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We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation.
Challenging computational problems arising in the practical world are frequently tackled by heuristic algorithms. Small universal quantum computers will emerge in the next year or two, enabling a substantial broadening of the types of quantum heuristics that can be investigated beyond quantum annealing. The immediate question is What experiments should we prioritize that will give us insight into quantum heuristics? One leading candidate is the quantum approximate optimization algorithm (QAOA) metaheuristic. Here, we provide a framework for designing QAOA circuits for a variety of combinatorial optimization problems with both hard constraints that must be met and soft constraints whose violation we wish to minimize. We work through a number of examples, and discuss design principles and implementation considerations.
Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.
We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing.
My research activities for the summer of 2003 consisted of two projects: One project was concerned with determining a method for predicting the static and dynamic assembly properties of nano-structures using laser tweezers. The other project was to investigate the generation of Laguerre-Gaussian modes using a spatial light modulator incorporated into an optical tweezers system. Concerning the first project, I initially pursued the approach suggested by my NASA colleague Dr. Art Decker. This approach involved mimicking the model of the structure of atomic nucleus for the assembly of 1 to 100 atoms using allowed quadruple transitions induced by orbital angular momentums of a Laguerre- Gaussian (Doughnut) laser mode. After realizing the inaptness of the nuclear model with the nanostructure model as far as the binding forces and transitions were concerned, I focused on using quantum dot modei. This model was not attuned also for the host lattice influences the electronic structure of the quantum dot. Thus one other option that I decided to pursue was the approach of molecular quantum mechanics. In this approach the nanostructure is treated as a large (10-100 nm) molecule constructed from single element or multi-elements. Subsequent to consultation with Dr. Fred Morales, a chemical engineer at NASA GRC, and Dr. David Ball, a computational chemist at Cleveland State University, I acquired a molecular-quantum computation software, Hyperchem 7.0. This software allows simulation of different molecular structures as far as their static and dynamic behaviors are concerned. The time that I spent on this project was about eight weeks. Once this suitable approach was identified, I realized the need to collaborate with a computational quantum chemist to pursue searching for stable nanostructures in the range of 10-100 nm that we can be assembled using laser tweezers. The second project was about generating laser tweezers that possess orbital angular momentum. As shown, we were able to generate laser tweezers modes of different orbital angular momentum using a spatial light modulator incorporated into a laser tweezers system. The motivation for investigating these types of modes stems from being able to spin particles at high speeds and also to orient two particles in separate traps and then join them together. Also, there has been recent intense interest on fundamental physics research on orbital angular momentum of light. The fact that circularly polarized light may have associated with it angular momentum that relates to the spin of individual photons (spin 0 for the plane polarized light, spin +1 for the right-circularly polarized light and spin -1 for the left-circularly polarized light) was first demonstrated by Beth in 1936. Orbital angular momentum is, however, distinct from spin in that the spin angular momentum of light is intrinsically linked to the behavior of the electric field in the light whereas orbital angular momentum is a consequence of inclined wavefronts. In 1992 L. Allen, et al showed that the Laguerre-Gaussian (LG) modes could possess well-defined orbital angular momentum that can exceed 1 planck's constant, i.e. l plancks constant per photon, where l is the azimuthal index of the mode.
The main promise of Quantum Dot Cellular Automata (QCA) as a new computing paradigm is the possbility of implementing a set of universal logic gates and thus feasibility of general-purpose computing.
Units of superconducting circuitry that exploit the concept of the single- Cooper-pair box (SCB) have been built and are undergoing testing as prototypes of logic gates that could, in principle, constitute building blocks of clocked quantum computers. These units utilize quantized charge states as the quantum information-bearing degrees of freedom. An SCB is an artificial two-level quantum system that comprises a nanoscale superconducting electrode connected to a reservoir of Cooper-pair charges via a Josephson junction. The logical quantum states of the device, .0. and .1., are implemented physically as a pair of charge-number states that differ by 2e (where e is the charge of an electron). Typically, some 109 Cooper pairs are involved. Transitions between the logical states are accomplished by tunneling of Cooper pairs through the Josephson junction. Although the two-level system contains a macroscopic number of charges, in the superconducting regime, they behave collectively, as a Bose-Einstein condensate, making possible a coherent superposition of the two logical states. This possibility makes the SCB a candidate for the physical implementation of a qubit. A set of quantum logic operations and the gates that implement them is characterized as universal if, in principle, one can form combinations of the operations in the set to implement any desired quantum computation. To be able to design a practical quantum computer, one must first specify how to decompose any valid quantum computation into a sequence of elementary 1- and 2-qubit quantum gates that are universal and that can be realized in hardware that is feasible to fabricate. Traditionally, the set of universal gates has been taken to be the set of all 1-qubit quantum gates in conjunction with the controlled-NOT (CNOT) gate, which is a 2-qubit gate. Also, it has been known for some time that the SWAP gate, which implements square root of the simple 2-qubit exchange interaction, is as computationally universal as is the CNOT operation.
Comparisons are made between potential energy surfaces (PES) for N2 + N and N2 + N2 collisions and between rate coefficients for N2 dissociation that were computed using the quasiclassical trajectory method (QCT) on these PESs. For N2 + N we compare the Laganas empirical LEPS surface with one from NASA Ames Research Center based on ab initio quantum chemistry calculations. For N2 + N2 we compare two ab initio PESs (from NASA Ames and from the University of Minnesota). These use different methods for computing the ground state electronic energy for N4, but give similar results. Thermal N2 dissociation rate coefficients, for the 10,000K-30,000K temperature range, have been computed using each PES and the results are in excellent agreement. Quasi-stationary state (QSS) rate coefficients using both PESs have been computed at these temperatures using the Direct Molecular Simulation of Schwartentruber and coworkers. The QSS rate coefficients are up to a factor of 5 lower than the thermal ones and the thermal and QSS values bracket the results of shock-tube experiments. We conclude that the combination of ab initio quantum chemistry PESs and QCT calculations provides an attractive approach for the determination of accurate high-temperature rate coefficients for use in aerothermodynamics modeling.
This paper, following a brief introduction, is divided into five parts. Part I outlines the theory of the molecular orbital method for the ground, ionized and excited states of molecules. Part II gives a brief summary of the interaction integrals and their tabulation. Part III outlines an automatic program designed for the computation of various states of molecules. Part IV gives examples of the study of ground, ionized and excited states of CO, BH and N2 where the program of automatic computation and molecular integrals have been utilized. Part V enlists some special problems of Molecular Quantum Mechanics are being tackled at New York University.
Exploration and colonization of the universe awaits, but Earth-adapted biological humans are ill-equipped to respond to the challenge. Machines have gone farther and seen more, limited though they presently are by insect-like behavior inflexibility. As they become smarter over the coming decades, space will be theirs. Organizations of robots of ever increasing intelligence and sensory and motor ability will expand and transform what they occupy, working with matter, space and time. As they grow, a smaller and smaller fraction of their territory will be undeveloped frontier. Competitive success will depend more and more on using already available matter and space in ever more refined and useful forms. The process, analogous to the miniaturization that makes today's computers a trillion times more powerful than the mechanical calculators of the past, will gradually transform all activity from grossly physical homesteading of raw nature, to minimum-energy quantum transactions of computation. The final frontier will be urbanized, ultimately into an arena where every bit of activity is a meaningful computation: the inhabited portion of the universe will be transformed into a cyberspace. Because it will use resources more efficiently, a mature cyberspace of the distant future will be effectively much bigger than the present physical universe. While only an infinitesimal fraction of existing matter and space is doing interesting work, in a well developed cyberspace every bit will be part of a relevant computation or storing a useful datum. Over time, more compact and faster ways of using space and matter will be invented, and used to restructure the cyberspace, effectively increasing the amount of computational spacetime per unit of physical spacetime. Computational speed-ups will affect the subjective experience of entities in the cyberspace in a paradoxical way. At first glimpse, there is no subjective effect, because everything, inside and outside the individual, speeds up equally. But, more subtly, speed-up produces an expansion of the cyber universe, because, as thought accelerates, more subjective time passes during the fixed (probably lightspeed) physical transit time of a message between a given pair of locations - so those fixed locations seem to grow farther apart. Also, as information storage is made continually more efficient through both denser utilization of matter and more efficient encodings, there will be increasingly more cyber-stuff between any two points. The effect may somewhat resemble the continuous-creation process in the old steady-state theory of the physical universe of Hoyle, Bondi and Gold, where hydrogen atoms appear just fast enough throughout the expanding cosmos to maintain a constant density.
The volume contains recommendations for space-and ground-based programs in gravitational physics, cosmology, and cosmic-ray physics. The section on gravitation examines current and planned experimental tests of general relativity; the theory behind, and search for, gravitational waves, including sensitive laser-interferometric tests and other observations; and advances in gravitation theory (for example, incorporating quantum effects). The section on cosmology deals with the big-bang model, the standard model from elementary-particle theory, the inflationary model of the Universe. Computational needs are presented for both gravitation and cosmology. Finally, cosmic-ray physics theory (nucleosynthesis, acceleration models, high-energy physics) and experiment (ground and spaceborne detectors) are discussed.
Instead of a quantum computer where the fundamental units are 2-dimensional qubits, the author considers a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to d-dimensional systems, and he discusses the theory of fault-tolerant computation using such codes. He proves that universal fault-tolerant computation is possible with any higher-dimensional stabilizer code for prime d.
The relative connectedness of the high- and low-density regions in the universe is studied using a median density contour which divides space into two equal volumes. The CfA data are found to show a sponge-like topology where the highand low-density regions are both interlocking and equivalent. The boundary surface between the two regions has a general negative curvature, and is characterized by a large number of holes. In the initial conditions the connectedness of the two regions must be identical because a change of sign in the random quantum fluctuations would reverse their roles. It is noted that in the cold dark matter and neutrino scenarios the hole sizes are typically of the order of the smoothing diameter or the damping length, whichever is larger. The sponge-like topology is consistent with the universe having a frothy appearance without being divided neatly into cells. A computer algorithm for measuring topology is discussed.
In this report, we focus on the calculations of the energetics and chemical kinetics of heterogeneous reactions for Organometallic vapor phase epitaxy (OMVPE). The work described in this report builds upon our own previous thermochemical and chemical kinetics studies. The first of these articles refers to the prediction of thermochemical properties, and the latter one deals with the prediction of rate constants for gaseous homolytic dissociation reactions. The calculations of this investigation are at the microscopic level. The systems chosen consisted of a gallium nitride (GaN) substrate, and molecular nitrogen (N2) and ammonia (NH3) as adsorbants. The energetics for the adsorption and the adsorbant dissociation processes were estimated, and reaction rate constants for the dissociation reactions of free and adsorbed molecules were predicted. The energetics for substrate decomposition was also computed. The ONIOM method, implemented in the Gaussian98 program, was used to perform the calculations. This approach has been selected since it allows dividing the system into two layers that can be treated at different levels of accuracy. The atoms of the substrate were modeled using molecular mechanics6 with universal force fields, whereas the adsorbed molecules were approximated using quantum mechanics, based on density functional theory methods with B3LYP functionals and 6-311G(d,p) basis sets. Calculations for the substrate were performed in slabs of several unit cells in each direction. The N2 and NH3 adsorbates were attached to a central location at the Ga-lined surface.
We present results from several projects in the new field of computational astrobiology, which is devoted to advancing our understanding of the origin, evolution and distribution of life in the Universe using theoretical and computational tools. We have developed a procedure for calculating long-range effects in molecular dynamics using a plane wave expansion of the electrostatic potential. This method is expected to be highly efficient for simulating biological systems on massively parallel supercomputers. We have perform genomics analysis on a family of actin binding proteins. We have performed quantum mechanical calculations on carbon nanotubes and nucleic acids, which simulations will allow us to investigate possible sources of organic material on the early earth. Finally, we have developed a model of protobiological chemistry using neural networks.
Suitably patterned arrays (blocks) of quantum-dot cellular automata (QCA) have been proposed as fault-tolerant universal logic gates. These block QCA gates could be used to realize the potential of QCA for further miniaturization, reduction of power consumption, increase in switching speed, and increased degree of integration of very-large-scale integrated (VLSI) electronic circuits. The limitations of conventional VLSI circuitry, the basic principle of operation of QCA, and the potential advantages of QCA-based VLSI circuitry were described in several NASA Tech Briefs articles, namely Implementing Permutation Matrices by Use of Quantum Dots (NPO-20801), Vol. 25, No. 10 (October 2001), page 42; Compact Interconnection Networks Based on Quantum Dots (NPO-20855) Vol. 27, No. 1 (January 2003), page 32; Bit-Serial Adder Based on Quantum Dots (NPO-20869), Vol. 27, No. 1 (January 2003), page 35; and Hybrid VLSI/QCA Architecture for Computing FFTs (NPO-20923), which follows this article. To recapitulate the principle of operation (greatly oversimplified because of the limitation on space available for this article): A quantum-dot cellular automata contains four quantum dots positioned at or between the corners of a square cell. The cell contains two extra mobile electrons that can tunnel (in the quantummechanical sense) between neighboring dots within the cell. The Coulomb repulsion between the two electrons tends to make them occupy antipodal dots in the cell. For an isolated cell, there are two energetically equivalent arrangements (denoted polarization states) of the extra electrons. The cell polarization is used to encode binary information. Because the polarization of a nonisolated cell depends on Coulomb-repulsion interactions with neighboring cells, universal logic gates and binary wires could be constructed, in principle, by arraying QCA of suitable design in suitable patterns. Heretofore, researchers have recognized two major obstacles to realization of QCA-based logic gates: One is the need for (and the difficulty of attaining) operation of QCA circuitry at room temperature or, for that matter, at any temperature above a few Kelvins. It has been theorized that room-temperature operation could be made possible by constructing QCA as molecular-scale devices. However, in approaching the lower limit of miniaturization at the molecular level, it becomes increasingly imperative to overcome the second major obstacle, which is the need for (and the difficulty of attaining) high precision in the alignments of adjacent QCA in order to ensure the correct interactions among the quantum dots.
A proposed integrated circuit based on quantum-dot cellular automata (QCA) would function as a bit-serial adder. This circuit would serve as a prototype building block for demonstrating the feasibility of quantum-dots computing and for the further development of increasingly complex and increasingly capable quantum-dots computing circuits. QCA-based bit-serial adders would be especially useful in that they would enable the development of highly parallel and systolic processors for implementing fast Fourier, cosine, Hartley, and wavelet transforms. The proposed circuit would complement the QCA-based circuits described in "Implementing Permutation Matrices by Use of Quantum Dots" (NPO-20801), NASA Tech Briefs, Vol. 25, No. 10 (October 2001), page 42 and "Compact Interconnection Networks Based on Quantum Dots" (NPO-20855), which appears elsewhere in this issue. Those articles described the limitations of very-large-scale-integrated (VLSI) circuitry and the major potential advantage afforded by QCA. To recapitulate: In a VLSI circuit, signal paths that are required not to interact with each other must not cross in the same plane. In contrast, for reasons too complex to describe in the limited space available for this article, suitably designed and operated QCA-based signal paths that are required not to interact with each other can nevertheless be allowed to cross each other in the same plane without adverse effect. In principle, this characteristic could be exploited to design compact, coplanar, simple (relative to VLSI) QCA-based networks to implement complex, advanced interconnection schemes. To enable a meaningful description of the proposed bit-serial adder, it is necessary to further recapitulate the description of a quantum-dot cellular automation from the first-mentioned prior article: A quantum-dot cellular automaton contains four quantum dots positioned at the corners of a square cell. The cell contains two extra mobile electrons that can tunnel (in the quantum-mechanical sense) between neighboring dots within the cell. The Coulomb repulsion between the two electrons tends to make them occupy antipodal dots in the cell. For an isolated cell, there are two energetically equivalent arrangements (denoted polarization states) of the extra electrons. The cell polarization is used to encode binary information. Because the polarization of a nonisolated cell depends on Coulomb-repulsion interactions with neighboring cells, universal logic gates and binary wires could be constructed, in principle, by arraying QCA of suitable design in suitable patterns. Again, for reasons too complex to describe here, in order to ensure accuracy and timeliness of the output of a QCA array, it is necessary to resort to an adiabatic switching scheme in which the QCA array is divided into subarrays, each controlled by a different phase of a multiphase clock signal. In this scheme, each subarray is given time to perform its computation, then its state is frozen by raising its inter-dot potential barriers and its output is fed as the input to the successor subarray. The successor subarray is kept in an unpolarized state so it does not influence the calculation of preceding subarray. Such a clocking scheme is consistent with pipeline computation in the sense that each different subarray can perform a different part of an overall computation. In other words, QCA arrays are inherently suitable for pipeline and, moreover, systolic computations. This sequential or pipeline aspect of QCA would be utilized in the proposed bit-serial adders.
Topics covered include: Valve-"Health"-Monitoring System; Microstrip Antenna for Remote Sensing of Soil Moisture and Sea Surface Salinity; Biomedical Wireless Ambulatory Crew Monitor; Wireless Avionics Packet to Support Fault Tolerance for Flight Applications; Aerobot Autonomy Architecture; Submillimeter Confocal Imaging Active Module; Traveling-Wave Maser for 32 GHz; System Synchronizes Recordings from Separated Video Cameras; Piecewise-Planar Parabolic Reflectarray Antenna; Reducing Interference in ATC Voice Communication; EOS MLS Level 1B Data Processing, Version 2.2; Auto-Generated Semantic Processing Services; Geospatial Authentication; Maneuver Automation Software; Event Driven Messaging with Role-Based Subscriptions; Estimating Relative Positions of Outer-Space Structures; Fabricating PFPE Membranes for Capillary Electrophoresis; Linear Actuator Has Long Stroke and High Resolution; Installing a Test Tap on a Metal Battery Case; Fabricating PFPE Membranes for Microfluidic Valves and Pumps; Room-Temperature-Cured Copolymers for Lithium Battery Gel Electrolytes; Catalysts for Efficient Production of Carbon Nanotubes; Amorphous Silk Fibroin Membranes for Separation of CO2; "Zero-Mass" Noninvasive Pressure Transducers; Radial-Electric-Field Piezoelectric Diaphragm Pumps; Ejector-Enhanced, Pulsed, Pressure-Gain Combustor; Suppressing Ghost Diffraction in E-Beam-Written Gratings; Target-Tracking Camera for a Metrology System; Polarimetric Imaging using Two Photoelastic Modulators; Miniature Wide-Angle Lens for Small-Pixel Electronic Camera; Modal Filters for Infrared Interferometry; Mo(3)Sb(7-x)Te(x) for Thermoelectric Power Generation; Two-Dimensional Quantum Model of a Nanotransistor; Scanning Miniature Microscopes without Lenses; Manipulating Neutral Atoms in Chip-Based Magnetic Traps; Expansion Compression Contacts for Thermoelectric Legs; Processing Electromyographic Signals to Recognize Words; Physical Principle for Generation of Randomness; DSN Beowulf Cluster-Based VLBI Correlator; Hybrid NN/SVM Computational System for Optimizing Designs; Criteria for Modeling in LES of Multicomponent Fuel Flow; Computerized Machine for Cutting Space Shuttle Thermal Tiles; Orbiting Depot and Reusable Lander for Lunar Transportation; FPGA-Based Networked Phasemeter for a Heterodyne Interferometer; Aquarius Digital Processing Unit; Three-Dimensional Optical Coherence Tomography; Benchtop Antigen Detection Technique using Nanofiltration and Fluorescent Dyes; Isolation of Precursor Cells from Waste Solid Fat Tissue; Identification of Bacteria and Determination of Biological Indicators; Further Development of Scaffolds for Regeneration of Nerves; Chemically Assisted Photocatalytic Oxidation System; Use of Atomic Oxygen for Increased Water Contact Angles of Various Polymers for Biomedical Applications; Crashworthy Seats Would Afford Superior Protection; Open-Access, Low-Magnetic-Field MRI System for Lung Research; Microfluidic Mixing Technology for a Universal Health Sensor; Microfluidic Extraction of Biomarkers using Water as Solvent; Microwell Arrays for Studying Many Individual Cells; Droplet-Based Production of Liposomes; and Identifying and Inactivating Bacterial Spores