Gated based quantum computer algorithm for geophysical inversion

Magnetotelluric (MT) inversion algorithms are an essential tool in exploration geophysics because they provide us with resistivity models of the subsurface. Inverse problems are ill-posed and non-unique. Resistivity models produced by geologically unconstrained MT inversions are typically smooth, which means that the geological interpretations obtained based on the resistivity models will be ambiguous and uncertain. To solve the above problems, geophysicists have made many efforts over the years to introduce any prior information (such as geological structure information and physical property data) into models, which could help to better constrain the inverted model with the inversion algorithms. In the last few years, there has been renewed interest in machine learning techniques. Various machine learning methods have been applied to inversions. Using the fuzzy c-means (FCM) clustering method, geophysicists proposed new inversion algorithms that are capable of building petrophysical information into the inversion. Although the FCM has been used and advanced in previous work, geophysicists concluded that a priori information of the correct number and value of cluster centers is very important for a successful FCM inversion. In fact, it is difficult to obtain the appropriate clustering information in some geophysical survey areas. In this study, we present an effective way to build the petrophysical information for the MT inversion based on FCM clustering algorithm. When the actual petrophysical information is insufficient, considering the characteristics of MT data, we perform a one-dimensional blocky inversion that can clearly identify the interface with distinct electrical property contrast; then, we obtain the number and value of cluster centers from 1D blocky inversion for the further MT inversion with FCM clustering. The algorithm uses guided FCM clustering to improve the model within the iterative minimization during MT inversion. In our MT inversion method, we integrate the geophysical inversion and geological differentiation into a unified scheme, which interact and enhance each other. The resistivity models obtained from the inversion respect the geophysical and petrophysical data and are easy to geologically interpret. We tested the algorithm using two synthetic examples and a field data example.

As we seek to make geophysical models more consistent with geological models, more and more a priori information is incorporated into geophysical inverse problems. How we make the most use of a priori information is still a key issue in geophysical inversion, particularly for effectively representing such information in inversion problems. To address this problem, we propose a symmetric polynomial constrained inversion algorithm that can represent multiple known physical properties for the lithology. The electrical resistivity synthetic model tests show that the inversion results constrained with symmetric polynomials can make the model resistivity be in line with a priori information and obtain more realistic sharp boundaries. Finally, we give a practical verification of our inversion algorithm with field data.

In mineral exploration, geophysical inversion is a common mathematical tool to obtain reliable information on subsurface density properties based on gravity measurements. Many inversion algorithms were developed to obtain the density distribution in the Earth’s subsurface. Recovered density values are usually lower/higher than the actual density as a consequence of inversion algorithm. This paper presents the use of a fuzzy cross-update inversion (FCUI) procedure to improve the subsurface density model based on a triangular grid. The algorithm is written in MATLAB and uses fuzzy c means clustering to improve the density modeling result per iteration. Two additional input parameters are added, namely the number of geologic units in the model (i.e., number of clusters) and the cluster center values of the geologic units (mean density value of each geologic unit). Inversion results from the FCUI are presented and compared with conventional inversion. The effectiveness of the developed technique is tested for the interpretation of synthetic data and two sets of field data. The FCUI approach shows improvement over conventional inversion approaches in differentiating geologic units. Further, FCUI was performed to reduce ambiguity of interpretation for the delineation of chromite and uranium deposits as the first and second case studies, respectively. We integrated favorable information and show the efficacy of FCUI over conventional inversion for the field datasets.

This paper explores the impact of quantum computing on modern information security technologies, especially the threat to traditional encryption methods. The parallel processing capability of quantum computing and Shor algorithm make traditional encryption methods face the risk of being cracked. To address this challenge, this paper introduces novel cryptographic methods based on quantum computing, including quantum walking (QW) and quantum entanglement based cryptographic schemes, as well as quantum attack-resistant cryptographic algorithms (PQC). The computing principles, advantages and disadvantages of NTRUEncrypt and Lattice-based encryption algorithms are discussed in detail, and the application and prospect of these new encryption methods in information security are analyzed.

Characterization of plastically graded nanostructured material: Part I. The theories and the inverse algorithm of nanoindentation

The area of feasible solutions (AFS) of a multivariate curve resolution method is the continuum of feasible solutions under the given constraints. In the current paper, the AFS is computed only on the condition of nonnegative solutions. This work is a continuation of a paper (J. Chemometrics 28:106–116, 2013) on the polygon inflation algorithm for AFS computations. In this second part, various properties of the AFS are analyzed. First, its boundedness is proved, which is a necessary condition for its numerical computation. Second, it is shown that the origin is never contained in the area of feasible solutions. This fact is the basis for the inverse polygon inflation algorithm, which allows to compute specific types of an AFS containing a hole.The numerical computation of the AFS is a complicated and computationally expensive process. The construction of proper objective functions for the AFS optimization problem appears to be decisive. The paper contains a comparative analysis of two objective functions and describes the ideas of the new FAC‐PACK toolbox for MATLAB. This freely available toolbox contains a numerical implementation of the polygon inflation and of the inverse polygon inflation algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

The main purpose of this review is to deal with questions related to the nature of quantum information and particularly with quantum entanglement as an important component of quantum information and computing. We will not discuss here quantum computer algorithms, like the algorithm by Shor, or their advantages and disadvantages. We only cover the material that lies at the foundations of quantum information and computing and epistemological questions. We attempt to connect the famous debate between Einstein and Bohr on quantum entanglement to some of the latest work on qubits and quantum computing and to the mathematical theorems that form the basis of these discussions, particularly the theorem of Bell. We present a critical analysis of this material and hope that this will give the reader a better understanding of what can be said with certainty about the nature of quantum information.

Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four "cache qubits" and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.

A quadratic programming algorithm for geophysical gravity inversion and other applications

Solving Computational Fluid Dynamics (CFD) problems requires the inversion of a linear system of equations, which can be done using a quantum algorithm for matrix inversion.
 However, the number of shots required to measure the output of the system can be prohibitive and remove any advantage obtained by quantum computing.
 In this work we propose a scheme for measuring the output of a Quantum Singular Value Transform (QSVT) matrix inversion algorithm specifically for the CFD use case.
 We use a Quantum Signal Processing (QSP) based amplitude estimation algorithm and show how it can be combined with the QSVT matrix inversion algorithm.
 We perform a detailed resource estimation of the amount of computational resources required for a single iteration of amplitude estimation, and compare the costs of amplitude estimation with the cost of not doing amplitude estimation and measuring the whole wavefunction.
 We also propose a measurement scheme to reduce the number of amplitudes measured in the CFD example by focussing on large amplitudes only. We simulate the whole CFD loop, finding that thus measuring only a small number of the total amplitudes in the output vector still results in an acceptable level of overall error.

Fedi and Rapolla (1999) state that potential-field inverse problems can be improved by using data collected at different levels above the source. This result seem to contradict Gauss’ theorem, which states that a harmonic field (e.g., the gravitational potential) is uniquely determined by its values on a surface surrounding the sources. Although we do not disagree that discreetly sampled data in different levels contain some additional information as compared to data collected at a single level, we believe that such additional information cannot qualitatively improve the fundamental problem of potential-field data inversion, i.e., its inherent ambiguity. For a formal analysis of the ambiguity problem we refer to Strykowski (1997) and Boschetti et al. (1999). Here, we emphasize, using simple examples, the crucial importance in potential field inverse problems of (1) the algorithm employed in the inversion process, (2) the horizontal extent of the data collection, and (3) the problem parameterization. We believe that these factors, not the presence of data at multiple levels, are responsible for the high quality of the results presented in Fedi and Rapolla (1999). inversion algorithm. In Figure 1, we reproduce the results showed by Fedi and Rapolla (1999), except for the gravity problem. All the numerical experiments presented here have been performed in 3D, following the same parameterization as in Fedi and Rapolla. However, we show the results as a 2D vertical cross-section in the y-direction through the center of the area. Fedi and Rapolla tackle the (underdetermined) inverse problem using Penrose's pseudoinverse solver. As with other algorithms used for geophysical inversion, such an operator solves for a minimum ( l 2) norm solution. Minimum norm not only implies …

Unlike some other well-known challenges such as facial recognition, where Machine Learning and Inversion algorithms are widely developed, the geosciences suffer from a lack of large, labelled datasets that can be used to validate or train robust Machine Learning and inversion schemes. Publicly available 3D geological models are far too restricted in both number and the range of geological scenarios to serve these purposes. With reference to inverting geophysical data this problem is further exacerbated as in most cases real geophysical observations result from unknown 3D geology, and synthetic test datasets are often not particularly geological, nor geologically diverse. To overcome these limitations, we have used the Noddy modelling platform to generate one million models, which represent the first publicly accessible massive training set for 3D geology and resulting gravity and magnetic datasets. This model suite can be used to train Machine Learning systems, and to provide comprehensive test suites for geophysical inversion. We describe the methodology for producing the model suite, and discuss the opportunities such a model suit affords, as well as its limitations, and how we can grow and access this resource.

Quantum Machine Learning (QML) is a new phraseology in the world today. With various upcoming Artificial Intelligence (AI) technologies, everyday data scientists and corporate around the world are trying to harness its power. QML borrows concepts of Quantum Computing and QML algorithms enhance the existing Machine Learning (ML) algorithms by processing datasets more efficiently. Quantum Computers are a powering force driving QML algorithms that boosts computational power and helps analyse data. QML algorithms can be applied in sectors involving number crunching, pattern identification and so on. In the existing world, QML can be a game-changer for organizations that work on identifying product correlations and customer behaviour in a brief time. This paper discusses studies related to principles of Quantum Mechanics, Quantum Computing and QML algorithm. Additionally, it explores opportunities and challenges faced in the field of QML. Lastly, the paper talks about QML applications and compares various available QML toolkits from the market. Future direction and exhaustive survey of papers from various spectrums related to Quantum Computing is presented in this paper.

The deterministic quantum computing with one qubit (DQC1) is a mixed-state quantum computation algorithm that evaluates the normalized trace of a unitary matrix and is more powerful than the classical counterpart. We find that the normalized trace of the unitary matrix can be directly described by the entangling power of the quantum circuit of the DQC1, so the nontrivial DQC1 is always accompanied with the non-vanishing entangling power. In addition, it is shown that the entangling power also determines the intrinsic complexity of this quantum computation algorithm, i.e., the larger entangling power corresponds to higher complexity. Besides, it is also shown that the non-vanishing entangling power does always exist in other similar tasks of DQC1.

An application of an evolutionary approach to hardware design is presented. A genetic algorithm was developed to discover good designs for quantum computer algorithms. The algorithms are expressed as quantum operator sequences applied in a circuit model. The circuits discovered are configurations of special purpose quantum computers. We have been exploring the evolution of algorithms as alternative configurations of hardware. By simulation it is established that the circuits will correctly compute a small collection of basic, low-level functions. Experiments produced designs for primitive quantum computers that evaluate logical or arithmetic functions with a total of twelve or fewer inputs and outputs.