A QUANTUM ALGORITHM FOR AUTOMATA ENCODING

Encoding of finite automata or state machines is critical to modern digital logic design methods for sequential circuits. Encoding is the process of assigning to every state, input value, and output value of a state machine a binary string, which is used to represent that state, input value, or output value in digital logic. Usually, one wishes to choose an encoding that, when the state machine is implemented as a digital logic circuit, will optimize some aspect of that circuit. For instance, one might wish to encode in such a way as to minimize power dissipation or silicon area. For most such optimization objectives, no method to find the exact solution, other than a straightforward exhaustive search, is known. Recent progress towards producing a quantum computer of large enough scale to surpass modern supercomputers has made it increasingly relevant to consider how quantum computers may be used to solve problems of practical interest. A quantum computer using Grover’s well-known search algorithm can perform exhaustive searches that would be impractical on a classical computer, due to the speedup provided by Grover’s algorithm. Therefore, we propose to use Grover’s algorithm to find optimal encodings for finite state machines via exhaustive search. We demonstrate the design of quantum circuits that allow Grover’s algorithm to be used for this purpose. The quantum circuit design methods that we introduce are potentially applicable to other problems as well

Peptide Bond Distortions from Planarity: New Insights from Quantum Mechanical Calculations and Peptide/Protein Crystal Structures

By combining quantum-mechanical analysis and statistical survey of peptide/protein structure databases we here report a thorough investigation of the conformational dependence of the geometry of peptide bond, the basic element of protein structures. Different peptide model systems have been studied by an integrated quantum mechanical approach, employing DFT, MP2 and CCSD(T) calculations, both in aqueous solution and in the gas phase. Also in absence of inter-residue interactions, small distortions from the planarity are more a rule than an exception, and they are mainly determined by the backbone ψ dihedral angle. These indications are fully corroborated by a statistical survey of accurate protein/peptide structures. Orbital analysis shows that orbital interactions between the σ system of Cα substituents and the π system of the amide bond are crucial for the modulation of peptide bond distortions. Our study thus indicates that, although long-range inter-molecular interactions can obviously affect the peptide planarity, their influence is statistically averaged. Therefore, the variability of peptide bond geometry in proteins is remarkably reproduced by extremely simplified systems since local factors are the main driving force of these observed trends. The implications of the present findings for protein structure determination, validation and prediction are also discussed

A Method for Reducing Ill-Conditioning of Polynomial Root Finding Using a Change of Basis

The problem of solving polynomial equations is one of the oldest problems in mathematics. Many ancient civilizations developed systems of algebra which included methods for solving linear equations. Around 2000 B.C.E. the Babylonians found a method for solving quadratic equations which is equivalent to the modern quadratic formula. Several Italian Renaissance mathematicians found general methods for finding roots of cubic and quartic polynomials. But it is known that there is no general formula for finding the roots of any polynomial of degree 5 or higher using only arithmetic operations and root extraction. Therefore, when presented with the problem of solving a fifth degree or higher polynomial equation, it is necessary to resort to numerical approximations. The best existing numerical methods for polynomial root-finding are already able to produce accurate and precise results with errors on the order of machine precision. However, these methods assume that the polynomial coefficients are known exactly. In real-world situations where polynomial functions are used to interpolate measured data this is not the case. This leads to unacceptably large errors in the computed roots due to a phenomenon known as ill-conditioning, where small changes to the coefficients result in disproportionately large changes to the roots. The objective of this research is to develop a methodology for finding polynomial roots with reasonable accuracy even in a real-world situation where the polynomial itself is not known exactly. This is achieved by using a change of basis; in other words, representing an arbitrary polynomial in terms of so-called Chebyshev polynomials. The proposed methodology is experimentally shown to tolerate uncertainties at least a thousand times larger than those which can be tolerated without using Chebyshev polynomials

A Quantum Algorithm for Automata Encoding

Encoding of finite automata or state machines is critical to modern digital logic design methods for sequential circuits. Encoding is the process of assigning to every state, input value, and output value of a state machine a binary string, which is used to represent that state, input value, or output value in digital logic. Usually, one wishes to choose an encoding that, when the state machine is implemented as a digital logic circuit, will optimize some aspect of that circuit. For instance, one might wish to encode in such a way as to minimize power dissipation or silicon area. For most such optimization objectives, no method to find the exact solution, other than a straightforward exhaustive search, is known. Recent progress towards producing a quantum computer of large enough scale to surpass modern supercomputers has made it increasingly relevant to consider how quantum computers may be used to solve problems of practical interest. A quantum computer using Grover’s well-known search algorithm can perform exhaustive searches that would be impractical on a classical computer, due to the speedup provided by Grover’s algorithm. Therefore, we propose to use Grover’s algorithm to find optimal encodings for finite state machines via exhaustive search. We demonstrate the design of quantum circuits that allow Grover’s algorithm to be used for this purpose. The quantum circuit design methods that we introduce are potentially applicable to other problems as well

Methodologies for Quantum Circuit and Algorithm Design at Low and High Levels

Although the concept of quantum computing has existed for decades, the technology needed to successfully implement a quantum computing system has not yet reached the level of sophistication, reliability, and scalability necessary for commercial viability until very recently. Significant progress on this front was made in the past few years, with IBM planning to create a 1000-qubit chip by the end of 2023, and Google already claiming to have achieved quantum supremacy. Other major industry players such as Intel and Microsoft have also invested significant amounts of resources into quantum computing research. Any viable computing system requires both hardware and software to work together harmoniously in order to perform useful computations. While the achievements of IBM and other companies represent a large step forward for quantum hardware, many gaps remain to be filled with respect to the corresponding software. Specifically, there is currently no clear path towards a complete process for translating quantum algorithms into physical operations that are directly executable on quantum hardware. Such a process is analogous to a compiler that translates programs written in a high-level language into executable machine instructions on a conventional digital computer, and it is necessary if quantum computers are to be harnessed to perform practically useful computations. Existing work has addressed individual components of this process, but so far no unified method for translating the whole of a quantum algorithm into executable operations has been described. I make substantial progress towards filling this gap by describing a set of high-level and low-level quantum circuit design techniques, which when taken together reduce the need of a circuit designer to be concerned with low-level details. On the high-level side, I describe an approach or strategy to designing quantum oracles for Grover\u27s algorithm that allows it to be applied to several types of problems. This approach involves designing oracles in terms of high-level blocks such as counters, multiplexers, comparators, and arbitrary Boolean functions. The implementations of these blocks in terms of lower-level quantum gates are demonstrated in a way that makes it clear that scaled-up versions of them can be generated in a completely automated fashion. For a specific class of problems, which I call state-space path planning problems, I also introduce a paradigm for quantum oracle design that involves representing the problem in terms of individual states and moves. Problems of this sort have applications in robotics and games. Low-level techniques that I introduce include methods for realizing both single-output and multiple-output Boolean functions, as well as reversible functions with multiple-valued inputs and outputs, on the quantum gate level. These realization methods can be used to translate the Boolean functions used as high-level blocks in quantum oracle design into low-level gates. The low-level gates used are two-qubit controlled gates such as controlled-NOT and controlled-V whose physical realizations have been extensively studied. In particular, I demonstrate that realizing symmetric functions, which are a subset of Boolean functions, directly using these low-level gates can give better results than the usual method of using higher-level Toffoli gates as intermediates. I also demonstrate that the problem of realizing a reversible Boolean function with many inputs and many outputs in place , that is, using the same qubits to hold the inputs and outputs of the function, can be converted into realizing a sequence of single-output Boolean functions. I describe the realization methods in sufficient detail for a skilled programmer to implement them as part of a CAD tool for quantum circuit design

Mass transfer area of structured packing

textThe mass transfer area of nine structured packings was measured as a function of liquid load, surface tension, liquid viscosity, and gas rate in a 0.427 m (16.8 in) ID column via absorption of CO₂ from air into 0.1 mol/L NaOH. Surface tension was decreased from 72 to 30 mN/m via the addition of a surfactant (TERGITOL[trademark] NP-7). Viscosity was varied from 1 to 15 mPa·s using poly(ethylene oxide) (POLYOX[trademark] WSR N750). A wetted-wall column was used to verify the kinetics of these systems. Literature model predictions matched the wetted-wall column data within 10%. These models were applied in the interpretation of the packing results. The packing mass transfer area was most strongly dictated by geometric area (125 to 500 m²/m³) and liquid load (2.5 to 75 m³/m²·h or 1 to 30 gpm/ft²). A reduction in surface tension enhanced the effective area. The difference was more pronounced for the finer (higher surface area) packings (15 to 20%) than for the coarser ones (10%). Gas velocity (0.6 to 2.3 m/s), liquid viscosity, and channel configuration (45° vs. 60° or smoothed element interfaces) had no appreciable impact on the area. Surface texture (embossing) increased the area by 10% at most. The ratio of effective area to specific area (a[subscript e]/a[subscript p]) was correlated within limits of ±13% for the experimental database: [mathematical formula]. This area model is believed to offer better predictive accuracy than the alternatives in the literature, particularly under aqueous conditions. Supplementary hydraulic measurements were obtained. The channel configuration significantly impacted the pressure drop. For a 45°-to-60° inclination change, pressure drop decreased by more than a factor of two and capacity expanded by 20%. Upwards of a two-fold increase in hold-up was observed from 1 to 15 mPa·s. Liquid load strongly affected both pressure drop and hold-up, increasing them by several-fold over the operational range. An economic analysis of an absorber in a CO₂ capture process was performed. Mellapak[trademark] 250X yielded the most favorable economics of the investigated packings. The minimum cost for a 7 m MEA system was around $5-7/tonne CO₂ removed for capacities in the 100 to 800 MW range.Chemical Engineerin

Developing a data warehouse using MDBMS and OLAP techniques

In today’s highly specialized business environment, efficient management and product distribution determine the success of an organization. This advocates seeking potential efficiency improvements and hidden sales opportunities. Every organization has a lot of information about its customers, suppliers, and operations or has the ability to gather such information. The problem is extracting and making good use of this information. Purely transactional processing systems are no longer sufficient to ensure long-term competitiveness. If a firm is unable to utilize available information and generate new sales opportunities, it will quickly lose its competitive advantage. The purpose of this research is to help executives of any organization to improve operational performance, reveal hidden information and patterns, and increase sales opportunities. This is done through developing a data warehouse that will assist the management of an organization to look at the data in different perspectives. This paper explores the technology and considers a number of practical issues of concern in applying the technique. A series of key concepts regarding the field of data warehousing are presented. In particular, the concepts of OLAP and Data Warehouse are illuminated, which are the fundamental components of modern data warehouses. The conceptual and logical design techniques of the analytical databases and the multidimensional analyses, made available by this model of data, are also presented. More importantly, it tells you where organizational units can improve and how data warehousing systems can help increase business opportunities

Grover-based Ashenhurst-Curtis Decomposition Using Quantum Language Quipper

Functional decomposition plays a key role in several areas such as system design, digital circuits, database systems, and Machine Learning. This paper presents a novel quantum computing approach based on Grover’s search algorithm for a generalized Ashenhurst-Curtis decomposition. The method models the decomposition problem as a search problem and constructs the oracle circuit based on the set-theoretic partition algebra. A hybrid quantum-based algorithm takes advantage of the quadratic speedup achieved by Grover’s search algorithm with quantum oracles for finding the minimum-cost decomposition. The method is implemented and simulated in the quantum programming language Quipper. This work constitutes the first attempt to apply quantum computing to functional decompositio