Post hoc verification of quantum computation

With recent progress on experimental quantum information processing, an important question has arisen as to whether it is possible to verify arbitrary computation performed on a quantum processor. A number of protocols have been proposed to achieve this goal, however all are interactive in nature, requiring that the computation be performed in an interactive manner with back and forth communication between the verifier and one or more provers. Here we propose two methods for verifying quantum computation in a non-interactive manner based on recent progress in the understanding of the local Hamiltonian problem. Provided that the provers compute certain witnesses for the computation, this allows the result of a quantum computation to be verified after the fact, a property not seen in current verification protocols.Comment: 4 pages, 2 figure

Návrh vozidla Baja SAE

Tato diplomová práce popisuje koncepční návrh vozidla Baja SAE dle aktuálních pravidel organizace SAE. V úvodu je práce zaměřena na rešerši konkurenčních vozidel a následně na základě těchto na samotný návrh prvního vozidla Baja SAE v České republice. Celá práce je systematicky členěna do jednotlivých kapitol dle reálného postupu návrhu vozidla. Hlavní částí práce je návrh kinematiky náprav provedený v programu Adams a spolu s tím návrh rámu vozidla. Model celého vozidla je vytvořen v programu Catia V5 a navržené verze rámu následně podrobeny analýze torzní tuhosti a analýze napjatosti v programu Ansys.This master’s thesis describes the design of the Baja SAE vehicle according to the applicable rules. In the beginning is the work focused on search competing vehicles and subsequently on design the first Baja SAE vehicle in the Czech republic. This thesis is systematically divided into chapters according process to the vehicle design. The main part of a master's thesis is design of axle kinematics in software Adams and frame design. The model was designed in Catia V5. The frame was analysed of torsional stiffness and stress in software ANSYS.

Direct evaluation of pure graph state entanglement

We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory, namely the identification of maximum independent set, allows us to evaluate three multipartite entanglement measures for pure graph states. We construct the minimal linear decomposition into product states for a large group of pure graph states, allowing us to evaluate the Schmidt measure. Furthermore we show that computation of distance-like measures such as relative entropy of entanglement and geometric measure becomes tractable for these states by explicit construction of closest separable and closest product states respectively. We show how these separable states can be described using stabiliser formalism as well as PEPs-like construction. Finally we discuss the way in which introducing noise to the system can optimally destroy entanglement.Comment: 23 pages, 9 figure

Quantum Synchronisation in Nanoscale Heat Engines

Owing to the ubiquity of synchronization in the classical world, it is interesting to study its behavior in quantum systems. Though quantum synchronisation has been investigated in many systems, a clear connection to quantum technology applications is lacking. We bridge this gap and show that nanoscale heat engines are a natural platform to study quantum synchronization and always possess a stable limit cycle. Furthermore, we demonstrate an intimate relationship between the power of a heat engine and its phase-locking properties by proving that synchronization places an upper bound on the achievable steady-state power of the engine. Finally, we show that the efficiency of the engine sets a point in terms of the bath temperatures where synchronization vanishes. We link the physical phenomenon of synchronization with the emerging field of quantum thermodynamics by establishing quantum synchronization as a mechanism of stable phase coherence.Comment: 5 pages, 3 pages appendix, 2 figure

Measurement Induced Continuous Time Crystals

Strong measurements usually restrict the dynamics of measured finite dimensional systems to the Zeno subspace, where subsequent evolution is unitary due to the suppression of dissipative terms. Here we show qualitatively different behaviour due to the competition between strong measurements and the thermodynamic limit, inducing a time-translation symmetry breaking phase transition resulting in a continuous time crystal. We consider a spin star model, where the central spin is subject to a strong continuous measurement, and qualify the dynamic behaviour of the system in various parameter regimes. We show that above a critical value of measurement strength, the magnetization of the thermodynamically large ancilla spins develops limit cycle oscillations. Our result also demonstrates that a coherent drive is not necessary in order to induce continuous time-translation symmetry breaking.Comment: 9 pages total (5 pages plus appendix

Role of Coherence and Degeneracies in Quantum Synchronisation

Progress on the study of synchronisation in quantum systems has been largely driven by specific examples which resulted in several examples of frequency entrainment as well as mutual synchronisation. Here we study quantum synchronisation by utilising Liouville space perturbation theory. We begin by clarifying the role of centers, symmetries and oscillating coherences in the context of quantum synchronisation. We then analyse the eigenspectrum of the Liouville superoperator generating the dynamics of the quantum system and determine the conditions under which synchronisation arises. We apply our framework to derive a powerful relationship between energy conservation, degeneracies and synchronisation in quantum systems. Finally, we demonstrate our approach by analysing two mutually coupled thermal machines and the close relationship between synchronisation and thermodynamic quantities.Comment: 9 total pages, comments welcom