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World Congress on Computer and Information Technology (WCCIT)

Quantum observable

Wafa Elmannai, Varun Pande, Ajay Shrestha, Khaled M. Elleithy

Published Jun 1, 2013• 1 citation
Publisher

Abstract

Over the last decade, many researchers have studied the implementation of quantum systems and the states of the quantum systems. Most of the focus has been on the quantum states strategy. Researchers have found it to be more advanced than classical strategies. Complementary quantum Observables interaction and information are the most important features that are refereed by Observables. This shows us how uniquely these features can define a packet of information in mathematical terms as a state. Also, it provides technological information that indeed captures the properties of quantum systems. In this paper, we demonstrate how to implement certain logical methods in quantum computing to obtain more accurate information than classical computing systems provide. This new methodology can make the computation more efficient. First, we examine the photons and consider the various spin states, and then we consider the direction of the spinning photons to handle more information. Next, we use the unique property of photons to behave both as a wave and a particle and exploit it by passing the photon through mirrors and beam splitters to demonstrate and achieve results that are not possible in the classical world.

DOI
10.1109/wccit.2013.6618769

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Over the last decade, many researchers have studied the implementation of quantum systems and the states of the quantum systems. Most of the focus has been on the quantum states strategy. Researchers have found it to be more advanced than classical strategies. Complementary quantum Observables interaction and information are the most important features that are refereed by Observables. This shows us how uniquely these features can define a packet of information in mathematical terms as a state. Also, it provides technological information that indeed captures the properties of quantum systems. In this paper, we demonstrate how to implement certain logical methods in quantum computing to obtain more accurate information than classical computing systems provide. This new methodology can make the computation more efficient. First, we examine the photons and consider the various spin states, and then we consider the direction of the spinning photons to handle more information. Next, we use the unique property of photons to behave both as a wave and a particle and exploit it by passing the photon through mirrors and beam splitters to demonstrate and achieve results that are not possible in the classical world.
This paper investigates the core principles of quantum computation, providing an in-depth understanding of quantum phenomena and illustrating how these principles form the scientific foundation of the field. The pivotal physical concepts, such as properties of subatomic particles, including electrons and photons, as well as their mathematical description through linear algebra are examined. It focuses on the qubit, the quantum analogue of a classical bit, featuring properties like superposition, entanglement, and wave function collapse, which redefine the traditional concept of information processing. The mathematical structures that underlie quantum system modelling—vector spaces, tensor products, and Dirac notation—are also systematically explained. Essential components of quantum computation involve logic gates such as Pauli matrices and Hadamard gates, which demonstrate the novel application of qubits in unique ways. This sets up an important theme of the interdependence and potential for transformation of quantum states through the illustration of advanced ideas of quantum entanglement and teleportation. Quantum circuits serve as an outstanding example of how reversibility and superposition are exploited to solve complex problems at unprecedented levels of efficiency. The paper also highlights the Deutsch-Jozsa algorithm as a compelling example of quantum superiority over traditional computational approaches. Together, these findings emphasize the transformative potential of quantum computing for science and industry.
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Information is something that can be encoded in the state of a physical system, and a computation is a task that can be performed with a physically realizable device. Therefore, since the physical world is fundamentally quantum mechanical, the foundations of information theory and computer science should be sought in quantum physics. In fact, quantum information has weird properties that contrast sharply with the familiar properties of classical information. A quantum computer -- a new type of machine that exploits the quantum properties of infomation -- could perform certain typ$s of calculations far more efficiently than any foreseeable classical computer. To build a functional quantum computer will be an enormous technical challenge. New methods for quantum error correction are being developed that can help to prevent a quantum computer from crashing.
The superiority of hypothetical quantum computers is not due to faster calculations but due to different schemes of calculations running on special hardware. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In conventional approach it is implemented through tensor product of qubits. In the geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on three-dimensional sphere.
As this century unfolds we will witness the rise of the quantum computer. A quantum computer is a device that utilizes the laws of one of the most fundamental theories of physics— quantum mechanics. By utilizing properties of quantum mechanics a quantum computer is able to perform certain information processing tasks much more effciently than an ordinary classical computer. The last century of modern society was revolutionized by some of the simplest ideas in quantum mechanics like energy quantization and quantum tunnelling, which led to technologies like the laser and the transistor. We can expect to see additional technological revolutions occur in this century since we are beginning to build technologies with some of the more complex properties of quantum mechanics such as quantum entanglement and quantum superposition. These quantum effects make more radical technologies like the quantum computer possible. This thesis is based upon the work I have done during my PhD candidature at Macquarie University. In this work we develop quantum technologies that are directed towards realising a quantum computer. Specifically, we have made many theoretical advancements in a type of quantum information processing protocol called Boson Sampling. This device effciently simulates the interaction of quantum particles called bosons, which no classical computer can effciently simulate. In this thesis we explore quantum random walks, which are the basis of how the bosons in Boson Sampling interfere with each other. We explore implementing BosonSampling using the most readily available photon source technology. We invented a completely new architecture which can implement Boson Sampling in time rather than space and has since been used to make the worlds largest Boson Sampling experiment ever performed. We look at variations to the traditional Boson Sampling architecture by considering other quantum states of light. We show a worlds first application inspired by Boson Sampling in quantum metrology where measurements may be made more accurately than with any classical method. Lastly, dealing with Boson Sampling, we look at reformulating the formalism of Boson Sampling using a quantum optics approach. In addition, but not related to BosonSampling, we show a protocol for effciently generating large-photon Fock states, which are a type of quantum state of light, that are useful for quantum computation. Also, we show a method for generating a specific quantum state of light that is useful for quantum error correction — an essential component of realising a quantum computer — by coupling together light and atoms.
Quantum control theory is a rapidly evolving research field, which has developed over the last three decades. Quantum optics has practical importance in quantum technology and provides a promising means of implementing quantum information and computing device. \nIn quantum control, it is difficult to acquire information about quantum states without destroying them since microscopic quantum systems have many unique characteristics such as entanglement and coherence which do not occur in classical mechanical system. Therefore, \nthe Lyapunov-based control methodology is used to first construct an artificial closed-loop controller and then an open-loop law is derived by simulation of the artificial closed-loop system. \n \nThis work considers the stabilization of laser cavity as the main integral part of quantum optical systems through squeezing the output beam of the cavity. As a comprehensive example of this type of system, quantum optomechanical sensors are investigated. To this end, a nonlinear model \nof quantum optomechanical sensors is first extended incorporating various noises. Then, linear quadratic Gaussian (LQG) control method is used to tackle the problem of mode-squeezing in optomechanical sensors. \nCoherent feedback quantum control is synthesized by incorporating both shot noise and back-action noise to attenuate the output noise well below the shot noise level (Two waves are said to be coherent if they have a constant relative phase). In the second phase of this work, due to entanglement of the system with critical uncertainties and technical limitations such as laser noise and detector imprecision, robust H [infinity] method is employed for the robust stabilization and robust performance of the system in practice. In H [infinity] methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this. The effectiveness of the proposed control strategy in squeezing the cavity output beam is demonstrated by simulation.