Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it provide a new quantum approach which combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled-unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32-bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with minor typos corrected.

Design And Optimization Of Nanostructured Optical Filters

Optical filters encompass a vast array of devices and structures for a wide variety of applications. Generally speaking, an optical filter is some structure that applies a designed amplitude and phase transform to an incident signal. Different classes of filters have vastly divergent characteristics, and one of the challenges in the optical design process is identifying the ideal filter for a given application and optimizing it to obtain a specific response. In particular, it is highly advantageous to obtain a filter that can be seamlessly integrated into an overall device package without requiring exotic fabrication steps, extremely sensitive alignments, or complicated conversions between optical and electrical signals. This dissertation explores three classes of nano-scale optical filters in an effort to obtain different types of dispersive response functions. First, dispersive waveguides are designed using a sub-wavelength periodic structure to transmit a single TE propagating mode with very high second order dispersion. Next, an innovative approach for decoupling waveguide trajectories from Bragg gratings is outlined and used to obtain a uniform second-order dispersion response while minimizing fabrication limitations. Finally, high Q-factor microcavities are coupled into axisymmetric pillar structures that offer extremely high group delay over very narrow transmission bandwidths. While these three novel filters are quite diverse in their operation and target applications, they offer extremely compact structures given the magnitude of the dispersion or group delay they introduce to an incident signal. They are also designed and structured as to be formed on an optical wafer scale using standard integrated circuit fabrication techniques. A number of frequency-domain numerical simulation methods are developed to fully characterize and model each of the different filters. The complete filter response, which includes the dispersion and delay characteristics and optical coupling, is used to evaluate each filter design concept. However, due to the complex nature of the structure geometries and electromagnetic interactions, an iterative optimization approach is required to improve the structure designs and obtain a suitable response. To this end, a Particle Swarm Optimization algorithm is developed and applied to the simulated filter responses to generate optimal filter designs

Theory and simulation of subwavelength high contrast gratings and their applications in vertical-cavity surface-emitting laser devices

This work intends to fully explore the qualities and applications of subwavelength gratings. Subwavelength gratings are diffraction gratings with physical dimensions less than the wavelength of incident light. It has been found that by tailoring specific dimension parameters, a number of different reflection profiles can be attained by these structures including high reflectivity or low reflectivity with broad and narrow spectral responses. In the course of this thesis the physical basis for this phenomenon will be presented as well as a mathematical derivation. After discussion of the mechanics of the reflection behavior, the methods used in modeling subwavelength gratings and designing them for specific functions will be explored. Following this, the fundamentals of vertical-cavity surface-emitting lasers (VCSELs) will be discussed, and the applications of subwavelength gratings when used with these lasers will follow. Several devices, both theoretical proposals and fabricated examples, will be presented in addition to the available performance measurements. Finally, the fabrication challenges that restrict subwavelength gratings from adoption as standard components in VCSEL design will be considered with regard to ongoing fabrication research

Dynamic Wireless Information and Power Transfer Scheme for Nano-Empowered Vehicular Networks

In this paper, we investigate the wireless power transfer and energy-efficiency (EE) optimization problem for nano-centric vehicular networks operating over the terahertz band. The inbody nano-sensors harvest energy from a power station via radio-frequency signal and then use the harvested energy to transmit data to the sink node. By considering the properties of terahertz band (i.e., sensitivity to distance and frequency over the communication path), we adopt the Brownian motion model to develop a time-variant terahertz channel model and to describe the mobility of the nano-sensors. Thus, based on the channel model and energy resources, we further develop a long-term EE optimization problem. The EE optimization is further converted into a series of energy-efficient resource allocation problems over the time slots via equivalent transformation method. The resource allocation problem for each timeslot, which is formulated as a mixed integer nonlinear programming (MINLP), is solved based on the particle swarm optimization (PSO) method. In addition, a dynamic PSO-based EE optimization (DPEEO) algorithm is developed to obtain the sub-optimal solution for the EE optimization problem. By exploiting the special structure of the reformulated problem, an improved DPEEO algorithm, is presented which can handle the problem’s constraints quite well, decreases the research space, and greatly reduces the length of the convergence time. Simulation results validate the theoretical analysis of our system