Implementation and performance study of a practical quantum algorithm for solving linear systems of
(COSSE student, double degree with
Site of the project: TU Delft
Supervisor TU Delft: Matthias Moeller
start of the project: October 2019
In March 2020 the
has been given. Here is a
Python Notebook version
of the talk.
The Master project has been finished in January 2021
by the completion of the
and a final
has been given.
For working address etc. we refer to our
Summary of the master project:
One of the few quantum algorithms that can be of direct practical use is the
named after its inventors Harrow, Hassidin, and Lloyd, for solving linear systems of equations (Ax=b) exponentially faster that this is possible with classical computers. The aim of this master project is to develop a fully functional implementation of the HHL algorithm and test it on various quantum simulator and, possibly, hardware platforms available in the cloud. The main focus is on the efficient and accurate implementation of a quantum phase estimation (QPE) subroutine, which transfers the Hermitian NxN matrix into its eigenvalue/vector decomposition and thereby forms the starting procedure of the HHL algorithm. Prototypical implementations of the two other building blocks (inversion and uncomputation of eigenvalues) are available from a previous project. After a literature study of quantum phase estimation, the student will implement!
the QPE procedure in the Quantum Assembly Language for the Quantum Inspire simulator platform and analyze its performance both with respect to accuracy and efficiency. Combined with the existing subroutines, the project will deliver a practical implementation of the HHL algorithm. The second part of the project will analyze the performance of the overall algorithm for different types of input matrices (different sparsity pattern, different condition numbers). If time permits, the HHL algorithm will be analyzed for more realistic qubits, which are sensitive to errors. This analysis will first use error models of the quantum simulator and, possibly, extend to real quantum computer hardware available in the cloud (IBM Q Experience).
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Master students page of Kees Vuik