European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
10:30   MS5: Numerical Mathematics on Quantum Computers (Part 1)
Chair: Matthias Möller
10:30
25 mins
Tutorial on Quantum Computing
Carmen G. Almudever
Abstract: Quantum computing is a very active and promising topic. Since the physicist Richard Feynman proposed the idea of building a quantum computer to simulate quantum systems in the early 80’s, different quantum algorithms have been developed. By exploiting quantum phenomena (superposition and entanglement), they promise to solve complex problems that are intractable for even the most powerful current supercomputers. One of the most famous examples is the factorization of large numbers using Shor’s algorithm. For instance, a 2000-bit number could be decomposed in a bit more than one day using a quantum computer whereas a data center of approx. 400.000 km2 built with the fastest today’s supercomputer would require around 100 years. Great progress has been made in recent years in quantum hardware based on different technologies such are superconducting qubits, ion traps, silicon quantum dots, topological qubits and Nitrogen Vacancy (NV) centers. Although quantum technologies still need to mature to get better coherence times and gate fidelities, quantum computation in the cloud is already a reality with small quantum processors that are capable of handling basic programs. Large companies (Google, Intel, Microsoft, IBM, Alibaba) and research groups are working on building the first universal quantum computer, which requires contributions from several disciplines including physics, mathematics, computer science, informatics and electrical engineering, among others. This tutorial will introduce the basic notions of quantum computing; going from quantum bits, superposition and entanglement, to quantum gates and circuits. The tutorial will also provide some hands-on exercises.
10:55
25 mins
Tutorial on Quantum Computing
Carmen G. Almudever
Abstract: Quantum computing is a very active and promising topic. Since the physicist Richard Feynman proposed the idea of building a quantum computer to simulate quantum systems in the early 80’s, different quantum algorithms have been developed. By exploiting quantum phenomena (superposition and entanglement), they promise to solve complex problems that are intractable for even the most powerful current supercomputers. One of the most famous examples is the factorization of large numbers using Shor’s algorithm. For instance, a 2000-bit number could be decomposed in a bit more than one day using a quantum computer whereas a data center of approx. 400.000 km2 built with the fastest today’s supercomputer would require around 100 years. Great progress has been made in recent years in quantum hardware based on different technologies such are superconducting qubits, ion traps, silicon quantum dots, topological qubits and Nitrogen Vacancy (NV) centers. Although quantum technologies still need to mature to get better coherence times and gate fidelities, quantum computation in the cloud is already a reality with small quantum processors that are capable of handling basic programs. Large companies (Google, Intel, Microsoft, IBM, Alibaba) and research groups are working on building the first universal quantum computer, which requires contributions from several disciplines including physics, mathematics, computer science, informatics and electrical engineering, among others. This tutorial will introduce the basic notions of quantum computing; going from quantum bits, superposition and entanglement, to quantum gates and circuits. The tutorial will also provide some hands-on exercises.
11:20
25 mins
Towards a practical implementation of the HHL algorithm on the QX quantum computer simulator
Otmar Ubbens, Carmina G. Almudever, Matthias Möller
Abstract: Many mathematical and engineering problems of practical interest involve the solution of linear systems of equations with large and sparse system matrices. In their pioneering paper, Harrow, Hassidim, and Lloyd proposed a quantum algorithm that achieves an exponential speedup over any classical computer algorithm, under the additional constraint that a scalar measurement on the solution vector is returned as result. In this talk we present a practical implementation of the HHL quantum algorithm on the QX quantum computer simulator platform. After a brief introduction of the overall algorithm, we will shed some light on two main subroutines, eigenvalue inversion and ancilla rotation, and discuss several approaches to implement them efficiently.
11:45
25 mins
Quantum algorithms for graph problems based on span programs
Alvaro Piedrafita
Abstract: In this talk, I will present a model of computation called span programs that are suited for designing quantum algorithms. Span programs are deeply connected to quantum query complexity and quantum query algorithms. I will introduce the span program for st-connectivity and show how this can be used as a primitive for designing quantum algorithms for problems like cycle detection, bipartiteness, formulae evaluation etc.