Robust gates for holonomic quantum computation

Non Abelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. We study the effects of the environment (modelled as an ensemble of harmonic oscillators) on a holonomic transformation and write the corresponding master equation. The solution is analytically and numerically investigated and the behavior of the fidelity analyzed: fidelity revivals are observed and an optimal finite operation time is determined at which the gate is most robust against noise.Comment: 11 pages, 6 figure

Robustness of optimal working points for non-adiabatic holonomic quantum computation

Geometric phases are an interesting resource for quantum computation, also in view of their robustness against decoherence effects. We study here the effects of the environment on a class of one-qubit holonomic gates that have been recently shown to be characterized by "optimal" working times. We numerically analyze the behavior of these optimal points and focus on their robustness against noise.Comment: 14 pages, 8 figure

On the stability of quantum holonomic gates

We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the adiabatic evolution but can reduce the logical gate performance. Using the intrinsic geometric properties of the holonomic gates, we show under which conditions on noise's correlation time and strength, the fluctuations in the driving field cancel out. In this way, we provide theoretical support to previous numerical simulations. We also briefly comment on the error due to the mismatch between real and nominal time of the period of the driving fields and show that it can be reduced by suitably increasing the adiabatic time.Comment: 7 page

From quantum circuits to adiabatic algorithms

This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.Comment: Version accepted by and to appear in Phys. Rev.

Stochastic Variational Integrators

This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds. The main result is to derive stochastic governing equations for such systems from a critical point of a stochastic action. Using this result the paper derives Langevin-type equations for constrained mechanical systems and implements a stochastic analog of Lagrangian reduction. These are easy consequences of the fact that the stochastic action is intrinsically defined. Stochastic variational integrators (SVIs) are developed using a discretized stochastic variational principle. The paper shows that the discrete flow of an SVI is a.s. symplectic and in the presence of symmetry a.s. momentum-map preserving. A first-order mean-square convergent SVI for mechanical systems on Lie groups is introduced. As an application of the theory, SVIs are exhibited for multiple, randomly forced and torqued rigid-bodies interacting via a potential.Comment: 21 pages, 8 figure

Technical report on Optimization-Based Bearing-Only Visual Homing with Applications to a 2-D Unicycle Model

We consider the problem of bearing-based visual homing: Given a mobile robot which can measure bearing directions with respect to known landmarks, the goal is to guide the robot toward a desired "home" location. We propose a control law based on the gradient field of a Lyapunov function, and give sufficient conditions for global convergence. We show that the well-known Average Landmark Vector method (for which no convergence proof was known) can be obtained as a particular case of our framework. We then derive a sliding mode control law for a unicycle model which follows this gradient field. Both controllers do not depend on range information. Finally, we also show how our framework can be used to characterize the sensitivity of a home location with respect to noise in the specified bearings. This is an extended version of the conference paper [1].Comment: This is an extender version of R. Tron and K. Daniilidis, "An optimization approach to bearing-only visual homing with applications to a 2-D unicycle model," in IEEE International Conference on Robotics and Automation, 2014, containing additional proof

Sensor Network Based Collision-Free Navigation and Map Building for Mobile Robots

Safe robot navigation is a fundamental research field for autonomous robots including ground mobile robots and flying robots. The primary objective of a safe robot navigation algorithm is to guide an autonomous robot from its initial position to a target or along a desired path with obstacle avoidance. With the development of information technology and sensor technology, the implementations combining robotics with sensor network are focused on in the recent researches. One of the relevant implementations is the sensor network based robot navigation. Moreover, another important navigation problem of robotics is safe area search and map building. In this report, a global collision-free path planning algorithm for ground mobile robots in dynamic environments is presented firstly. Considering the advantages of sensor network, the presented path planning algorithm is developed to a sensor network based navigation algorithm for ground mobile robots. The 2D range finder sensor network is used in the presented method to detect static and dynamic obstacles. The sensor network can guide each ground mobile robot in the detected safe area to the target. Furthermore, the presented navigation algorithm is extended into 3D environments. With the measurements of the sensor network, any flying robot in the workspace is navigated by the presented algorithm from the initial position to the target. Moreover, in this report, another navigation problem, safe area search and map building for ground mobile robot, is studied and two algorithms are presented. In the first presented method, we consider a ground mobile robot equipped with a 2D range finder sensor searching a bounded 2D area without any collision and building a complete 2D map of the area. Furthermore, the first presented map building algorithm is extended to another algorithm for 3D map building