Implementations of Quantum Algorithms for Solving Linear Systems

Implementations of Quantum Algorithms for Solving Linear Systems

Sigurđsson, Sigurdsson (TU Delft Electrical Engineering, Mathematics and Computer Science)

Möller, M. (mentor)
Vuik, Cornelis (mentor)

Delft University of Technology
Technical University of Berlin

Applied Mathematics | COSSE (Computer Simulations for Science and Engineering)

Computer Simulations for Science and Engineering

2021-01-26

In this thesis, I make a comparison of two quantum algorithms for solving systems of linear equations. The two approaches are tested using both simulations of quantum processes and simulations of noisy intermediary-scale quantum computers, i.e., NISQ. Both methods are tested on the same problems to compare sensitivity and runtime efficiency, varying the tests along with different levels of condition numbers, sparsity and regularity. The first of the two methods compared is the method introduced by Harrow, Hassim, and Lloyd referred to as the HHL method, after the author's initials. The second method is by a research team at Los Alamos National Laboratory called the variational quantum linear solver, or VQLS for short. The first method, HHL, was the original discovery of solving linear systems using quantum computing methods and so has served as the backdrop and benchmark for other algorithms doing the same thing. The HHL method showed that an advantage can be had when using quantum computing to solve linear systems, in fact they show that this quantum method can have exponential speed up over the commonly used classical method.

Quantum algorithms
Linear Solvers
HHL
VQLS

http://resolver.tudelft.nl/uuid:820157f7-5350-4908-acba-7f419f0a7ec9

Student theses

master thesis

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