Keynote Speakers

Plenary Speakers


Mathematical Challenges Advancing Quantum Computing for Chemical Sciences
Bert de Jong, Lawrence Berkeley National Laboratory (USA)

Abstract:

In recent years significant advances have been made to deliver quantum computing as a platform enabling scientific discovery. One of the early fields to adopt this technology is chemical sciences. While progress has been made in hardware, software and algorithms, much work is still to be done to make scientific quantum computing a reality. Much work is to be done to further improve hardware. Further advancements are needed in mathematics, from solvers and optimizers to efficiently encoding complex quantum information.

In this talk I will discuss the current state-of-the art in quantum computing, and I will outline some of the open challenges in computer science and applied mathematics. I will discuss some of the advances made by the Quantum Algorithms Team led out of Lawrence Berkeley National Laboratory, an integrated team of quantum algorithm developers, mathematicians, and computer scientists with a mission to deliver algorithmic, computational and mathematical advances to enable scientific discovery in chemical sciences on quantum computers. Our team has assessed the robustness of state preparation, devised new sparse techniques with lower gate depth, and have explored the use of tensor networks. Preparation of scientifically relevant states is a key challenge for chemical simulations. We have developed a protocol to discriminate between decoherence and information scrambling as a way to verify quantum circuits, which was experimentally validated on an ion trap. Gate depth of a quantum circuit plays a critical role in achieving results with high fidelity. The team, in partnership with NASA, has demonstrated low depth circuits for k-local gates in QAOA and Trotterized fermionic Hamiltonians. We extended the open-source quantum simulation software framework ProjectQ with gate-level noise injection capabilities for error analysis, and used it to demonstrate that a rudimentary approach to mitigate errors in a CNOT gate operation can improve the gate fidelity. Additional efforts for error mitigation are ongoing. We have developed a large suite of stochastic classical optimizers, needed for variational quantum eigensolvers and qubit gate optimization. We are continuing to develop new and better stochastic optimizers.


Mathematics: a useful tool in farming and ecosystems management
Ezio Venturino, Dipartmento di Matematica "Giuseppe Peano", Torino (Italy)

Abstract:

Some recent contributions in the models of ecological systems will be presented, with special emphasis on current relevant issues such as invading alien species, diseases of animals and plants and pests that pose a renewed threat to agricultural practices in view also of the current trend in climatic conditions. We will focus first on two current hot issues in Italy, the invasion of grey squirrels, and the European hare, that are replacing the respective native species. Models of the positive and negative role that fungi possess are the next subject: they can be used for instance for wastewater bioremediation.

On the other hand, some of them exert a pathogenic effect on plants, in which however also phyllo sphere microorganisms may play a beneficial influence for the plant. Applications to typical cultures in the Mediterranean region will be discussed, Plant diseases caused by insects and some biological ways of fighting them constitute the next topic. The focus will be on the use of parasitism against aphids, and a type of innocuous insecticide against the fly responsible for the mosaic disease in “Jatropha curcas” plants. Finally a somewhat recently discovered goat disease will be considered.


Iterative processes for nonlinear problems: from Newton to nowadays
Alicia Cordero1, Miguel Ángel Hernández-Verón2, Juan R. Torregrosa1

(1)Instituto de Matemáticas Multidisciplinar,
Universitat Politècnica de València, Valencia, Spain

(2)Departamento de Matemáticas y Computación,
Universidad de La Rioja, Logroño, Spain

Abstract:

Solving nonlinear problems (scalar, vectorial or matrix equations) is a classical problem with many applications in Science and Engineering. Usually, this kind of problems does not have exact solutions. So, we must appeal to iterative processes for obtaining an estimation of the solution.

Although in the ancient ages there were some iterative-like methods, it is Newton’s scheme the beginning of what we consider as an iterative method. It has been widely used (in fact, it is still used) for solving many applied problems, but also its performance has been studied from different points of view: its semilocal, local or global convergence in Banach spaces, its dynamical behavior, its computational efficiency, etc.

Thanks to the huge development of computing in recent years, many researchers have designed different iterative methods trying to improve Newton’s scheme in any of its faces: convergence, stability, efficiency,... In this talk, we give an overview of how research in this area has evolved and which are the future challenges.


Algorithms for convex minimization problems with convergence analysis with Applications
Poom Kumam, (Ph.D), Theoretical and Computational Science (TaCS) Center & KMUTT-Fixed Point Theory and Applications Research Group (Thailand)

Abstract:

It is our purpose to we investigated on some new computational methods for such optimality under the major assumption about geodesic convexity to deal with relevant non-convex problems, while we use standard convexity assumption to deal with problems of simpler behavior. Numerical experiments are also interesting in order to illustrate the actual usage of the proposed methods. Moreover, for the continuation of our research, applications of such problems including, but not limited to image restoration and network allocation, are also interesting to explore.

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