Introduction to Quantum Computing
|
|
- Daisy Neal
- 6 years ago
- Views:
Transcription
1 Introduction to Quantum Computing Petros Wallden Lecture 1: Introduction 18th September 2017 School of Informatics, University of Edinburgh
2 Resources 1. Quantum Computation and Quantum Information by Michael A. Nielsen & Isaac L. Chuang 2. Lecture Notes available on 1
3 Moore s Law & Quantum Mechanics The number of transistors in each microchip double every two years Soon we will reach atomic scale Quantum Mechanics govern physical systems at this scale Quantum Fluctuations and Uncertainty will affect classical computations 2
4 Bits Vs Qubits Bit Takes values either 0 or 1 Measurement reveals the value of the bit Can be copied String of bits are described in terms of single bits (local) Qubit Can behave as being simultaneously 0 and 1: α 0 + β 1 Measurement disturbs the system Cannot be copied String of qubits can have properties that cannot be described in terms of single qubits (non-local) Qubits behave as waves and interfere with each other Qubits are physical systems. Many different systems have been used such as: Photons (polarization, number, time-bin encoding), Coherent Light, Electrons (spin, number), Nuclear spin, Optical lattices, Superconductors, etc. 3
5 Quantumness as Resource Nobel laureate Richard Feynman 1982: Quantum Computer is a computer that uses QM to its advantage. It can simulate quantum systems. Great Developments: - Quantum Algorithms can lead to speed-up - Quantum Computers can break classical Cryptosystems such as the RSA - Quantum Cryptogaphy can encrypt messages with Unconditionally Security (not relying in computational assumptions) - Principles of Quantum Computation can be used to simulate and explore physical phenomena at domains that are not accessible from Black Hole thermodynamics to Condense Matter Physics 4
6 Secure Quantum Communication - Many quantum cryptographic protocols: Encryption, secret sharing, digital signatures, coin flipping, Unconditionally secure homomorphic encryption - Implementations of Quantum Key Distribution Networks between cities exist in many countries. QKD systems are provided by commercial companies (e.g. idquantique) Quantum Computers - There exist different models of Quantum Computation: Quantum Circuit, Measurement Based (these two will be covered), Adiabatic QC, Topological QC - Implementations have attempted to used different physical systems. Still not scalable (only few qubits operations e.g. factored 143). Superconductor based, Trapped ion, Optical lattices, Nuclear magnetic resonance, quantum optics NQIT (Networked Quantum Information Technologies) Hub (lead by Oxford, Edinburgh is part of): Q20:20, 20 ion traps of 20 qubits each, connected with photons.
7 Quantum Algorithms Speed-up Deutsch & Jozsa showed the first speed up Given a Boolean function f : {0, 1} n {0, 1} determine if it is constant or balanced f = 1 2 n x {0,1} ( 1) f(x) x n The state for any constant function is orthogonal to the state of any balanced function 5
8 Simon s Problem Given a function f : {0, 1} n {0, 1} n finds a such that f(x + a) = f(x) Shor s Algorithm Given n-bit integer, find the prime factorisation. Breaks the RSA cryptosystem (most currently used public key encryptions are based on this)
9 History 1980s Idea of quantum computation. Paul Benioff, Yuri Manin, Richard Feynman, David Deutsch 1990s Theory of efficient quantum simulation. Seth Lloyd 1994 Peter Shor s algorithms for factoring and discrete log. Quantum computers can break RSA, Diffie-Hellman, El Gamal, Elliptic Curve Cryptography and others 2001 Experiment factors 15 using Shor s algorithm 2010s D-Wave, Google, IBM, NQIT and various universities work on developing quantum computers How serious is the involvement in quantum computation? 6
10 Who invests in Quantum Computing? 7
11 Who invests in Quantum Computing? 8
12 Applications 9
13 Misconceptions 10
14 Misconceptions 11
15 State of Art 2001 Shor s algorithm factors 15 on 7 qubits 2011 Shor s algorithm factors Universal quantum computation on 2 fault tolerant qubits Qubits and gates in silicon chips 2015 D-Wave 2X, 1000 qubits, optimization problems, no fault tolerance 2016 IBM, universal quantum computation on 5 fault tolerant qubits (publicly available) 2020 NQIT, Q20:20, fault tolerant (20 qubits), scalable 12
16 State of Art: Cryptography 13
17 State of Art: Cryptography 14
18 What can you buy 15
19 What can you buy 16
20 Quantum Mechanics Nobel laureate Niels Bohr (photo with Einstein) Anyone who is not shocked by quantum theory has not understood it - Basic resource for QC is the distinct properties of quantum theory - To appreciate this one needs to (attempt to) understand QM - QM has been proven very successful and all so far tested predictions has been verified at a unprecedent level of accuracy - However, the conceptual challenges posed by QM are profound. Classical notions such as locality, non-contextuality, determinism even realism has been challenged 17
21 - The role of the observer and of the measurement are very different - Properties with no classical analogue: Uncertainty, wave-particle duality, no-cloning, indistinguishability of quantum states, teleportation - Also QM is incompatible with the other most successful physical theory General Relativity. This is possible because the former deals with the micro-world while the latter with macro-world. However, for a complete theory of nature one needs to construct a theory that includes both QM and GR and this is probably the greatest challenge for contemporary physics.
22 Content of the Course Basic concepts from Linear Algebra Axioms of Quantum Mechanics Non-locality, Bell s inequalities and the interpretations of QM No-cloning and no-deleting theorem Quantum Computing via the circuit model Quantum complexity Quantum Algorithms Quantum Cryptography Quantum Computing via the measurement-based model 18
Cryptography in a quantum world
T School of Informatics, University of Edinburgh 25th October 2016 E H U N I V E R S I T Y O H F R G E D I N B U Outline What is quantum computation Why should we care if quantum computers are constructed?
More information1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation
QSIT09.V01 Page 1 1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation What is quantum mechanics good for? traditional historical perspective: beginning of 20th century: classical
More informationquantum mechanics is a hugely successful theory... QSIT08.V01 Page 1
1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation What is quantum mechanics good for? traditional historical perspective: beginning of 20th century: classical physics fails
More informationCyber Security in the Quantum Era
T Computer Security Guest Lecture University of Edinburgh 27th November 2017 E H U N I V E R S I T Y O H F R G E D I N B U Outline Quantum Computers: Is it a threat to Cyber Security? Why should we act
More informationQuantum Information Science (QIS)
Quantum Information Science (QIS) combination of three different fields: Quantum Physics QIS Computer Science Information Theory Lecture 1 - Outline 1. Quantum Mechanics 2. Computer Science History 3.
More informationPhysics is becoming too difficult for physicists. David Hilbert (mathematician)
Physics is becoming too difficult for physicists. David Hilbert (mathematician) Simple Harmonic Oscillator Credit: R. Nave (HyperPhysics) Particle 2 X 2-Particle wave functions 2 Particles, each moving
More informationQuantum Computing 101. ( Everything you wanted to know about quantum computers but were afraid to ask. )
Quantum Computing 101 ( Everything you wanted to know about quantum computers but were afraid to ask. ) Copyright Chris Lomont, 2004 2 67 1 = 193707721 761838257287 Took American Mathematician Frank Nelson
More informationQuantum Information & Quantum Computation
CS290A, Spring 2005: Quantum Information & Quantum Computation Wim van Dam Engineering 1, Room 5109 vandam@cs http://www.cs.ucsb.edu/~vandam/teaching/cs290/ Administrivia Required book: M.A. Nielsen and
More informationHacking Quantum Cryptography. Marina von Steinkirch ~ Yelp Security
Hacking Quantum Cryptography Marina von Steinkirch ~ Yelp Security Agenda 1. Quantum Mechanics in 10 mins 2. Quantum Computing in 11 mins 3. Quantum Key Exchange in 100 mins (or more minutes) Some disclaimers
More informationA brief survey on quantum computing
A brief survey on quantum computing Edward Poon University of Ottawa Edward Poon (Ottawa) A brief survey on quantum computing March 19, 2018 1 / 7 Outline Goal: Provide a high-level overview of what quantum
More informationLogic gates. Quantum logic gates. α β 0 1 X = 1 0. Quantum NOT gate (X gate) Classical NOT gate NOT A. Matrix form representation
Quantum logic gates Logic gates Classical NOT gate Quantum NOT gate (X gate) A NOT A α 0 + β 1 X α 1 + β 0 A N O T A 0 1 1 0 Matrix form representation 0 1 X = 1 0 The only non-trivial single bit gate
More informationIntroduction to Quantum Information Processing QIC 710 / CS 768 / PH 767 / CO 681 / AM 871
Introduction to Quantum Information Processing QIC 710 / CS 768 / PH 767 / CO 681 / AM 871 Lecture 1 (2017) Jon Yard QNC 3126 jyard@uwaterloo.ca TAs Nitica Sakharwade nsakharwade@perimeterinstitute.ca
More informationAn Introduction to Quantum Information and Applications
An Introduction to Quantum Information and Applications Iordanis Kerenidis CNRS LIAFA-Univ Paris-Diderot Quantum information and computation Quantum information and computation How is information encoded
More informationQuantum Computing. Richard Jozsa Centre for Quantum Information and Foundations DAMTP University of Cambridge
Quantum Computing Richard Jozsa Centre for Quantum Information and Foundations DAMTP University of Cambridge Physics and Computation A key question: what is computation....fundamentally? What makes it
More informationQuantum Key Distribution and the Future of Encryption
Quantum Key Distribution and the Future of Encryption Konstantinos Karagiannis Global Technical Lead, Ethical Hacking BT Security Amsterdam, October 16 th, 2014 Understanding QM? I think I can safely say
More informationOther Topics in Quantum Information
p. 1/23 Other Topics in Quantum Information In a course like this there is only a limited time, and only a limited number of topics can be covered. Some additional topics will be covered in the class projects.
More informationphys4.20 Page 1 - the ac Josephson effect relates the voltage V across a Junction to the temporal change of the phase difference
Josephson Effect - the Josephson effect describes tunneling of Cooper pairs through a barrier - a Josephson junction is a contact between two superconductors separated from each other by a thin (< 2 nm)
More informationQuantum Computing. Vraj Parikh B.E.-G.H.Patel College of Engineering & Technology, Anand (Affiliated with GTU) Abstract HISTORY OF QUANTUM COMPUTING-
Quantum Computing Vraj Parikh B.E.-G.H.Patel College of Engineering & Technology, Anand (Affiliated with GTU) Abstract Formerly, Turing Machines were the exemplar by which computability and efficiency
More informationQuantum Computing is Here, Powered by Open Source. Konstantinos Karagiannis CTO, Security Consulting BT
Quantum Computing is Here, Powered by Open Source Konstantinos Karagiannis CTO, Security Consulting BT Americas @KonstantHacker It all started with the need to crack encryption We re there again Snowden
More informationMAA509: Quantum Computing and Information Introduction
MAA509: Quantum Computing and Information Introduction November 7, 2016 November 7, 2016 1 / 19 Why make computers? Computation by hand is difficult and not very stimulating. Why not make a machine do
More informationThe Relativistic Quantum World
The Relativistic Quantum World A lecture series on Relativity Theory and Quantum Mechanics Marcel Merk University of Maastricht, Sept 24 Oct 15, 2014 Relativity Quantum Mechanics The Relativistic Quantum
More informationQOT - Quantum Optical Technologies
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2018 230 - ETSETB - Barcelona School of Telecommunications Engineering 739 - TSC - Department of Signal Theory and Communications
More informationIntroduction to Quantum Information Processing
Introduction to Quantum Information Processing Lecture 6 Richard Cleve Overview of Lecture 6 Continuation of teleportation Computation and some basic complexity classes Simple quantum algorithms in the
More informationQuantum Computation 650 Spring 2009 Lectures The World of Quantum Information. Quantum Information: fundamental principles
Quantum Computation 650 Spring 2009 Lectures 1-21 The World of Quantum Information Marianna Safronova Department of Physics and Astronomy February 10, 2009 Outline Quantum Information: fundamental principles
More informationSecrets of Quantum Information Science
Secrets of Quantum Information Science Todd A. Brun Communication Sciences Institute USC Quantum computers are in the news Quantum computers represent a new paradigm for computing devices: computers whose
More informationQuantum technology popular science description
Quantum technology popular science description 1 Quantum physics, from theory to ongoing revolution In the early 1900s observations were made that were not consistent with traditional, classical physics.
More informationReversible and Quantum computing. Fisica dell Energia - a.a. 2015/2016
Reversible and Quantum computing Fisica dell Energia - a.a. 2015/2016 Reversible computing A process is said to be logically reversible if the transition function that maps old computational states to
More information1500 AMD Opteron processor (2.2 GHz with 2 GB RAM)
NICT 2019 2019 2 7 1 RSA RSA 2 3 (1) exp $ 64/9 + *(1) (ln 0) 1/2 (ln ln 0) 3/2 (2) 2009 12 768 (232 ) 1500 AMD Opteron processor (2.2 GHz with 2 GB RAM) 4 (3) 18 2 (1) (2) (3) 5 CRYPTREC 1. 2. 3. 1024,
More informationTutorial on Quantum Computing. Vwani P. Roychowdhury. Lecture 1: Introduction
Tutorial on Quantum Computing Vwani P. Roychowdhury Lecture 1: Introduction 1 & ) &! # Fundamentals Qubits A single qubit is a two state system, such as a two level atom we denote two orthogonal states
More informationQuantum Computing. Thorsten Altenkirch
Quantum Computing Thorsten Altenkirch Is Computation universal? Alonzo Church - calculus Alan Turing Turing machines computable functions The Church-Turing thesis All computational formalisms define the
More informationQuantum Computing. Separating the 'hope' from the 'hype' Suzanne Gildert (D-Wave Systems, Inc) 4th September :00am PST, Teleplace
Quantum Computing Separating the 'hope' from the 'hype' Suzanne Gildert (D-Wave Systems, Inc) 4th September 2010 10:00am PST, Teleplace The Hope All computing is constrained by the laws of Physics and
More informationExperimental Quantum Computing: A technology overview
Experimental Quantum Computing: A technology overview Dr. Suzanne Gildert Condensed Matter Physics Research (Quantum Devices Group) University of Birmingham, UK 15/02/10 Models of quantum computation Implementations
More informationRichard Cleve David R. Cheriton School of Computer Science Institute for Quantum Computing University of Waterloo
CS 497 Frontiers of Computer Science Introduction to Quantum Computing Lecture of http://www.cs.uwaterloo.ca/~cleve/cs497-f7 Richard Cleve David R. Cheriton School of Computer Science Institute for Quantum
More informationQuantum Technology 101: Overview of Quantum Computing and Quantum Cybersecurity
Quantum Technology 0: Overview of Quantum Computing and Quantum Cybersecurity Warner A. Miller* Department of Physics & Center for Cryptography and Information Security Florida Atlantic University NSF
More informationQuantum Technologies for Cryptography
University of Sydney 11 July 2018 Quantum Technologies for Cryptography Mario Berta (Department of Computing) marioberta.info Quantum Information Science Understanding quantum systems (e.g., single atoms
More informationChallenges in Quantum Information Science. Umesh V. Vazirani U. C. Berkeley
Challenges in Quantum Information Science Umesh V. Vazirani U. C. Berkeley 1 st quantum revolution - Understanding physical world: periodic table, chemical reactions electronic wavefunctions underlying
More informationIntroduction to Quantum Information, Quantum Computation, and Its Application to Cryptography. D. J. Guan
Introduction to Quantum Information, Quantum Computation, and Its Application to Cryptography D. J. Guan Abstract The development of quantum algorithms and quantum information theory, as well as the design
More information*WILEY- Quantum Computing. Joachim Stolze and Dieter Suter. A Short Course from Theory to Experiment. WILEY-VCH Verlag GmbH & Co.
Joachim Stolze and Dieter Suter Quantum Computing A Short Course from Theory to Experiment Second, Updated and Enlarged Edition *WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XIII 1 Introduction
More informationIntroduction to Quantum Computing
Introduction to Quantum Computing Part I Emma Strubell http://cs.umaine.edu/~ema/quantum_tutorial.pdf April 12, 2011 Overview Outline What is quantum computing? Background Caveats Fundamental differences
More informationQUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling
QUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling Quantum Science & Technologies Group Hearne Institute for Theoretical Physics Louisiana State University http://quantum.phys.lsu.edu
More informationEntanglement. arnoldzwicky.org. Presented by: Joseph Chapman. Created by: Gina Lorenz with adapted PHYS403 content from Paul Kwiat, Brad Christensen
Entanglement arnoldzwicky.org Presented by: Joseph Chapman. Created by: Gina Lorenz with adapted PHYS403 content from Paul Kwiat, Brad Christensen PHYS403, July 26, 2017 Entanglement A quantum object can
More informationQUANTUM COMPUTING & CRYPTO: HYPE VS. REALITY ABHISHEK PARAKH UNIVERSITY OF NEBRASKA AT OMAHA
QUANTUM COMPUTING & CRYPTO: HYPE VS. REALITY ABHISHEK PARAKH UNIVERSITY OF NEBRASKA AT OMAHA QUANTUM COMPUTING: I CAN SUM IT UP IN ONE SLIDE Pure Magic! 2 SERIOUSLY: HOW DOES IT WORK? That s simple: Even
More informationTopological Quantum Computation. George Toh 11/6/2017
Topological Quantum Computation George Toh 11/6/2017 Contents Quantum Computing Comparison of QC vs TQC Topological Quantum Computation How to implement TQC? Examples, progress Industry investment Future
More informationQuantum Information Processing
Quantum Information Processing Jonathan Jones http://nmr.physics.ox.ac.uk/teaching The Information Age Communication Shannon Computation Turing Current approaches are essentially classical which is wrong
More informationLecture Quantum Information Processing II: Implementations. spring term (FS) 2017
Lecture Quantum Information Processing II: Implementations spring term (FS) 2017 Lectures & Exercises: Andreas Wallraff, Christian Kraglund Andersen, Christopher Eichler, Sebastian Krinner Please take
More informationQuantum Computing. Joachim Stolze and Dieter Suter. A Short Course from Theory to Experiment. WILEY-VCH Verlag GmbH & Co. KGaA
Joachim Stolze and Dieter Suter Quantum Computing A Short Course from Theory to Experiment Second, Updated and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Preface XIII 1 Introduction and
More informationLecture 1: Introduction to Public key cryptography
Lecture 1: Introduction to Public key cryptography Thomas Johansson T. Johansson (Lund University) 1 / 44 Key distribution Symmetric key cryptography: Alice and Bob share a common secret key. Some means
More information10 - February, 2010 Jordan Myronuk
10 - February, 2010 Jordan Myronuk Classical Cryptography EPR Paradox] The need for QKD Quantum Bits and Entanglement No Cloning Theorem Polarization of Photons BB84 Protocol Probability of Qubit States
More informationThe quantum threat to cryptography
The quantum threat to cryptography Ashley Montanaro School of Mathematics, University of Bristol 20 October 2016 Quantum computers University of Bristol IBM UCSB / Google University of Oxford Experimental
More informationQuantum computing. Jan Černý, FIT, Czech Technical University in Prague. České vysoké učení technické v Praze. Fakulta informačních technologií
České vysoké učení technické v Praze Fakulta informačních technologií Katedra teoretické informatiky Evropský sociální fond Praha & EU: Investujeme do vaší budoucnosti MI-MVI Methods of Computational Intelligence(2010/2011)
More informationBreaking RSA with Quantum Computing
University of Ljubljana Faculty of Mathematics and Physics Breaking RSA with Quantum Computing Blaž Bačnik Under mentorship of dr. Marko Žnidarič Ljubljana, 26 May 2008 Abstract We take a look at RSA encryption
More informationThe long road of Quantum Computing
The long road of Quantum Computing Thierry Ferrus Hitachi Cambridge Laboratory Tutorial Outline Evolution of thoughts : from corpuscles to quantum world Quantum Information and Quantum Computers Various
More informationQuantum Computing: Foundations to Frontier
Quantum Computing: Foundations to Frontier CSC2451HF/MAT1751HF Lecture 1 Welcome! Bird s eye view Administrivia 10 minute break Quantum information basics Welcome! Bird s eye view Administrivia 10 minute
More informationQuantum Computing. Part I. Thorsten Altenkirch
Quantum Computing Part I Thorsten Altenkirch Is Computation universal? Alonzo Church - calculus Alan Turing Turing machines computable functions The Church-Turing thesis All computational formalisms define
More informationIntroduction to Quantum Computing for Folks
Introduction to Quantum Computing for Folks Joint Advanced Student School 2009 Ing. Javier Enciso encisomo@in.tum.de Technische Universität München April 2, 2009 Table of Contents 1 Introduction 2 Quantum
More informationLattice-Based Cryptography
Liljana Babinkostova Department of Mathematics Computing Colloquium Series Detecting Sensor-hijack Attacks in Wearable Medical Systems Krishna Venkatasubramanian Worcester Polytechnic Institute Quantum
More informationQuantum Computers. Todd A. Brun Communication Sciences Institute USC
Quantum Computers Todd A. Brun Communication Sciences Institute USC Quantum computers are in the news Quantum computers represent a new paradigm for computing devices: computers whose components are individual
More informationA central problem in cryptography: the key distribution problem.
Scientific American 314, 48-55 (2016) A central problem in cryptography: the key distribution problem. Mathematics solution: public key cryptography. Public-key cryptography relies on the computational
More informationQuantum information and the future of physics
Quantum information and the future of physics Q Quantum Computer John Preskill NSF workshop 15 March 2007 The Quantum Century Though quantum theory is over 100 years old, there are profound aspects of
More informationQuantum Optics and Quantum Informatics 7.5hp (FKA173) Introductory Lecture
Quantum Optics and Quantum Informatics 7.5hp (FKA173) Introductory Lecture Fasrummet (A820) 09:00 Oct. 31-2017 Lectures: Jonas Bylander (jonas.bylander@chalmers.se) and Thilo Bauch (bauch@chalmers.se)
More informationDevice-Independent Quantum Information Processing
Device-Independent Quantum Information Processing Antonio Acín ICREA Professor at ICFO-Institut de Ciencies Fotoniques, Barcelona Chist-Era kick-off seminar, March 2012, Warsaw, Poland Quantum Information
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 informationQuantum Computation: From Quantum Teleportation to the Shor s Algorithm
Quantum Computation: From Quantum Teleportation to the Shor s Algorithm J. J. Ruiz-Lorenzo Dep. Física, Universidad de Extremadura Instituto de Computación Científica Avanzada de Extremadura (ICCAEx) http://www.eweb.unex.es/eweb/fisteor/juan
More informationCS257 Discrete Quantum Computation
CS57 Discrete Quantum Computation John E Savage April 30, 007 Lect 11 Quantum Computing c John E Savage Classical Computation State is a vector of reals; e.g. Booleans, positions, velocities, or momenta.
More information5th March Unconditional Security of Quantum Key Distribution With Practical Devices. Hermen Jan Hupkes
5th March 2004 Unconditional Security of Quantum Key Distribution With Practical Devices Hermen Jan Hupkes The setting Alice wants to send a message to Bob. Channel is dangerous and vulnerable to attack.
More informationQuantum information. Vlatko Vedral INSTANT
Quantum information Vlatko Vedral INSTANT EXPERT 33 Quantum economy In recent decades, we have done very well in cramming ever more transistors into classical computer chips. But the density of heat generated
More informationThe Deutsch-Josza Algorithm in NMR
December 20, 2010 Matteo Biondi, Thomas Hasler Introduction Algorithm presented in 1992 by Deutsch and Josza First implementation in 1998 on NMR system: - Jones, JA; Mosca M; et al. of a quantum algorithm
More informationQuantum Cryptography. Areas for Discussion. Quantum Cryptography. Photons. Photons. Photons. MSc Distributed Systems and Security
Areas for Discussion Joseph Spring Department of Computer Science MSc Distributed Systems and Security Introduction Photons Quantum Key Distribution Protocols BB84 A 4 state QKD Protocol B9 A state QKD
More informationQuantum Computation and Communication
Tom Lake tswsl1989@sucs.org 16/02/2012 quan tum me chan ics: The branch of mechanics that deals with the mathematical description of the motion and interaction of subatomic particles - OED quan tum me
More informationThe Reality of Quantum Computing
The Reality of Quantum Computing Now and in the Future @qant Christoph Lameter Jump Trading LLC Great Expectations But the current state: Wild West Funding: Governments see a chance to win
More informationWhat are we talking about when we talk about post-quantum cryptography?
PQC Asia Forum Seoul, 2016 What are we talking about when we talk about post-quantum cryptography? Fang Song Portland State University PQC Asia Forum Seoul, 2016 A personal view on postquantum cryptography
More informationDefinition: For a positive integer n, if 0<a<n and gcd(a,n)=1, a is relatively prime to n. Ahmet Burak Can Hacettepe University
Number Theory, Public Key Cryptography, RSA Ahmet Burak Can Hacettepe University abc@hacettepe.edu.tr The Euler Phi Function For a positive integer n, if 0
More informationQuantum Computers. Peter Shor MIT
Quantum Computers Peter Shor MIT 1 What is the difference between a computer and a physics experiment? 2 One answer: A computer answers mathematical questions. A physics experiment answers physical questions.
More informationQuantum Computers Is the Future Here?
Quantum Computers Is the Future Here? Tal Mor CS.Technion ISCQI Feb. 2016 128?? [ 2011 ; sold to LM ] D-Wave Two :512?? [ 2013 ; sold to NASA + Google ] D-Wave Three: 1024?? [ 2015 ; also installed at
More informationQuantum Information Transfer and Processing Miloslav Dušek
Quantum Information Transfer and Processing Miloslav Dušek Department of Optics, Faculty of Science Palacký University, Olomouc Quantum theory Quantum theory At the beginning of 20 th century about the
More informationBasics on quantum information
Basics on quantum information Mika Hirvensalo Department of Mathematics and Statistics University of Turku mikhirve@utu.fi Thessaloniki, May 2016 Mika Hirvensalo Basics on quantum information 1 of 52 Brief
More informationTalk by Johannes Vrana
Decoherence and Quantum Error Correction Talk by Johannes Vrana Seminar on Quantum Computing - WS 2002/2003 Page 1 Content I Introduction...3 II Decoherence and Errors...4 1. Decoherence...4 2. Errors...6
More information+ = OTP + QKD = QC. ψ = a. OTP One-Time Pad QKD Quantum Key Distribution QC Quantum Cryptography. θ = 135 o state 1
Quantum Cryptography Quantum Cryptography Presented by: Shubhra Mittal Instructor: Dr. Stefan Robila Intranet & Internet Security (CMPT-585-) Fall 28 Montclair State University, New Jersey Introduction
More informationQuantum Computing. The Future of Advanced (Secure) Computing. Dr. Eric Dauler. MIT Lincoln Laboratory 5 March 2018
The Future of Advanced (Secure) Computing Quantum Computing This material is based upon work supported by the Assistant Secretary of Defense for Research and Engineering and the Office of the Director
More informationBasics on quantum information
Basics on quantum information Mika Hirvensalo Department of Mathematics and Statistics University of Turku mikhirve@utu.fi Thessaloniki, May 2014 Mika Hirvensalo Basics on quantum information 1 of 49 Brief
More informationPromise of Quantum Computation
Quantum Computation, and Epilog: The Future of Computing 1 Promise of Quantum Computation Classical computers have their limitations: Factoring large numbers takes exponential time. No faster algorithm
More informationQLang: Qubit Language
QLang: Qubit Language Christopher Campbell Clément Canonne Sankalpa Khadka Winnie Narang Jonathan Wong September 24, 24 Introduction In 965, Gordon Moore predicted that the number of transistors in integrated
More informationA Matlab Realization of Shor s Quantum Factoring Algorithm
1 A Matlab Realization of Shor s Quantum Factoring Algorithm S. Jha, P. Chatterjee, A.Falor and M. Chakraborty, Member IEEE Department of Information Technology Institute of Engineering & Management Kolkata,
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 informationQuantum theory has opened to us the microscopic world of particles, atoms and photons..and has given us the keys of modern technologies
Power and strangeness of the quantum Quantum theory has opened to us the microscopic world of particles, atoms and photons.and has given us the keys of modern technologies This is a theory whose logics
More informationAn Introduction. Dr Nick Papanikolaou. Seminar on The Future of Cryptography The British Computer Society 17 September 2009
An Dr Nick Papanikolaou Research Fellow, e-security Group International Digital Laboratory University of Warwick http://go.warwick.ac.uk/nikos Seminar on The Future of Cryptography The British Computer
More informationLectures on Fault-Tolerant Quantum Computation
Lectures on Fault-Tolerant Quantum Computation B.M. Terhal, IBM Research I. Descriptions of Noise and Quantum States II. Quantum Coding and Error-Correction III. Fault-Tolerant Error-Correction. Surface
More informationLecture 19: Public-key Cryptography (Diffie-Hellman Key Exchange & ElGamal Encryption) Public-key Cryptography
Lecture 19: (Diffie-Hellman Key Exchange & ElGamal Encryption) Recall In private-key cryptography the secret-key sk is always established ahead of time The secrecy of the private-key cryptography relies
More informationIntroduction to Quantum Computing
Introduction to Quantum Computing Petros Wallden Lecture 3: Basic Quantum Mechanics 26th September 2016 School of Informatics, University of Edinburgh Resources 1. Quantum Computation and Quantum Information
More informationQuantum Communication. Serge Massar Université Libre de Bruxelles
Quantum Communication Serge Massar Université Libre de Bruxelles Plan Why Quantum Communication? Prepare and Measure schemes QKD Using Entanglement Teleportation Communication Complexity And now what?
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 Computer. Jaewan Kim School of Computational Sciences Korea Institute for Advanced Study
Quantum Computer Jaewan Kim jaewan@kias.re.kr School of Computational Sciences Korea Institute for Advanced Study KIAS (Korea Institute for Advanced Study) Established in 1996 Located in Seoul, Korea Pure
More informationFactoring on a Quantum Computer
Factoring on a Quantum Computer The Essence Shor s Algorithm Wolfgang Polak wp@pocs.com Thanks to: Eleanor Rieffel Fuji Xerox Palo Alto Laboratory Wolfgang Polak San Jose State University, 4-14-010 - p.
More informationHOMOMORPHIC ENCRYPTION AND LATTICE BASED CRYPTOGRAPHY 1 / 51
HOMOMORPHIC ENCRYPTION AND LATTICE BASED CRYPTOGRAPHY Abderrahmane Nitaj Laboratoire de Mathe matiques Nicolas Oresme Universite de Caen Normandie, France Nouakchott, February 15-26, 2016 Abderrahmane
More informationQuantum Information. and Communication
Quantum Information 2015.7.22 and Communication quantum mechanics uncertainty principle wave function superposition state information/communication cryptography signal processing Quantum Information/Communication
More information6.080/6.089 GITCS May 6-8, Lecture 22/23. α 0 + β 1. α 2 + β 2 = 1
6.080/6.089 GITCS May 6-8, 2008 Lecturer: Scott Aaronson Lecture 22/23 Scribe: Chris Granade 1 Quantum Mechanics 1.1 Quantum states of n qubits If you have an object that can be in two perfectly distinguishable
More informationQuantum Information Processing
Quantum Information Processing Harry Buhrman CWI & University of Amsterdam Physics and Computing Computing is physical Miniaturization quantum effects Quantum Computers 1) Enables continuing miniaturization
More informationThe Elliptic Curve in https
The Elliptic Curve in https Marco Streng Universiteit Leiden 25 November 2014 Marco Streng (Universiteit Leiden) The Elliptic Curve in https 25-11-2014 1 The s in https:// HyperText Transfer Protocol
More informationQuantum Computing: From Science to Application Dr. Andreas Fuhrer Quantum technology, IBM Research - Zurich
Quantum Computing: From Science to Application Dr. Andreas Fuhrer Quantum technology, IBM Research - Zurich IBM Research - Zurich Established in 1956 Focus: science & technology, systems research, computer
More informationD.5 Quantum error correction
D. QUANTUM ALGORITHMS 157 Figure III.34: E ects of decoherence on a qubit. On the left is a qubit yi that is mostly isoloated from its environment i. Ontheright,aweakinteraction between the qubit and the
More information