Optimization of Transmon Design for Longer Coherence Time
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The Theory of Quantum Coherence María García Díaz
ADVERTIMENT. Lʼaccés als continguts dʼaquesta tesi queda condicionat a lʼacceptació de les condicions dʼús establertes per la següent llicència Creative Commons: http://cat.creativecommons.org/?page_id=184 ADVERTENCIA. El acceso a los contenidos de esta tesis queda condicionado a la aceptación de las condiciones de uso establecidas por la siguiente licencia Creative Commons: http://es.creativecommons.org/blog/licencias/ WARNING. The access to the contents of this doctoral thesis it is limited to the acceptance of the use conditions set by the following Creative Commons license: https://creativecommons.org/licenses/?lang=en Universitat Aut`onomade Barcelona The theory of quantum coherence by Mar´ıaGarc´ıaD´ıaz under supervision of Prof. Andreas Winter A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in Unitat de F´ısicaTe`orica:Informaci´oi Fen`omensQu`antics Departament de F´ısica Facultat de Ci`encies Bellaterra, December, 2019 “The arts and the sciences all draw together as the analyst breaks them down into their smallest pieces: at the hypothetical limit, at the very quick of epistemology, there is convergence of speech, picture, song, and instigating force.” Daniel Albright, Quantum poetics: Yeats, Pound, Eliot, and the science of modernism Abstract Quantum coherence, or the property of systems which are in a superpo- sition of states yielding interference patterns in suitable experiments, is the main hallmark of departure of quantum mechanics from classical physics. Besides its fascinating epistemological implications, quantum coherence also turns out to be a valuable resource for quantum information tasks, and has even been used in the description of fundamental biological processes. -
Path Integrals in Quantum Mechanics
Path Integrals in Quantum Mechanics Dennis V. Perepelitsa MIT Department of Physics 70 Amherst Ave. Cambridge, MA 02142 Abstract We present the path integral formulation of quantum mechanics and demon- strate its equivalence to the Schr¨odinger picture. We apply the method to the free particle and quantum harmonic oscillator, investigate the Euclidean path integral, and discuss other applications. 1 Introduction A fundamental question in quantum mechanics is how does the state of a particle evolve with time? That is, the determination the time-evolution ψ(t) of some initial | i state ψ(t ) . Quantum mechanics is fully predictive [3] in the sense that initial | 0 i conditions and knowledge of the potential occupied by the particle is enough to fully specify the state of the particle for all future times.1 In the early twentieth century, Erwin Schr¨odinger derived an equation specifies how the instantaneous change in the wavefunction d ψ(t) depends on the system dt | i inhabited by the state in the form of the Hamiltonian. In this formulation, the eigenstates of the Hamiltonian play an important role, since their time-evolution is easy to calculate (i.e. they are stationary). A well-established method of solution, after the entire eigenspectrum of Hˆ is known, is to decompose the initial state into this eigenbasis, apply time evolution to each and then reassemble the eigenstates. That is, 1In the analysis below, we consider only the position of a particle, and not any other quantum property such as spin. 2 D.V. Perepelitsa n=∞ ψ(t) = exp [ iE t/~] n ψ(t ) n (1) | i − n h | 0 i| i n=0 X This (Hamiltonian) formulation works in many cases. -
Quantum Computers
Quantum Computers ERIK LIND. PROFESSOR IN NANOELECTRONICS Erik Lind EIT, Lund University 1 Disclaimer Erik Lind EIT, Lund University 2 Quantum Computers Classical Digital Computers Why quantum computers? Basics of QM • Spin-Qubits • Optical qubits • Superconducting Qubits • Topological Qubits Erik Lind EIT, Lund University 3 Classical Computing • We build digital electronics using CMOS • Boolean Logic • Classical Bit – 0/1 (Defined as a voltage level 0/+Vdd) +vDD +vDD +vDD Inverter NAND Logic is built by connecting gates Erik Lind EIT, Lund University 4 Classical Computing • We build digital electronics using CMOS • Boolean Logic • Classical Bit – 0/1 • Very rubust! • Modern CPU – billions of transistors (logic and memory) • We can keep a logical state for years • We can easily copy a bit • Mainly through irreversible computing However – some problems are hard to solve on a classical computer Erik Lind EIT, Lund University 5 Computing Complexity Searching an unsorted list Factoring large numbers Grovers algo. – Shor’s Algorithm BQP • P – easy to solve and check on a 푛 classical computer ~O(N) • NP – easy to check – hard to solve on a classical computer ~O(2N) P P • BQP – easy to solve on a quantum computer. ~O(N) NP • BQP is larger then P • Some problems in P can be more efficiently solved by a quantum computer Simulating quantum systems Note – it is still not known if 푃 = 푁푃. It is very hard to build a quantum computer… Erik Lind EIT, Lund University 6 Basics of Quantum Mechanics A state is a vector (ray) in a complex Hilbert Space Dimension of space – possible eigenstates of the state For quantum computation – two dimensional Hilbert space ۧ↓ Example - Spin ½ particle - ȁ↑ۧ 표푟 Spin can either be ‘up’ or ‘down’ Erik Lind EIT, Lund University 7 Basics of Quantum Mechanics • A state of a system is a vector (ray) in a complex vector (Hilbert) Space. -
On Coherence and the Transverse Spatial Extent of a Neutron Wave Packet
On coherence and the transverse spatial extent of a neutron wave packet C.F. Majkrzak, N.F. Berk, B.B. Maranville, J.A. Dura, Center for Neutron Research, and T. Jach Materials Measurement Laboratory, National Institute of Standards and Technology Gaithersburg, MD 20899 (18 November 2019) Abstract In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. -
Partial Coherence Effects on the Imaging of Small Crystals Using Coherent X-Ray Diffraction
INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 13 (2001) 10593–10611 PII: S0953-8984(01)25635-5 Partial coherence effects on the imaging of small crystals using coherent x-ray diffraction I A Vartanyants1 and I K Robinson Department of Physics, University of Illinois, 1110 West Green Street, Urbana, IL 61801, USA Received 8 June 2001 Published 9 November 2001 Online at stacks.iop.org/JPhysCM/13/10593 Abstract Recent achievements in experimental and computational methods have opened up the possibility of measuring and inverting the diffraction pattern from a single-crystalline particle on the nanometre scale. In this paper, a theoretical approach to the scattering of purely coherent and partially coherent x-ray radiation by such particles is discussed in detail. Test calculations based on the iterative algorithms proposed initially by Gerchberg and Saxton and generalized by Fienup are applied to reconstruct the shape of the scattering crystals. It is demonstrated that partially coherent radiation produces a small area of high intensity in the reconstructed image of the particle. (Some figures in this article are in colour only in the electronic version) 1. Introduction Even in the early years of x-ray studies [1–4] it was already understood that the diffraction pattern from small perfect crystals is directly connected with the shape of these crystals through Fourier transformation. Of course, in a real diffraction experiment on a ‘powder’ sample, where many particles with different shapes and orientations are illuminated by an incoherent beam, only an averaged shape of these particles can be obtained. -
Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere
Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere Elias Okon1 and Daniel Sudarsky2 1Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, Mexico City, Mexico. 2Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico. Abstract: In [1] it is argued that, in order to confront outstanding problems in cosmol- ogy and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, [1] concludes that our focus on conceptual and interpretational issues, while dealing with such matters in [2], is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergence of classicality. 1 Introduction Since its inception, more than 90 years ago, quantum theory has been a source of heated debates in relation to interpretational and conceptual matters. The prominent exchanges between Einstein and Bohr are excellent examples in that regard. An avoid- ance of such issues is often justified by the enormous success the theory has enjoyed in applications, ranging from particle physics to condensed matter. However, as people like John S. Bell showed [3], such a pragmatic attitude is not always acceptable. In [2] we argue that the standard interpretation of quantum mechanics is inadequate in cosmological contexts because it crucially depends on the existence of observers external to the studied system (or on an artificial quantum/classical cut). We claim that if the system in question is the whole universe, such observers are nowhere to be found, so we conclude that, in order to legitimately apply quantum mechanics in such contexts, an observer independent interpretation of the theory is required. -
Superconducting Transmon Machines
Quantum Computing Hardware Platforms: Superconducting Transmon Machines • CSC591/ECE592 – Quantum Computing • Fall 2020 • Professor Patrick Dreher • Research Professor, Department of Computer Science • Chief Scientist, NC State IBM Q Hub 3 November 2020 Superconducting Transmon Quantum Computers 1 5 November 2020 Patrick Dreher Outline • Introduction – Digital versus Quantum Computation • Conceptual design for superconducting transmon QC hardware platforms • Construction of qubits with electronic circuits • Superconductivity • Josephson junction and nonlinear LC circuits • Transmon design with example IBM chip layout • Working with a superconducting transmon hardware platform • Quantum Mechanics of Two State Systems - Rabi oscillations • Performance characteristics of superconducting transmon hardware • Construct the basic CNOT gate • Entangled transmons and controlled gates • Appendices • References • Quantum mechanical solution of the 2 level system 3 November 2020 Superconducting Transmon Quantum Computers 2 5 November 2020 Patrick Dreher Digital Computation Hardware Platforms Based on a Base2 Mathematics • Design principle for a digital computer is built on base2 mathematics • Identify voltage changes in electrical circuits that map base2 math into a “zero” or “one” corresponding to an on/off state • Build electrical circuits from simple on/off states that apply these basic rules to construct digital computers 3 November 2020 Superconducting Transmon Quantum Computers 3 5 November 2020 Patrick Dreher From Previous Lectures It was -
Lecture 21 (Interference III Thin Film Interference and the Michelson Interferometer) Physics 2310-01 Spring 2020 Douglas Fields Thin Films
Lecture 21 (Interference III Thin Film Interference and the Michelson Interferometer) Physics 2310-01 Spring 2020 Douglas Fields Thin Films • We are all relatively familiar with the phenomena of thin film interference. • We’ve seen it in an oil slick or in a soap bubble. "Dieselrainbow" by John. Licensed under CC BY-SA 2.5 via Commons - • But how is this https://commons.wikimedia.org/wiki/File:Dieselrainbow.jpg#/media/File:Diesel rainbow.jpg interference? • What are the two sources? • Why are there colors instead of bright and dark spots? "Thinfilmbubble" by Threetwoone at English Wikipedia - Transferred from en.wikipedia to Commons.. Licensed under CC BY 2.5 via Commons - https://commons.wikimedia.org/wiki/File:Thinfilmbubble.jpg#/media/File:Thinfilmb ubble.jpg The two sources… • In thin film interference, the two sources of coherent light come from reflections from two different interfaces. • Different geometries will provide different types of interference patterns. • The “thin film” could just be an air gap, for instance. Coherence and Thin Film Interference • Why “thin film”? • Generally, when talking about thin film interference, the source light is what we would normally call incoherent – sunlight or room light. • However, most light is coherent on a small enough distance/time scale… • The book describes it like this: Coherence - Wikipedia • Perfectly coherent: "Single frequency correlation" by Glosser.ca - Own work. Licensed under CC BY-SA 4.0 via Commons - https://commons.wikimedia.org/wiki/File:Single_frequency_correlation.svg#/media/File:Single_frequency_correlation.svg • Spatially partially coherent: "Spatial coherence finite" by Original uploader was J S Lundeen at en.wikipedia - Transferred from en.wikipedia; transferred to Commons by User:Shizhao using CommonsHelper. -
Uncertainty Relations for Quantum Coherence
Article Uncertainty Relations for Quantum Coherence Uttam Singh 1,*, Arun Kumar Pati 1 and Manabendra Nath Bera 2 1 Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India; [email protected] 2 ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain; [email protected] * Correspondence: [email protected]; Tel.: +91-532-2274-407; Fax: +91-532-2567-748 Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari Received: 4 April 2016; Accepted: 9 July 2016; Published: 16 July 2016 Abstract: Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative entropy of coherence in two or more noncommuting reference bases respects uncertainty like relations for a given state of single and bipartite quantum systems. In the case of bipartite systems, we find that the presence of entanglement may tighten the above relation. Further, we find an upper bound on the sum of the relative entropies of coherence of bipartite quantum states in two noncommuting reference bases. Moreover, we provide an upper bound on the absolute value of the difference of the relative entropies of coherence calculated with respect to two incompatible bases. Keywords: uncertainty relations; coherence; quantum correlations 1. Introduction The linearity of quantum mechanics gives rise to the concept of superposition of quantum states of a quantum system and is one of the characteristic properties that makes a clear distinction between the ways a classical and a quantum system can behave. -
Caputo Fractional Derivative and Quantum-Like Coherence
entropy Article Caputo Fractional Derivative and Quantum-Like Coherence Garland Culbreth 1,* , Mauro Bologna 2, Bruce J. West 3 and Paolo Grigolini 1 1 Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76201, USA; [email protected] 2 Departamento de Ingeniería Eléctrica-Electrónica, Universidad de Tarapacá, 1000000 Arica, Chile; [email protected] 3 Army Research Office, DEVCOM US Army Research Laboratory, Research Triangle Park, NC 27708, USA; [email protected] * Correspondence: [email protected] Abstract: We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence. We discuss the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. We prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed. We discuss these results in the framework of the growing interest in fractional derivatives and the emergence of cognition in nature. We conclude that the Caputo fractional derivative is a signature of the connection between cognition and self-organization, a form of cognition emergence different from the other source of anomalous diffusion, which is closely related to quantum coherence. We propose a criterion to detect the action of self-organization even in the presence of significant quantum coherence. We argue that statistical analysis of data using diffusion entropy should help the analysis of physiological processes hosting both forms of deviation from ordinary scaling. -
Measurement of Superconducting Qubits and Causality Alexander Korotkov University of California, Riverside
Michigan State Univ., 09/21/15 Measurement of superconducting qubits and causality Alexander Korotkov University of California, Riverside Outline: Introduction (causality, POVM measurement) Circuit QED setup for measurement of superconducting qubits (transmons, Xmons) Qubit evolution due to measurement in circuit QED (simple and better theories) Experiments Alexander Korotkov University of California, Riverside Causality principle in quantum mechanics objects a and b observers A and B (and C) observers have “free will”; A B they can choose an action A choice made by observer A can affect light a b evolution of object b “back in time” cones time However, this retroactive control cannot pass space “useful” information to B (no signaling) C Randomness saves causality (even C Our focus: continuous cannot predict result of A measurement) |0 collapse Ensemble-averaged evolution of object b cannot depend on actions of observer A |1 Alexander Korotkov University of California, Riverside Werner Heisenberg Books: Physics and Philosophy: The Revolution in Modern Science Philosophical Problems of Quantum Physics The Physicist's Conception of Nature Across the Frontiers Niels Bohr Immanuel Kant (1724-1804), German philosopher Critique of pure reason (materialism, but not naive materialism) Nature - “Thing-in-itself” (noumenon, not phenomenon) Humans use “concepts (categories) of understanding”; make sense of phenomena, but never know noumena directly A priori: space, time, causality A naïve philosophy should not be a roadblock for good physics, -
Nthorder Multifrequency Coherence Functions: a Functional Path Integral Approach Conrad M
Nthorder multifrequency coherence functions: A functional path integral approach Conrad M. Rose and Ioannis M. Besieris Citation: Journal of Mathematical Physics 20, 1530 (1979); doi: 10.1063/1.524213 View online: http://dx.doi.org/10.1063/1.524213 View Table of Contents: http://scitation.aip.org/content/aip/journal/jmp/20/7?ver=pdfcov Published by the AIP Publishing This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.173.125.76 On: Mon, 24 Mar 2014 17:26:14 Nth-order multifrequency coherence functions: A functional path integral approach~ Conrad M. Rose Naval Surface Weapons Center, Dahlgren, Virginia 22448 loannis M. Besieris Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 (Received 21 August 1978) A functional (or path) integral applicable to a broad class of randomly perturbed media is constructed for the nth-order multi frequency coherence function (a quantity intimately linked to nth-order pulse statistics). This path integral is subsequently carried out explicitly in the case of a nondispersive, deterministically homogeneous medium, with a simplified (quadratic) Kolmogorov spectrum, and a series of new results are derived. Special cases dealing with the two-frequency mutual coherence function for plane and beam pulsed waves are considered, and comparisons are made with previously reported findings. 1. INTRODUCTION gation in the atmosphere and in lightguides, and underwater sound wave propagation) where the restriction to spatially There has been recently a mounting interest in the sub ject of propagation of pulsed signals through randomly per planar sources must be lifted.