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Undergraduate Research Journal

LiGHT TRAP MANiPULATiON AND iTS POTENTiAL USE iN QUANTUM COMPUTiNG

David Copsey, Glen Gillen

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

During winter quarter 2007, the light polarization dependence of light traps used in quantum computing was researched. Throughout the quarter, a Mathematica program that simulates the trapping potential of light traps was modified; it now takes into account the polarization of light used, as well as the internal state of atoms used in the light traps. The goal for the next quarter, spring 2007, was to use the program that was generated to simulate the trapping potentials of varying parameters. This research was conducted to deduce whether there is any possible way to implement the light polarization dependence of light traps in quantum computing. More specifically, the intent was to investigate potential ways to create a two-qubit gate using the light polarization dependence of the light traps.

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During winter quarter 2007, the light polarization dependence of light traps used in quantum computing was researched. Throughout the quarter, a Mathematica program that simulates the trapping potential of light traps was modified; it now takes into account the polarization of light used, as well as the internal state of atoms used in the light traps. The goal for the next quarter, spring 2007, was to use the program that was generated to simulate the trapping potentials of varying parameters. This research was conducted to deduce whether there is any possible way to implement the light polarization dependence of light traps in quantum computing. More specifically, the intent was to investigate potential ways to create a two-qubit gate using the light polarization dependence of the light traps.
Many methods of quantum computing are currently being researched because quantum computers may be able to perform certain calculations that we currently cannot because they would take the age of the universe. To create a viable quantum computer one must be able to create a multiple qubit gate. For our specific ap­ proach, neutral atom quantum computing, one must find a way to bring two atoms together, entangle them and separate them in order to create a multiple qubit gate. In our research we explored a way of facilitating the creation of a multiple qubit gate using the diffraction pattern created by two polarized lasers incident upon a
The concept of a "quantum computer" has attracted much attention in recent years. Many research groups around the world are studying the extraordinary potential of quantum computers and attempting their realisation. Current fundamental experiments are directed towards the individual building blocks of such a computer. The concept of using quantum mechanical systems to calculate complex problems was created in 1982 with Feynmans proposal of the quantum simulator. This concept represents a well controlled framework of interacting quantum systems. The intention is to map a different system of interest not mastered in the lab onto the quantum simulator. From the behaviour of the quantum simulator the behaviour of the system of interest can be deduced. A quantum mechanical measurement on the quantum simulator is thus comparable to one run of a numerical simulation of the system of interest. The difference is that a numerical simulation can often only be run under severe simplifications that then challenge the practical relevance of the result. Only very small quantum systems can be calculated on today's computers without simplifications. In this work a system of ground state atoms stored in a 3D optical lattice is presented. Each of the up to 100,000 atoms is stored in its own potential minimum, isolated from the other atoms. This state is a formidable starting point for the realisation of a quantum simulator: every atom is considered the information carrier of a spin-1/2 system. Only very few of the other concepts currently under investigation have as many information carriers as a Mott-Insulator state in an optical lattice. We have already shown in preparatory experiments a long storage time and good coherence times. Here this system is extended by a major prerequisite for a quantum simulator: controllable interactions between individual atoms are essential in order to model the interaction terms of the system of interest. These interactions are realised by a state-selective in the optical lattice by state-selective trapping potentials. If the states of an atom are called |0> and |1>, then there are two distinct potentials V0 and V1 that each act on only one of the states. The two potentials are shifted with respect to each other and thus allow bringing neighbouring atoms into contact. Since the shifting is always performed along one of the three lattice axes, the interaction is not confined to a single pair of atoms, but all pairs of neighbouring atoms along a lattice axis interact. This inherent parallelism has allowed us to create entanglement in large systems in just a single operation. The entanglement has then been measured in a Ramsey interferometer. A sequence of one nearest-neighbour interaction produces the cluster state, a maximally entangled state. More recent proposals suggest to use a cluster state as the basis for a new kind of quantum computer. As opposed to today's computers, this quantum computer would not be a Touring machine whose working algorithm is only controlled by programming. Instead the wiring of the quantum gates would have to be changed in order to solve a new problem. This is loosely comparable to today's FPGA (Field Programmable Gate Arrays - programmable logic chips). Until these quantum computers are built, quite some improvements on the experimental techniques will be necessary. But the first quantum simulators are now practically within reach.
In this paper we propose a scheme to model the phonon analog of optical elements, including a polarizing beam splitter, a half-wave plate, and a quarter-wave plate, as well as an implementation of cnot and Pauli gates, by using two atoms confined in a two-dimensional plane. The internal states of the atoms are taken to be Rydberg circular states. Using this model we can manipulate the motional state of the atom, with possible applications in optomechanical integrated circuits for quantum information processing and quantum simulation. Towards this aim, we consider two trapped atoms and let only one of them interact simultaneously with two circularly polarized Laguerre-Gaussian beams.
I will present recent research results in optical one-way quantum computation and quantum information processing that I have been involved in. The first topic is an optimization of how to use the limited resources available in typical quantum-optics experiments. We show that the number of qubits available for implementing quantum computational circuits can be increased by replacing some of the projective single-qubit measurements in one-way quantum computation with generalized measurements. In particular, while one needs two single-qubit measurements to initialize an arbitrary logical qubit state, a single POVM is enough to achieve the sameI will present recent research results in optical one-way quantum computation and quantum information processing that I have been involved in. The first topic is an optimization of how to use the limited resources available in typical quantum-optics experiments. We show that the number of qubits available for implementing quantum computational circuits can be increased by replacing some of the projective single-qubit measurements in one-way quantum computation with generalized measurements. In particular, while one needs two single-qubit measurements to initialize an arbitrary logical qubit state, a single POVM is enough to achieve the same.