Solving parametrized liinear systems of equations with the variational quantum linear solver

Constantinos, Atzarakis; Κωνσταντίνος, Ατζαράκης

dc.contributor.author	Constantinos, Atzarakis	en
dc.contributor.author	Κωνσταντίνος, Ατζαράκης	el
dc.date.accessioned	2023-04-06T07:30:03Z
dc.date.available	2023-04-06T07:30:03Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/57490
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.25187
dc.description	Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) "Επιστήμη Δεδομένων και Μηχανική Μάθηση"	el
dc.rights	Αναφορά Δημιουργού - Μη Εμπορική Χρήση - Παρόμοια Διανομή 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-sa/3.0/gr/	*
dc.subject	Quantum information	en
dc.subject	Μηχανική μάθηση	el
dc.subject	Γραμμικά συστήματα	el
dc.subject	Κβαντικοί αλγόριθμοι	el
dc.subject	Κβαντικοί υπολογιστές	el
dc.subject	Παραμετρικά συστήματα εξισώσεων	el
dc.subject	Quantum computing	en
dc.subject	Linear systems of equations	en
dc.subject	Quantum algorithms	en
dc.subject	Variational quantum algorithms	en
dc.title	Solving parametrized liinear systems of equations with the variational quantum linear solver	en
heal.type	masterThesis
heal.secondaryTitle	A first attempt to pair a Variational Quantum Algorithm with Machine Learning	el
heal.classification	Quantum Computing	en
heal.classification	machine learning	el
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2023-02-20
heal.abstract	The potential of quantum computing for scientific and industrial breakthroughs is immense, however, we are still in the Noisy Intermediate-Scale quantum (NISQ) era, where the currently available quantum devices contain small numbers of qubits, are very sensitive to environmental conditions and prone to quantum decoherence. Even so, existing NISQ computers have already been shown to outperform conventional computers on specific problems and the key question is how to make use of today’s NISQ devices to achieve quantum advantage in the field of computational science and engineering (CSE). In this direction, this work proposes a hybrid computing formulation by combining quantum computing with machine learning for accelerating the solution of parameterized linear systems in NISQ devices. In particular, it focuses on the Variational Quantum Linear Solver (VQLS), which is hybrid quantum- classical algorithm to solve linear systems that employs a short-depth quantum circuit to efficiently evaluate a cost function related to the system solution. The circuit consists of a quantum gate sequence (unitary operators) that involves a set of tunable parameters. Then, well-established classical optimizers are being utilized to tune the parameters of the sequence so as to minimize the cost function, which is equivalent to finding the system solution at an acceptable level of accuracy. It is demonstrated in this work that we can successfully employ machine learning tools such as feed-forward neural networks and nearest-neighbor interpolation techniques to accelerate the convergence of the VQLS algorithm towards the optimal values for the circuit parameters, when applied to parameterized linear systems that need to be solved for multiple parameter instances. This of a great importance to the field of CSE as it paves the way to accelerating the solution to almost all multi-query problems (uncertainty propagation, parameter inference, optimization, sensitivity analysis etc.) as these essentially reduce to the solution of a parameterized linear system.	en
heal.advisorName	Papadopoulos, Vissarion	en
heal.committeeMemberName	Fragiadakis, Michalis	en
heal.committeeMemberName	Triantafyllou, Savvas	en
heal.committeeMemberName	Papadopoulos, Vissarion	en
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών	el
heal.academicPublisherID	ntua
heal.fullTextAvailability	false