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The handle http://hdl.handle.net/1887/43150 holds various files of this Leiden University dissertation.

Author: Tarasinski, B.M.

Title: On periodically driven quantum systems

Issue Date: 2016-09-20

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Stellingen

behorende bij het proefschrift On periodically driven quantum systems

1. Unlike their static counterparts, the bulk topological properties of one- dimensional periodically driven quantum systems are characterized by two (not one) independent invariants.

Chapter 2 2. The two invariants of a chiral symmetric driven system are the winding

numbers on a torus of half the Floquet operator.

Chapter 3, thesis cover 3. In an open driven quantum system, topological boundary states can actively

trap particles from the bulk.

Chapter 4 4. The magnetic-field dependent relaxation time τ

B

for weak localization in a nanowire with a hexagonal cross-section depends on the width W with a non-integer exponent, τ

B

∝ W

−γ

, γ = 3.174 ± 0.003, hinting to hidden fractal properties of electron dynamics in that geometry.

Chapter 6 5. The full density matrix simulation of the Surface-17 quantum error cor- rection code, requiring thousands of CPU hours as reported by Tomita &

Svore [PRA 90, 062320 (2014)], can be reproduced in a few hours on a single GPU.

https://github.com/brianzi/quantumsim 6. The computational universality of continuous-time quantum walks [Childs, PRL 102, 180501 (2008)] is of little practical use, because one would need a universal quantum computer to produce the quantum walk in the first place.

7. The construction of “Majorana bound states in non-topological supercon- ductors” described by San Jose et al. [Sci. Rep. 6, 21427 (2016)] relies not only on charge-conjugation symmetry but also on chiral symmetry.

8. The runtime of a sufficiently accurate decoding algorithm based on minimal- weight matching for the surface code [Fowler et al., PRA 86, 042313 (2012)]

will be dominated not by the matching subroutine, but by the subroutine for weight calculation, especially for low-distance codes.

Brian Tarasinski

20 september 2016

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