modes of deformation of the CNT-based energy storage element, vari-ous types of generators, different types of coupling between the storage element and the generator, and different size scales for the various components. One conceptual example is illustrated below, in which the axial relaxation of an axially-stretched CNT-based storage element is converted to rotational motion of a wheel. The wheel is coupled to a piezoelectric generator through a mechanism that regulates the rate of energy release, much as in a mechanical watch.

A critical step in experimental quantum information processing (QIP) is to implement control of quantum systems protected against decoherence via informational encodings, such as quantum error correcting codes, noiseless subsystems and decoherence free subspaces. These encodings lead to the promise of fault tolerant QIP, but they come at the expense of resource overheads. Part of the challenge in studying control over multiple logical qubits, is that QIP test-beds have not had sufficient resources to analyze encodings beyond the simplest ones. The most relevant resources are the number of available qubits and the cost to initialize and control them. Here we demonstrate an encoding of logical information that permits the control over multiple logical qubits without full initialization, an issue that is particularly challenging in liquid state NMR. The method of subsystem pseudo-pure state will allow the study of decoherence control schemes on up to 6 logical qubits using liquid state NMR implementations., 9 pages, 1 Figure