DOCSLIB.ORG

Incorporating the Stern-Gerlach Delayed-Choice Quantum Eraser Into the Undergraduate Quantum Mechanics Curriculum William F

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Incorporating the Stern-Gerlach Delayed-Choice Quantum Eraser Into the Undergraduate Quantum Mechanics Curriculum William F Incorporating the Stern-Gerlach delayed-choice quantum eraser into the undergraduate quantum mechanics curriculum William F. Courtney, Lucas B. Vieira, Paul S. Julienne, and James K. Freericks Citation: American Journal of Physics 88, 298 (2020); doi: 10.1119/10.0000519 View online: https://doi.org/10.1119/10.0000519 View Table of Contents: https://aapt.scitation.org/toc/ajp/88/4 Published by the American Association of Physics Teachers ARTICLES YOU MAY BE INTERESTED IN Seven formulations of the kinematics of special relativity American Journal of Physics 88, 269 (2020); https://doi.org/10.1119/10.0000851 The negative flow of probability American Journal of Physics 88, 325 (2020); https://doi.org/10.1119/10.0000856 A zeroth power is often a logarithm yearning to be free American Journal of Physics 88, 261 (2020); https://doi.org/10.1119/10.0000841 The Persian Immortals: A classical case of self-organization American Journal of Physics 88, 263 (2020); https://doi.org/10.1119/10.0000834 Angular momentum in the fractional quantum Hall effect American Journal of Physics 88, 286 (2020); https://doi.org/10.1119/10.0000831 Two-penny physics: Teaching 2D linear momentum conservation American Journal of Physics 88, 279 (2020); https://doi.org/10.1119/10.0000518 Incorporating the Stern-Gerlach delayed-choice quantum eraser into the undergraduate quantum mechanics curriculum William F. Courtney 2801 Montair Ave., Long Beach, California 90815-1054 Lucas B. Vieira Universidade Federal de Minas Gerais, 6627 Av. Antonio^ Carlos, Belo Horizonte, MG 31270-901, Brazil Paul S. Julienne Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, College Park, Maryland 20742 James K. Freericks Department of Physics, Georgetown University, 37th and O Streets NW, Washington, DC 20057 (Received 8 December 2017; accepted 18 December 2019) As “Stern-Gerlach first” becomes increasingly popular in the undergraduate quantum mechanics curriculum, we show how one can extend the treatment found in conventional textbooks to cover some exciting new quantum phenomena. Namely, we illustrate how one can describe a delayed choice variant of the quantum eraser which is realized within the Stern-Gerlach framework. Covering this material allows the instructor to reinforce notions of changes in basis functions, quantum superpositions, quantum measurements, and the complementarity principle as expressed in whether we know “which-way” information or not. It also allows the instructor to dispel common misconceptions of when a measurement occurs and when a system is in a superposition of states. VC 2020 American Association of Physics Teachers. https://doi.org/10.1119/10.0000519 5 I. INTRODUCTION quantum eraser by other authors, but we will be reserving that language for the more complex eraser we describe 1 The Stern-Gerlach experiment was originally performed below. It is at this stage that most educators (including us) by Otto Stern and Walter Gerlach in 1922. While it can be move from the real Stern-Gerlach experiment to more com- thought of as simply an experiment to separate an atomic plicated “experiments” that invoke the principles of the beam into its different projections of angular momentum, Stern-Gerlach experiment, but do so in a more complex for- the Stern-Gerlach experiment also illustrates a number of mat than can actually be carried out in a laboratory; we will different quantum phenomena. One can use it to show that use quotes to describe experiments that can in principle be quantum mechanics requires a probabilistic interpretation. carried out, but to our knowledge have never actually been One can use it to show that quantum states cannot simulta- performed in a laboratory. Sakurai employed the Stern- neously have definite projections of angular momentum on Gerlach experiment early in his textbook3 and used it to also two non-collinear axes. It also acts as one of the simplest discuss the Bell experiments. Our treatment of the subject is paradigms of a two-state quantum system (for the case of a influenced most by Styer’s wonderful text The Strange spin-one-half atom like silver), illustrating the discreteness World of Quantum Mechanics,4 which introduces a number of quantum eigenvalues. of complex quantum ideas with the Stern-Gerlach experi- Educators have long realized the importance of this ment. These are the two-slit experiment, Wheeler’s delayed 2–7 experiment. It has appeared in many textbooks. Here, we choice, the Einstein-Podolsky-Rosen paradox, and the Bell highlight a few texts that bring this experiment to the forefront, experiments. Styer’s text also carefully describes the classi- by employing it as one of the first quantum experiments that a cal version of the experiment, which is critical for students student encounters. These texts deviate from the far more com- to master in order to appreciate the quantum nature of the mon norm of covering quantum mechanics from a historical real experiment. perspective8,9 or by starting with the wave equation in coordi- Three recent undergraduate textbooks, Townsend’s A nate space.10 We believe that there are significant advantages Modern Approach to Quantum Mechanics,5 McIntyre, to proceeding in this Stern-Gerlach first methodology, as it Manogue and Tate’s Quantum Mechanics: A Paradigms allows the students to encounter experiments that they can Approach,6 and Beck’s Quantum Mechanics: Theory and easily analyze right from the beginning. Furthermore, as we Experiment,7 all adopt the Stern-Gerlach first paradigm, intro- show here, one can extend those treatments to allow the ducing students to this experiment as their initial (or early) students to encounter sophisticated quantum paradoxes even encounter with quantum mechanics. While these texts move before they learn what a coordinate-space wavefunction is. on to a more conventional style of quantum treatment after- The Feynman Lectures on Physics2 introduces the Stern- wards, this critical change allows students to dive into a quan- Gerlach experiment quite early in its discussion of quantum tum system that they can understand all aspects of and allows mechanics, actually covering the spin-one case before the them to lean on this knowledge as they learn about new and spin-one-half case. This text also describes what we will different quantum phenomena in the remainders of the books. call the Stern-Gerlach analyzer loop (following Styer,4 see This article is organized as follows: (i) in Sec. II, we pro- below); this device is sometimes called a Stern-Gerlach vide a short history of the Stern-Gerlach experiment, delayed 298 Am. J. Phys. 88 (4), April 2020 http://aapt.org/ajp VC 2020 American Association of Physics Teachers 298 choice, the quantum eraser, and their use in quantum know that it can be quantitatively described within the mechanics pedagogy; (ii) in Sec. III, we describe the differ- theory. ent apparatus needed for the Stern-Gerlach experiments and We end this section with a brief discussion of the history how one employs them in instruction; (iii) in Sec. IV,we of pedagogy of the Stern-Gerlach experiment in particular describe the details of how to create and analyze a delayed and quantum erasers in general. The Stern-Gerlach experi- choice Stern-Gerlach quantum eraser; (iv) in Sec. V,we ment first entered pedagogy with Wigner’s classic article discuss possible experimental implementations; and (v) in where the analyzer loop was introduced in 1963.17 Scully Sec. VI, we present our conclusions. et al. performed an in-depth analysis of the analyzer loop to show that it should be thought of as creating a superposition II. BRIEF HISTORY OF STERN-GERLACH of states unless a measurement is performed on it to deter- 18 EXPERIMENT PEDAGOGY mine which-way information. In addition, a series of papers have provided detailed calculations of the dynamics Quantum mechanics has seen numerous developments of the Stern-Gerlach experiment, paying particular attention that have not yet made it into most introductory quantum to the fact that the magnetic field must have a component texts. For example, in the 1980s, John Wheeler introduced perpendicular to the direction where the atomic beam is split the notion of delayed choice,11,12 where an experimental due to the fact that the field is divergenceless.19–24 A tutorial apparatus is modified while the particle is moving through it, has also been created to directly confront common miscon- in such a way that the modification post-selects what type of ceptions about the experiment.25 Finally, an example of a measurement will be performed. Wheeler hypothesized that quantum eraser, using quite different methodology from these types of experiments, which can determine whether a what we propose here (crossed Stern-Gerlach analyzers with particle goes through just one slit, or two slits at the same a two-slit experiment in between), has also appeared.26 time, in a two-slit experiment, have the spooky behavior of The quantum eraser has been discussed within many dif- acting like the quantum particle is able to influence what has ferent platforms. The simplest demonstrations use polariza- already occurred, by going backwards in time. It turns out tion of light within a two-slit experiment27,28 (including an that this awkward notion is easily dispelled when one prop- experimental setup29). Similarly, a Mach-Zehnder interfer- erly interprets when the system is in a superposition of states ometer30 can be used to also illustrate the quantum eraser. and precisely when a measurement collapses
Load more

Recommended publications
  • The Concept of Quantum State : New Views on Old Phenomena Michel Paty
    The concept of quantum state : new views on old phenomena Michel Paty To cite this version: Michel Paty. The concept of quantum state : new views on old phenomena. Ashtekar, Abhay, Cohen, Robert S., Howard, Don, Renn, Jürgen, Sarkar, Sahotra & Shimony, Abner. Revisiting the Founda- tions of Relativistic Physics : Festschrift in Honor of John Stachel, Boston Studies in the Philosophy and History of Science, Dordrecht: Kluwer Academic Publishers, p. 451-478, 2003. halshs-00189410 HAL Id: halshs-00189410 https://halshs.archives-ouvertes.fr/halshs-00189410 Submitted on 20 Nov 2007 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. « The concept of quantum state: new views on old phenomena », in Ashtekar, Abhay, Cohen, Robert S., Howard, Don, Renn, Jürgen, Sarkar, Sahotra & Shimony, Abner (eds.), Revisiting the Foundations of Relativistic Physics : Festschrift in Honor of John Stachel, Boston Studies in the Philosophy and History of Science, Dordrecht: Kluwer Academic Publishers, 451-478. , 2003 The concept of quantum state : new views on old phenomena par Michel PATY* ABSTRACT. Recent developments in the area of the knowledge of quantum systems have led to consider as physical facts statements that appeared formerly to be more related to interpretation, with free options.
    [Show full text]
  • Light and Matter Diffraction from the Unified Viewpoint of Feynman's
    European J of Physics Education Volume 8 Issue 2 1309-7202 Arlego & Fanaro Light and Matter Diffraction from the Unified Viewpoint of Feynman’s Sum of All Paths Marcelo Arlego* Maria de los Angeles Fanaro** Universidad Nacional del Centro de la Provincia de Buenos Aires CONICET, Argentine *[email protected] **[email protected] (Received: 05.04.2018, Accepted: 22.05.2017) Abstract In this work, we present a pedagogical strategy to describe the diffraction phenomenon based on a didactic adaptation of the Feynman’s path integrals method, which uses only high school mathematics. The advantage of our approach is that it allows to describe the diffraction in a fully quantum context, where superposition and probabilistic aspects emerge naturally. Our method is based on a time-independent formulation, which allows modelling the phenomenon in geometric terms and trajectories in real space, which is an advantage from the didactic point of view. A distinctive aspect of our work is the description of the series of transformations and didactic transpositions of the fundamental equations that give rise to a common quantum framework for light and matter. This is something that is usually masked by the common use, and that to our knowledge has not been emphasized enough in a unified way. Finally, the role of the superposition of non-classical paths and their didactic potential are briefly mentioned. Keywords: quantum mechanics, light and matter diffraction, Feynman’s Sum of all Paths, high education INTRODUCTION This work promotes the teaching of quantum mechanics at the basic level of secondary school, where the students have not the necessary mathematics to deal with canonical models that uses Schrodinger equation.
    [Show full text]
  • Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function
    Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function Shuming Wen ( [email protected] ) Faculty of Land and Resources Engineering, Kunming University of Science and Technology. Research Article Keywords: probability origin, wave-function collapse, uncertainty principle, quantum tunnelling, double-slit and single-slit experiments Posted Date: November 16th, 2020 DOI: https://doi.org/10.21203/rs.3.rs-95171/v2 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function Shuming Wen Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093 Abstract The theoretical calculation of quantum mechanics has been accurately verified by experiments, but Copenhagen interpretation with probability is still controversial. To find the source of the probability, we revised the definition of the energy quantum and reconstructed the wave function of the physical particle. Here, we found that the energy quantum ê is 6.62606896 ×10-34J instead of hν as proposed by Planck. Additionally, the value of the quality quantum ô is 7.372496 × 10-51 kg. This discontinuity of energy leads to a periodic non-uniform spatial distribution of the particles that transmit energy. A quantum objective system (QOS) consists of many physical particles whose wave function is the superposition of the wave functions of all physical particles. The probability of quantum mechanics originates from the distribution rate of the particles in the QOS per unit volume at time t and near position r. Based on the revision of the energy quantum assumption and the origin of the probability, we proposed new certainty and uncertainty relationships, explained the physical mechanism of wave-function collapse and the quantum tunnelling effect, derived the quantum theoretical expression of double-slit and single-slit experiments.
    [Show full text]
  • Testing the Limits of Quantum Mechanics the Physics Underlying
    Testing the limits of quantum mechanics The physics underlying non-relativistic quantum mechanics can be summed up in two postulates. Postulate 1 is very precise, and says that the wave function of a quantum system evolves according to the Schrodinger equation, which is a linear and deterministic equation. Postulate 2 has an entirely different flavor, and can be roughly stated as follows: when the quantum system interacts with a classical measuring apparatus, its wave function collapses, from being in a superposition of the eigenstates of the measured observable, to being in just one of the eigenstates. The outcome of the measurement is random and cannot be predicted; the quantum system collapses to one or the other eigenstates, with a probability that is proportional to the squared modulus of the wave function for that eigenstate. This is the Born probability rule. Since quantum theory is extremely successful, and not contradicted by any experiment to date, one can simply accept the 2nd postulate as such, and let things be. On the other hand, ever since the birth of quantum theory, some physicists have been bothered by this postulate. The following troubling questions arise. How exactly is a classical measuring apparatus defined? How large must a quantum system be, before it can be called classical? The Schrodinger equation, which in principle is supposed to apply to all physical systems, whether large or small, does not answer this question. In particular, the equation does not explain why the measuring apparatus, say a pointer, is never seen in a quantum superposition of the two states `pointer to the left’ and `pointer to the right’? And if the equation does apply to the (quantum system + apparatus) as a whole, why are the outcomes random? Why does collapse, which apparently violates linear superposition, take place? Where have the probabilities come from, in a deterministic equation (with precise initial conditions), and why do they obey the Born rule? This set of questions generally goes under the name `the quantum measurement problem’.
    [Show full text]
  • Wave-Particle Duality Relation with a Quantum Which-Path Detector
    entropy Article Wave-Particle Duality Relation with a Quantum Which-Path Detector Dongyang Wang , Junjie Wu * , Jiangfang Ding, Yingwen Liu, Anqi Huang and Xuejun Yang Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China; [email protected] (D.W.); [email protected] (J.D.); [email protected] (Y.L.); [email protected] (A.H.); [email protected] (X.Y.) * Correspondence: [email protected] Abstract: According to the relevant theories on duality relation, the summation of the extractable information of a quanton’s wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation.
    [Show full text]
  • Research-Based Interactive Simulations to Support Quantum Mechanics Learning and Teaching
    Research-based interactive simulations to support quantum mechanics learning and teaching Antje Kohnle School of Physics and Astronomy, University of St Andrews Abstract Quantum mechanics holds a fascination for many students, but its mathematical complexity can present a major barrier. Traditional approaches to introductory quantum mechanics have been found to decrease student interest. Topics which enthuse students such as quantum information are often only covered in advanced courses. The QuVis Quantum Mechanics Visualization project (www.st-andrews.ac.uk/physics/quvis) aims to overcome these issues through the development and evaluation of interactive simulations with accompanying activities for the learning and teaching of quantum mechanics. Simulations support model-building by reducing complexity, focusing on fundamental ideas and making the invisible visible. They promote engaged exploration, sense-making and linking of multiple representations, and include high levels of interactivity and direct feedback. Some simulations allow students to collect data to see how quantum-mechanical quantities are determined experimentally. Through text explanations, simulations aim to be self-contained instructional tools. Simulations are research-based, and evaluation with students informs all stages of the development process. Simulations and activities are iteratively refined using individual student observation sessions, where students freely explore a simulation and then work on the associated activity, as well as in-class trials using student surveys, pre- and post-tests and student responses to activities. A recent collection of QuVis simulations is embedded in the UK Institute of Physics Quantum Physics website (quantumphysics.iop.org), which consists of freely available resources for an introductory course in quantum mechanics starting from two-level systems.
    [Show full text]
  • The Elitzur-Vaidman Experiment Violates the Leggett-Garg Inequality
    Atomic “bomb testing”: the Elitzur-Vaidman experiment violates the Leggett-Garg inequality Carsten Robens,1 Wolfgang Alt,1 Clive Emary,2 Dieter Meschede,1 and Andrea Alberti1, ∗ 1Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, D-53115 Bonn, Germany 2Joint Quantum Centre Durham-Newcastle, Newcastle University, Newcastle upon Tyne NE1 7RU, UK (Dated: September 21, 2016) Abstract. Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum super- position principle, allows one to detect the presence of an object in a dramatic scenario, a bomb without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the “bomb test” with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett-Garg inequality a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett-Garg inequality. I. INTRODUCTION scopically distinct states. In a macro-realistic world- view, it is plausible to assume that a negative out- Measuring physical properties of an object whether come of a measurement cannot affect the evolution of macroscopic or microscopic is in most cases associated a macroscopic system, meaning that negative measure- with an interaction.
    [Show full text]
  • Non-Relativistic Quantum Mechanics Lecture Notes – FYS 4110
    Non-Relativistic Quantum Mechanics Lecture notes – FYS 4110 Jon Magne Leinaas Department of Physics, University of Oslo September 2004 2 Preface These notes are prepared for the physics course FYS 4110, Non-relativistic Quantum Me- chanics, which is a second level course in quantum mechanics at the Physics Department in Oslo. The course was first lectured in the fall semester of 2003, and the intention with this new course was to bring in more ”modern aspects” in the teaching of quantum physics. The lecture notes have been developed parallel with my teaching of the course. They are still in the process of being modified and extended. I apologize for misprints that have still survived and welcome feedback from students concerning misprints as well as opinions on the contents and presentation. Department of Physics, University of Oslo, August 2004. Jon Magne Leinaas Contents 1 Quantum formalism 5 1.1 Summary of quantum states and observables . 5 1.1.1 Classical and quantum states . 5 1.1.2 The fundamental postulates . 8 1.1.3 Coordinate representation and wave functions . 11 1.1.4 Spin-half system and the Stern Gerlach experiment . 12 1.2 Quantum Dynamics . 14 1.2.1 The Schrodinger¨ and Heisenberg pictures . 14 1.2.2 Path integrals . 18 1.2.3 Path integral for a free particle . 21 1.2.4 The classical theory as a limit of the path integral . 23 1.2.5 A semiclassical approximation . 24 1.2.6 The double slit experiment revisited . 25 1.3 Two-level system and harmonic oscillator . 27 1.3.1 The two-level system .
    [Show full text]
  • Particle Control in a Quantum World
    THE NOBEL PRIZE IN PHYSICS 2012 INFORMATION FOR THE PUBLIC Particle control in a quantum world Serge Haroche and David J. Wineland have independently invented and developed ground-breaking methods for measuring and manipulating individual particles while preserving their quantum-mechanical nature, in ways that were previously thought unattainable. Haroche and Wineland have opened the door to a new era of experimentation with quantum physics by demonstrating the direct observation of individual quantum systems without destroying them. Through their ingenious laboratory methods they have managed to measure and control very fragile quan- tum states, enabling their feld of research to take the very frst steps towards building a new type of super fast computer, based on quantum physics. These methods have also led to the construction of extremely precise clocks that could become Figure 1. Nobel Prize awarded for mastering particles. The Laureates have managed to make the future basis for a new standard of time, with more than trapped, individual particles to behave according hundred -fold greater precision than present-day caesium clocks. to the rules of quantum physics. For single particles of light or matter, the laws of classical physics cease to apply and quantum physics takes over. But single particles are not easily isolated from their surrounding environment and they lose their mysterious quantum properties as soon as they interact with the outside world. Thus many seemingly bizarre phenomena predicted by quantum mechanics could not be directly observed, and researchers could only carry out ‘thought experiments’ that might in principle manifest these bizarre phenomena. Both Laureates work in the feld of quantum optics studying the fundamental interaction between light and matter, a feld which has seen considerable progress since the mid-1980s.
    [Show full text]
  • Enhancing Student Learning of Two-Level Quantum Systems with Interactive Simulations
    Enhancing student learning of two-level quantum systems with interactive simulations Antje Kohnlea), Charles Baily, Anna Campbell, Natalia Korolkova School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, United Kingdom Mark J Paetkau Department of Physical Sciences, Thompson Rivers University, Kamloops, Canada V2C, OC8 ABSTRACT The QuVis Quantum Mechanics Visualization project aims to address challenges of quantum mechanics instruction through the development of interactive simulations for the learning and teaching of quantum mechanics. In this article, we describe evaluation of simulations focusing on two-level systems developed as part of the Institute of Physics Quantum Physics resources. Simulations are research-based and have been iteratively refined using student feedback in individual observation sessions and in-class trials. We give evidence that these simulations are helping students learn quantum mechanics concepts at both the introductory and advanced undergraduate level, and that students perceive simulations to be beneficial to their learning. I. INTRODUCTION Quantum mechanics holds a fascination for many students, but learning quantum mechanics is difficult. The counterintuitive behaviour of quantum systems often disagrees with our classical and common-sense ideas, leading to student difficulties that arise when classical thinking is applied to quantum systems.1-16 Quantum phenomena typically cannot be observed directly and are far-removed from everyday experience. Complicated mathematics is required
    [Show full text]
  • Quantum Information Processing with Superconducting Circuits: a Review
    Quantum Information Processing with Superconducting Circuits: a Review G. Wendin Department of Microtechnology and Nanoscience - MC2, Chalmers University of Technology, SE-41296 Gothenburg, Sweden Abstract. During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of Quantum Supremacy with fifty qubits is anticipated in just a few years. Quantum Supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of super- conducting devices, systems and applications. As such, the discussion of superconduct- ing qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry. Keywords: superconducting circuits, microwave resonators, Josephson junctions, qubits, quantum computing, simulation, quantum control, quantum error correction, superposition, entanglement arXiv:1610.02208v2 [quant-ph] 8 Oct 2017 Contents 1 Introduction 6 2 Easy and hard problems 8 2.1 Computational complexity . .9 2.2 Hard problems . .9 2.3 Quantum speedup . 10 2.4 Quantum Supremacy . 11 3 Superconducting circuits and systems 12 3.1 The DiVincenzo criteria (DV1-DV7) . 12 3.2 Josephson quantum circuits . 12 3.3 Qubits (DV1) .
    [Show full text]
  • Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources
    Article Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources Burhan Gulbahar Department of Electrical and Electronics Engineering, Ozyegin University, Istanbul 34794, Turkey; [email protected] Abstract: Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger–Horne–Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource in simple linear optical setups performing multiplane diffraction (MPD) of fermionic and bosonic particles with remarkable promises. This significantly motivates the definition of quantum histories of MPD as entanglement resources with the inherent capability of generating an exponentially increasing number of Feynman paths through diffraction planes in a scalable manner and experimental low complexity combining the utilization of coherent light sources and photon-counting detection. In this article, quantum temporal correlation and interference among MPD paths are denoted with quantum path entanglement (QPE) and interference (QPI), respectively, as novel quantum resources. Operator theory modeling of QPE and counterintuitive properties of QPI are presented by combining history-based formulations with Feynman’s path integral approach. Leggett–Garg inequality as temporal analog of Bell’s inequality is violated for MPD with all signaling constraints in the ambiguous form recently formulated by Emary. The proposed theory for MPD-based histories is highly promising for exploiting QPE and QPI as important resources for quantum computation and communications in future architectures. Keywords: multiplane diffraction; entangled histories; quantum path entanglement; quantum path interference; Leggett–Garg inequality 1.
    [Show full text]