Spin Chains for Perfect State Transfer and Quantum Computing. January 17th 2013 Martin Bruderer
|
|
- Andrea Cooper
- 6 years ago
- Views:
Transcription
1 Spin Chains for Perfect State Transfer and Quantum Computing January 17th 2013 Martin Bruderer
2 Overview Basics of Spin Chains Engineering Spin Chains for Qubit Transfer Inverse Eigenvalue Problem spinguin Boundary States Generating Graph States
3 Spin Chains as Quantum Channel Alice sends a qubit to Bob via a spin chain Spin up = 1 Spin down = 0 Qubit is tranferred (imperfectly) by natural time evolution Quantum Communication through an Unmodulated Spin Chain Sougato Bose, Phys. Rev. Lett. 91, (2003)
4 Spin Chains XX Spin Hamiltonian Map to 1d fermionic model using Jordon-Wigner trans. non-interacting fermions Hilbert space seperates into sectors n = 0, 1, 2,
5 Single Fermion States Sector of Hilbert space with n = 0and n = 1 H0 spanned by H1 spanned by N N matrix
6 Perfect Transfer of Qubits Qubit at t = 0 is prepared at site 1 superposition possible for JW-fermions After time t = τ want qubit at site N Have to engineer Hamiltonian HF for n = 1 sector with time evolution
7 Symmetry Condition Mirror symmetry <=> Eigenstates λk have decinite parity N free parameters fingerprint of spin chain
8 Eigenvalue Condition Condition for eigenvalues λk Simplest example: Double well potential anti-symmetric states are flipped
9 Inverse Eigenvalue Problem Condition for eigenvalues λk very weak! Take τ = π and Φ = 0 => eigenvalues λk are integers Infinitely many solutions e.g. λk= {2, 13, 16, 29, 34, 35} Structured inverse eigenvalue problem: Given N eigenvalues λk find the tridiagonal N N matrix
10 Orthogonal Polynomials Characteristic polynomial pj of submatrix Hj Structure and orthogonality Shohat-Favard theorem with weigths
11 Orthogonal Polynomials Inverse relations with norm Carl R. de Boor Gene H. Golub
12 Algorithm by de Boor & Golub Calculate weights wkfrom λkfor scalar product (p0= 1) For j = 1 to ~N/2 1. Calculate Computationally cheap & stable 2. Find 3. Calculate End The numerically stable reconstruction of a Jacobi matrix from spectral data C. de Boor and G.H. Golub, Linear Algebr. Appl. 21, 245 (1978)
13 Application No approximations... Example: If λk symmetrically distributed around zero => aj = 0
14 Optimize for Robustness Create spin chains with localized boundary states Robust against perturbations Simplified evolution
15 Adding Boundary States Zero modes ~ Boundary states (cf. Majorana states) 1. Take original spin chain 2. Shift spectrum 3. Calculate new couplings 4. Compare robustness λk= 0 Works if eigenvalues λk fulfill
16 Optimization Examples Linear Spectrum Inverted Quadratic Spectrum
17 Test Robustness Couplings are uniformly randomized (± few percent) Effect on transfer fidelity (numerics) = fidelity averaged over Bloch sphere Boundary states => more high-fidelity chains => smooth time evolution
18 Test Robustness Couplings are uniformly randomized (± few percent) Effect on transfer fidelity (numerics) = fidelity averaged over Bloch sphere Boundary states => more high-fidelity chains => smooth time evolution
19 Boundary States in Quantum Wires Quantum wire with superlattice potential weak link Boundary states form double quantum dot Localized End States in Density Modulated Quantum Wires and Rings S. Gangadharaiah, L. Trifunovic and D. Loss, Phys. Rev. Lett. 108, (2012)
20 spinguin spin chain Graphical User Interface for Matlab Playful approach to spin chains (education) Algorithm iepsolve.m & GUI Some small bugs...
21 Ex Linear Spectrum
22 Ex Boundary States
23 Ex Cubic Spectrum
24 Ex Three Band Model
25 Many Fermion States Quantum computation with fermions Previous results hold for n 2 sectors t = 0 t = τ Generate phases between subspaces Efficient generation of graph states for quantum computation S.R. Clark, C. Moura Alves and D. Jaksch, New J. Phys. 7, 124 (2005)
26 Controlled Phase Gate t = 0 t = τ = CZ Z Initialize each qubit as Very robust, but not enough for quantum computation
27 Generate Graph States Graph state of n vertices requires at most O(2n) operations
28 Summing up 1. For a given spectrum λkwe can construct the tight-binding Hamiltonian 2. Fermionic phases are useful for generating highly entangled states
29 Some People Involved Stephen R. Clark Quantum (t-drmg) Oxford, Singapore (CQT) Kurt Franke g-factor of Antiprotons CERN, Geneva Danail Obreschkow Astrophysics (SKA) Perth, Australia
30 References A Review of Perfect, Efficient, State Transfer and its Application as a Constructive Tool A. Kay, Int. J. Quantum Inform. 8, 641 (2010) Quantum Communication through an Unmodulated Spin Chain S. Bose, Phys. Rev. Lett. 91, (2003) Exploiting boundary states of imperfect spin chains for high-fidelity state transfer MB, K. Franke, S. Ragg, W. Belzig and D. Obreschkow, Phys. Rev. A 85, (2012) The numerically stable reconstruction of a Jacobi matrix from spectral data C. de Boor and G.H. Golub, Linear Algebr. Appl. 21, 245 (1978) Fermionic quantum computation S. B. Bravyi and A. Yu. Kitaev, Annals of Physics 298, 210 (2002) Efficient generation of graph states for quantum computation S.R. Clark, C. Moura Alves and D. Jaksch, New J. Phys. 7, 124 (2005) Graph state generation with noisy mirror-inverting spin chains S. R Clark, A. Klein, MB and D. Jaksch, New J. Phys. 9, 202 (2007) Localized End States in Density Modulated Quantum Wires and Rings S. Gangadharaiah, L. Trifunovic and D. Loss, Phys. Rev. Lett. 108, (2012)
TRANSPORT OF QUANTUM INFORMATION IN SPIN CHAINS
TRANSPORT OF QUANTUM INFORMATION IN SPIN CHAINS Joachim Stolze Institut für Physik, Universität Dortmund, 44221 Dortmund Göttingen, 7.6.2005 Why quantum computing? Why quantum information transfer? Entangled
More informationInstantaneous Nonlocal Measurements
Instantaneous Nonlocal Measurements Li Yu Department of Physics, Carnegie-Mellon University, Pittsburgh, PA July 22, 2010 References Entanglement consumption of instantaneous nonlocal quantum measurements.
More informationQuantum Communication & Computation Using Spin Chains
Quantum Communication & Computation Using Spin Chains Sougato Bose Institute for Quantum Information, Caltech & UCL, London Quantum Computation Part: S. C. Benjamin & S. Bose, quant-ph/02057 (to appear
More informationTopological Phases in One Dimension
Topological Phases in One Dimension Lukasz Fidkowski and Alexei Kitaev arxiv:1008.4138 Topological phases in 2 dimensions: - Integer quantum Hall effect - quantized σ xy - robust chiral edge modes - Fractional
More informationQuantum wires, orthogonal polynomials and Diophantine approximation
Quantum wires, orthogonal polynomials and Diophantine approximation Introduction Quantum Mechanics (QM) is a linear theory Main idea behind Quantum Information (QI): use the superposition principle of
More informationTensor network simulations of strongly correlated quantum systems
CENTRE FOR QUANTUM TECHNOLOGIES NATIONAL UNIVERSITY OF SINGAPORE AND CLARENDON LABORATORY UNIVERSITY OF OXFORD Tensor network simulations of strongly correlated quantum systems Stephen Clark LXXT[[[GSQPEFS\EGYOEGXMZMXMIWUYERXYQGSYVWI
More informationSpin-Orbit Interactions in Semiconductor Nanostructures
Spin-Orbit Interactions in Semiconductor Nanostructures Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, U.S.A. http://www.physics.udel.edu/~bnikolic Spin-Orbit Hamiltonians
More informationEfficient time evolution of one-dimensional quantum systems
Efficient time evolution of one-dimensional quantum systems Frank Pollmann Max-Planck-Institut für komplexer Systeme, Dresden, Germany Sep. 5, 2012 Hsinchu Problems we will address... Finding ground states
More informationLecture notes on topological insulators
Lecture notes on topological insulators Ming-Che Chang Department of Physics, National Taiwan Normal University, Taipei, Taiwan Dated: May 8, 07 I. D p-wave SUPERCONDUCTOR Here we study p-wave SC in D
More informationH ψ = E ψ. Introduction to Exact Diagonalization. Andreas Läuchli, New states of quantum matter MPI für Physik komplexer Systeme - Dresden
H ψ = E ψ Introduction to Exact Diagonalization Andreas Läuchli, New states of quantum matter MPI für Physik komplexer Systeme - Dresden http://www.pks.mpg.de/~aml laeuchli@comp-phys.org Simulations of
More informationWhat is possible to do with noisy quantum computers?
What is possible to do with noisy quantum computers? Decoherence, inaccuracy and errors in Quantum Information Processing Sara Felloni and Giuliano Strini sara.felloni@disco.unimib.it Dipartimento di Informatica
More informationIntroduction to Topological Error Correction and Computation. James R. Wootton Universität Basel
Introduction to Topological Error Correction and Computation James R. Wootton Universität Basel Overview Part 1: Topological Quantum Computation Abelian and non-abelian anyons Quantum gates with Abelian
More informationSingle qubit + CNOT gates
Lecture 6 Universal quantum gates Single qubit + CNOT gates Single qubit and CNOT gates together can be used to implement an arbitrary twolevel unitary operation on the state space of n qubits. Suppose
More information2. Introduction to quantum mechanics
2. Introduction to quantum mechanics 2.1 Linear algebra Dirac notation Complex conjugate Vector/ket Dual vector/bra Inner product/bracket Tensor product Complex conj. matrix Transpose of matrix Hermitian
More informationFrom Majorana Fermions to Topological Order
From Majorana Fermions to Topological Order Arxiv: 1201.3757, to appear in PRL. B.M. Terhal, F. Hassler, D.P. DiVincenzo IQI, RWTH Aachen We are looking for PhD students or postdocs for theoretical research
More informationQuantum Information Processing and Diagrams of States
Quantum Information and Diagrams of States September 17th 2009, AFSecurity Sara Felloni sara@unik.no / sara.felloni@iet.ntnu.no Quantum Hacking Group: http://www.iet.ntnu.no/groups/optics/qcr/ UNIK University
More informationQuantum Computing Lecture 3. Principles of Quantum Mechanics. Anuj Dawar
Quantum Computing Lecture 3 Principles of Quantum Mechanics Anuj Dawar What is Quantum Mechanics? Quantum Mechanics is a framework for the development of physical theories. It is not itself a physical
More informationHigh Fidelity to Low Weight. Daniel Gottesman Perimeter Institute
High Fidelity to Low Weight Daniel Gottesman Perimeter Institute A Word From Our Sponsor... Quant-ph/0212066, Security of quantum key distribution with imperfect devices, D.G., H.-K. Lo, N. Lutkenhaus,
More informationIntroduction to Quantum Information Hermann Kampermann
Introduction to Quantum Information Hermann Kampermann Heinrich-Heine-Universität Düsseldorf Theoretische Physik III Summer school Bleubeuren July 014 Contents 1 Quantum Mechanics...........................
More informationOptimal state reconstructions
Quantum observations talk 3 Vladimír Bužek Research Center for Quantum Information, Bratislava, Slovakia 4 September 0 Sharif University of Technology, Tehran Optimal state reconstructions Reconstructions
More informationSpin chain model for correlated quantum channels
Spin chain model for correlated quantum channels Davide Rossini Scuola Internazionale Superiore di Studi Avanzati SISSA Trieste, Italy in collaboration with: Vittorio Giovannetti (Pisa) Simone Montangero
More informationStorage of Quantum Information in Topological Systems with Majorana Fermions
Storage of Quantum Information in Topological Systems with Majorana Fermions Leonardo Mazza Scuola Normale Superiore, Pisa Mainz September 26th, 2013 Leonardo Mazza (SNS) Storage of Information & Majorana
More informationQuantum NP - Cont. Classical and Quantum Computation A.Yu Kitaev, A. Shen, M. N. Vyalyi 2002
Quantum NP - Cont. Classical and Quantum Computation A.Yu Kitaev, A. Shen, M. N. Vyalyi 2002 1 QMA - the quantum analog to MA (and NP). Definition 1 QMA. The complexity class QMA is the class of all languages
More informationOverview of Topological Cluster-State Quantum Computation on 2D Cluster-State
Overview of Topological Cluster-State Quantum Computation on 2D Cluster-State based on High-threshold universal quantum computation on the surface code -Austin G. Fowler, Ashley M. Stephens, and Peter
More informationEntanglement and Quantum Teleportation
Entanglement and Quantum Teleportation Stephen Bartlett Centre for Advanced Computing Algorithms and Cryptography Australian Centre of Excellence in Quantum Computer Technology Macquarie University, Sydney,
More information9. Distance measures. 9.1 Classical information measures. Head Tail. How similar/close are two probability distributions? Trace distance.
9. Distance measures 9.1 Classical information measures How similar/close are two probability distributions? Trace distance Fidelity Example: Flipping two coins, one fair one biased Head Tail Trace distance
More informationThe computational difficulty of finding MPS ground states
The computational difficulty of finding MPS ground states Norbert Schuch 1, Ignacio Cirac 1, and Frank Verstraete 2 1 Max-Planck-Institute for Quantum Optics, Garching, Germany 2 University of Vienna,
More informationSolutions Final exam 633
Solutions Final exam 633 S.J. van Enk (Dated: June 9, 2008) (1) [25 points] You have a source that produces pairs of spin-1/2 particles. With probability p they are in the singlet state, ( )/ 2, and with
More informationIntroduction into Quantum Computations Alexei Ashikhmin Bell Labs
Introduction into Quantum Computations Alexei Ashikhmin Bell Labs Workshop on Quantum Computing and its Application March 16, 2017 Qubits Unitary transformations Quantum Circuits Quantum Measurements Quantum
More informationSome Introductory Notes on Quantum Computing
Some Introductory Notes on Quantum Computing Markus G. Kuhn http://www.cl.cam.ac.uk/~mgk25/ Computer Laboratory University of Cambridge 2000-04-07 1 Quantum Computing Notation Quantum Computing is best
More informationLecture 4: Postulates of quantum mechanics
Lecture 4: Postulates of quantum mechanics Rajat Mittal IIT Kanpur The postulates of quantum mechanics provide us the mathematical formalism over which the physical theory is developed. For people studying
More informationUse of dynamical coupling for improved quantum state transfer
Use of dynamical coupling for improved quantum state transfer A. O. Lyakhov and C. Bruder Department of Physics and Astronomy, University of Basel, Klingelbergstr. 82, 45 Basel, Switzerland We propose
More informationPh 219/CS 219. Exercises Due: Friday 3 November 2006
Ph 9/CS 9 Exercises Due: Friday 3 November 006. Fidelity We saw in Exercise. that the trace norm ρ ρ tr provides a useful measure of the distinguishability of the states ρ and ρ. Another useful measure
More informationQuantum Information Types
qitd181 Quantum Information Types Robert B. Griffiths Version of 6 February 2012 References: R. B. Griffiths, Types of Quantum Information, Phys. Rev. A 76 (2007) 062320; arxiv:0707.3752 Contents 1 Introduction
More informationSeminar 1. Introduction to Quantum Computing
Seminar 1 Introduction to Quantum Computing Before going in I am also a beginner in this field If you are interested, you can search more using: Quantum Computing since Democritus (Scott Aaronson) Quantum
More informationFermionic quantum theory and superselection rules for operational probabilistic theories
Fermionic quantum theory and superselection rules for operational probabilistic theories Alessandro Tosini, QUIT group, Pavia University Joint work with G.M. D Ariano, F. Manessi, P. Perinotti Supported
More informationSpekkens Toy Model, Finite Field Quantum Mechanics, and the Role of Linearity arxiv: v1 [quant-ph] 15 Mar 2019
Spekkens Toy Model, Finite Field Quantum Mechanics, and the Role of Linearity arxiv:903.06337v [quant-ph] 5 Mar 209 Lay Nam Chang, Djordje Minic, and Tatsu Takeuchi Department of Physics, Virginia Tech,
More informationInformation quantique, calcul quantique :
Séminaire LARIS, 8 juillet 2014. Information quantique, calcul quantique : des rudiments à la recherche (en 45min!). François Chapeau-Blondeau LARIS, Université d Angers, France. 1/25 Motivations pour
More information2.0 Basic Elements of a Quantum Information Processor. 2.1 Classical information processing The carrier of information
QSIT09.L03 Page 1 2.0 Basic Elements of a Quantum Information Processor 2.1 Classical information processing 2.1.1 The carrier of information - binary representation of information as bits (Binary digits).
More informationarxiv: v1 [quant-ph] 7 Jun 2013
Optimal quantum state transfer in disordered spin chains arxiv:1306.1695v1 [quant-ph] 7 Jun 2013 Analia Zwick, 1, 2, 3 Gonzalo A. Álvarez, 1, 3 Joachim Stolze, 3 and Omar Osenda 2 1 Department of Chemical
More informationEntanglement in Topological Phases
Entanglement in Topological Phases Dylan Liu August 31, 2012 Abstract In this report, the research conducted on entanglement in topological phases is detailed and summarized. This includes background developed
More informationThe Fermionic Quantum Theory
The Fermionic Quantum Theory CEQIP, Znojmo, May 2014 Authors: Alessandro Tosini Giacomo Mauro D Ariano Paolo Perinotti Franco Manessi Fermionic systems in computation and physics Fermionic Quantum theory
More informationTopological quantum computation
School US-Japan seminar 2013/4/4 @Nara Topological quantum computation -from topological order to fault-tolerant quantum computation- The Hakubi Center for Advanced Research, Kyoto University Graduate
More informationLecture 6: Quantum error correction and quantum capacity
Lecture 6: Quantum error correction and quantum capacity Mark M. Wilde The quantum capacity theorem is one of the most important theorems in quantum hannon theory. It is a fundamentally quantum theorem
More informationFault-Tolerant Universality from Fault-Tolerant Stabilizer Operations and Noisy Ancillas
Fault-Tolerant Universality from Fault-Tolerant Stabilizer Operations and Noisy Ancillas Ben W. Reichardt UC Berkeley NSF, ARO [quant-ph/0411036] stabilizer operations, Q: Do form a universal set? prepare
More informationDetecting and using Majorana fermions in superconductors
Detecting and using Majorana fermions in superconductors Anton Akhmerov with Carlo Beenakker, Jan Dahlhaus, Fabian Hassler, and Michael Wimmer New J. Phys. 13, 053016 (2011) and arxiv:1105.0315 Superconductor
More informationBosonization of lattice fermions in higher dimensions
Bosonization of lattice fermions in higher dimensions Anton Kapustin California Institute of Technology January 15, 2019 Anton Kapustin (California Institute of Technology) Bosonization of lattice fermions
More informationGrover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick
Grover s algorithm Search in an unordered database Example: phonebook, need to find a person from a phone number Actually, something else, like hard (e.g., NP-complete) problem 0, xx aa Black box ff xx
More information3 Symmetry Protected Topological Phase
Physics 3b Lecture 16 Caltech, 05/30/18 3 Symmetry Protected Topological Phase 3.1 Breakdown of noninteracting SPT phases with interaction Building on our previous discussion of the Majorana chain and
More informationManipulation of Majorana fermions via single charge control
Manipulation of Majorana fermions via single charge control Karsten Flensberg Niels Bohr Institute University of Copenhagen Superconducting hybrids: from conventional to exotic, Villard de Lans, France,
More informationSecurity Implications of Quantum Technologies
Security Implications of Quantum Technologies Jim Alves-Foss Center for Secure and Dependable Software Department of Computer Science University of Idaho Moscow, ID 83844-1010 email: jimaf@cs.uidaho.edu
More informationQuantum Computing 1. Multi-Qubit System. Goutam Biswas. Lect 2
Quantum Computing 1 Multi-Qubit System Quantum Computing State Space of Bits The state space of a single bit is {0,1}. n-bit state space is {0,1} n. These are the vertices of the n-dimensional hypercube.
More informationNANOSCALE SCIENCE & TECHNOLOGY
. NANOSCALE SCIENCE & TECHNOLOGY V Two-Level Quantum Systems (Qubits) Lecture notes 5 5. Qubit description Quantum bit (qubit) is an elementary unit of a quantum computer. Similar to classical computers,
More informationA complete criterion for convex-gaussian states detection
A complete criterion for convex-gaussian states detection Anna Vershynina Institute for Quantum Information, RWTH Aachen, Germany joint work with B. Terhal NSF/CBMS conference Quantum Spin Systems The
More informationQuantum dots and Majorana Fermions Karsten Flensberg
Quantum dots and Majorana Fermions Karsten Flensberg Center for Quantum Devices University of Copenhagen Collaborator: Martin Leijnse and R. Egger M. Kjærgaard K. Wölms Outline: - Introduction to Majorana
More informationKitaev honeycomb lattice model: from A to B and beyond
Kitaev honeycomb lattice model: from A to B and beyond Jiri Vala Department of Mathematical Physics National University of Ireland at Maynooth Postdoc: PhD students: Collaborators: Graham Kells Ahmet Bolukbasi
More informationErrata list, Nielsen & Chuang. rrata/errata.html
Errata list, Nielsen & Chuang http://www.michaelnielsen.org/qcqi/errata/e rrata/errata.html Part II, Nielsen & Chuang Quantum circuits (Ch 4) SK Quantum algorithms (Ch 5 & 6) Göran Johansson Physical realisation
More informationIntroduction. Chapter One
Chapter One Introduction The aim of this book is to describe and explain the beautiful mathematical relationships between matrices, moments, orthogonal polynomials, quadrature rules and the Lanczos and
More informationQuantum walks: Definition and applications
Quantum walks: Definition and applications 尚云 2017 年 5 月 5 日 ( 量子计算与密码分析讨论班 ) Talk structure Introduction to quantum walks Defining a quantum walk...on the line...on the graphs Applications of quantum
More informationGolden chain of strongly interacting Rydberg atoms
Golden chain of strongly interacting Rydberg atoms Hosho Katsura (Gakushuin Univ.) Acknowledgment: Igor Lesanovsky (MUARC/Nottingham Univ. I. Lesanovsky & H.K., [arxiv:1204.0903] Outline 1. Introduction
More informationHilbert Space, Entanglement, Quantum Gates, Bell States, Superdense Coding.
CS 94- Bell States Bell Inequalities 9//04 Fall 004 Lecture Hilbert Space Entanglement Quantum Gates Bell States Superdense Coding 1 One qubit: Recall that the state of a single qubit can be written as
More informationNewton s Method and Localization
Newton s Method and Localization Workshop on Analytical Aspects of Mathematical Physics John Imbrie May 30, 2013 Overview Diagonalizing the Hamiltonian is a goal in quantum theory. I would like to discuss
More informationMagic States. Presented by Nathan Babcock
Magic States Presented by Nathan Babcock Overview I will discuss the following points:. Quantum Error Correction. The Stabilizer Formalism. Clifford Group Quantum Computation 4. Magic States 5. Derivation
More informationQuantum state transfer on distance regular. spin networks with intrinsic decoherence
Quantum state transfer on distance regular spin networks with intrinsic decoherence arxiv:1701.00647v1 [quant-ph] 3 Jan 2017 R. Sufiani a and A. Pedram a Department of Theoretical Physics and Astrophysics,
More informationFrom graphene to Z2 topological insulator
From graphene to Z2 topological insulator single Dirac topological AL mass U U valley WL ordinary mass or ripples WL U WL AL AL U AL WL Rashba Ken-Ichiro Imura Condensed-Matter Theory / Tohoku Univ. Dirac
More informationMeasuring Entanglement Entropy in Synthetic Matter
Measuring Entanglement Entropy in Synthetic Matter Markus Greiner Harvard University H A R V A R D U N I V E R S I T Y M I T CENTER FOR ULTRACOLD ATOMS Ultracold atom synthetic quantum matter: First Principles
More informationWhy does nature like the square root of negative one? William K. Wootters Williams College
Why does nature like the square root of negative one? William K. Wootters Williams College A simple quantum experiment Computing probabilities in a sensible way (½)(½)+(½)(½) = ½ ½ ½ Computing probabilities
More informationEECS 275 Matrix Computation
EECS 275 Matrix Computation Ming-Hsuan Yang Electrical Engineering and Computer Science University of California at Merced Merced, CA 95344 http://faculty.ucmerced.edu/mhyang Lecture 17 1 / 26 Overview
More informationTopological invariants for 1-dimensional superconductors
Topological invariants for 1-dimensional superconductors Eddy Ardonne Jan Budich 1306.4459 1308.soon SPORE 13 2013-07-31 Intro: Transverse field Ising model H TFI = L 1 i=0 hσ z i + σ x i σ x i+1 σ s:
More informationSelection rules - electric dipole
Selection rules - electric dipole As an example, lets take electric dipole transitions; when is j, m z j 2, m 2 nonzero so that j 1 = 1 and m 1 = 0. The answer is equivalent to the question when can j
More informationFidelity of Quantum Teleportation through Noisy Channels
Fidelity of Quantum Teleportation through Noisy Channels Sangchul Oh, Soonchil Lee, and Hai-woong Lee Department of Physics, Korea Advanced Institute of Science and Technology, Daejon, 305-701, Korea (Dated:
More informationMajorana bound states in spatially inhomogeneous nanowires
Master Thesis Majorana bound states in spatially inhomogeneous nanowires Author: Johan Ekström Supervisor: Assoc. Prof. Martin Leijnse Division of Solid State Physics Faculty of Engineering November 2016
More informationb) (5 points) Give a simple quantum circuit that transforms the state
C/CS/Phy191 Midterm Quiz Solutions October 0, 009 1 (5 points) Short answer questions: a) (5 points) Let f be a function from n bits to 1 bit You have a quantum circuit U f for computing f If you wish
More informationInverse Eigenvalue Problems: Theory, Algorithms, and Applications
Inverse Eigenvalue Problems: Theory, Algorithms, and Applications Moody T. Chu North Carolina State University Gene H. Golub Stanford University OXPORD UNIVERSITY PRESS List of Acronyms List of Figures
More informationarxiv:quant-ph/ v1 21 Nov 2003
Analytic solutions for quantum logic gates and modeling pulse errors in a quantum computer with a Heisenberg interaction G.P. Berman 1, D.I. Kamenev 1, and V.I. Tsifrinovich 2 1 Theoretical Division and
More informationQuantum computation in topological Hilbertspaces. A presentation on topological quantum computing by Deniz Bozyigit and Martin Claassen
Quantum computation in topological Hilbertspaces A presentation on topological quantum computing by Deniz Bozyigit and Martin Claassen Introduction In two words what is it about? Pushing around fractionally
More informationTime Independent Perturbation Theory Contd.
Time Independent Perturbation Theory Contd. A summary of the machinery for the Perturbation theory: H = H o + H p ; H 0 n >= E n n >; H Ψ n >= E n Ψ n > E n = E n + E n ; E n = < n H p n > + < m H p n
More informationarxiv: v2 [quant-ph] 9 Jan 2015
Quantum state transfer in disordered spin chains: How much engineering is reasonable? arxiv:1306.1695v2 [quant-ph] 9 Jan 2015 Analia Zwick, 1, 2, 3 Gonzalo A. Álvarez, 1, 3 Joachim Stolze, 3 and Omar Osenda
More informationFRG Workshop in Cambridge MA, May
FRG Workshop in Cambridge MA, May 18-19 2011 Programme Wednesday May 18 09:00 09:10 (welcoming) 09:10 09:50 Bachmann 09:55 10:35 Sims 10:55 11:35 Borovyk 11:40 12:20 Bravyi 14:10 14:50 Datta 14:55 15:35
More informationThe Future. Currently state of the art chips have gates of length 35 nanometers.
Quantum Computing Moore s Law The Future Currently state of the art chips have gates of length 35 nanometers. The Future Currently state of the art chips have gates of length 35 nanometers. When gate lengths
More informationLogical error rate in the Pauli twirling approximation
Logical error rate in the Pauli twirling approximation Amara Katabarwa and Michael R. Geller Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA (Dated: April 10, 2015)
More informationexample: e.g. electron spin in a field: on the Bloch sphere: this is a rotation around the equator with Larmor precession frequency ω
Dynamics of a Quantum System: QM postulate: The time evolution of a state ψ> of a closed quantum system is described by the Schrödinger equation where H is the hermitian operator known as the Hamiltonian
More informationarxiv: v1 [quant-ph] 3 Feb 2011
Heisenberg Spin Bus as a Robust Transmission Line for Perfect State Transfer Sangchul Oh, Lian-Ao Wu,, Yun-Pil Shim, Mark Friesen, and Xuedong Hu Department of Physics, University at Buffalo, State University
More informationIBM quantum experience: Experimental implementations, scope, and limitations
IBM quantum experience: Experimental implementations, scope, and limitations Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various
More informationCoulomb entangler and entanglement-testing network for waveguide qubits
PHYSICAL REVIEW A 72, 032330 2005 Coulomb entangler and entanglement-testing network for waveguide qubits Linda E. Reichl and Michael G. Snyder Center for Studies in Statistical Mechanics and Complex Systems,
More informationUnitary Dynamics and Quantum Circuits
qitd323 Unitary Dynamics and Quantum Circuits Robert B. Griffiths Version of 20 January 2014 Contents 1 Unitary Dynamics 1 1.1 Time development operator T.................................... 1 1.2 Particular
More informationSupervised quantum gate teaching for quantum hardware design
Supervised quantum gate teaching for quantum hardware design Leonardo Banchi1, Nicola Pancotti2 and Sougato Bose1 1- Department of Physics and Astronomy, University College London, Gower Street, London
More informationQuantum Cloning WOOTTERS-ZUREK CLONER
Quantum Cloning Quantum cloning has been a topic of considerable interest for many years. It turns out to be quantum limit for copying an input state and is closely related to linear amplification when
More informationAccelerating QMC on quantum computers. Matthias Troyer
Accelerating QMC on quantum computers Matthias Troyer International Journal of Theoretical Physics, VoL 21, Nos. 6/7, 1982 Simulating Physics with Computers Richard P. Feynman Department of Physics, California
More informationLecture 3: Superdense coding, quantum circuits, and partial measurements
CPSC 59/69: Quantum Computation John Watrous, University of Calgary Lecture 3: Superdense coding, quantum circuits, and partial measurements Superdense Coding January 4, 006 Imagine a situation where two
More information6. Quantum error correcting codes
6. Quantum error correcting codes Error correcting codes (A classical repetition code) Preserving the superposition Parity check Phase errors CSS 7-qubit code (Steane code) Too many error patterns? Syndrome
More informationPauli Exchange and Quantum Error Correction
Contemporary Mathematics Pauli Exchange and Quantum Error Correction Mary Beth Ruskai Abstract. In many physically realistic models of quantum computation, Pauli exchange interactions cause a special type
More informationFermions in Quantum Complexity Theory
Fermions in Quantum Complexity Theory Edwin Ng MIT Department of Physics December 14, 2012 Occupation Number Formalism Consider n identical particles in m modes. If there are x j particles in the jth mode,
More informationQuantum information and quantum computing
Middle East Technical University, Department of Physics January 7, 009 Outline Measurement 1 Measurement 3 Single qubit gates Multiple qubit gates 4 Distinguishability 5 What s measurement? Quantum measurement
More informationExact diagonalization methods
Summer School on Computational Statistical Physics August 4-11, 2010, NCCU, Taipei, Taiwan Exact diagonalization methods Anders W. Sandvik, Boston University Representation of states in the computer bit
More informationTopological Quantum Computation from non-abelian anyons
Topological Quantum Computation from non-abelian anyons Paul Fendley Experimental and theoretical successes have made us take a close look at quantum physics in two spatial dimensions. We have now found
More informationTopological Insulators
Topological Insulators Aira Furusai (Condensed Matter Theory Lab.) = topological insulators (3d and 2d) Outline Introduction: band theory Example of topological insulators: integer quantum Hall effect
More informationThe Klein-Gordon equation
Lecture 8 The Klein-Gordon equation WS2010/11: Introduction to Nuclear and Particle Physics The bosons in field theory Bosons with spin 0 scalar (or pseudo-scalar) meson fields canonical field quantization
More informationThe quantum speed limit
The quantum speed limit Vittorio Giovannetti a,sethlloyd a,b, and Lorenzo Maccone a a Research Laboratory of Electronics b Department of Mechanical Engineering Massachusetts Institute of Technology 77
More informationApplication of Structural Physical Approximation to Partial Transpose in Teleportation. Satyabrata Adhikari Delhi Technological University (DTU)
Application of Structural Physical Approximation to Partial Transpose in Teleportation Satyabrata Adhikari Delhi Technological University (DTU) Singlet fraction and its usefulness in Teleportation Singlet
More information