This document provides an introduction to quantum computing and quantum information theory. It discusses how technological limitations of conventional computing motivate the development of quantum computing. The key laws of quantum mechanics that enable quantum computing are introduced, including superposition, entanglement, and the Heisenberg uncertainty principle. The document explains how quantum bits (qubits) can represent more than the two states of classical bits, and how quantum gates operate on qubits. It provides examples of one-qubit gates like the Hadamard gate. The potential for quantum computers to massively scale parallelism through quantum effects like entanglement is also summarized.
What is Quantum Computing
What is Quantum bits (Qubit)
What is Reversible Logic gates and Logic Circuits
What is Quantum Neuron (Quron)
What are the methods of implementing ANN using Quantum computing
Quantum computing - A Compilation of ConceptsGokul Alex
Excerpts of the Talk Delivered at the 'Bio-Inspired Computing' Workshop conducted by Department of Computational Biology and Bioinformatics, University of Kerala.
A Shore Introduction to Quantum Computer and the computation of ( Quantum Mechanics),
Nowadays we work on classical computer that work with bits which is either 0s or 1s, but Quantum Computer work with qubits which is either 0s or 1s or 0 and 1 in the same time.
The Extraordinary World of Quantum ComputingTim Ellison
Originally presented at QCon London - 6 March-2018.
The classical computer on your lap or housed in your data centre manipulates data represented with a binary encoding -- quantum computers are different. They use atomic level mechanics to represent multiple data states simultaneously, leading to a phenomenal exponential increase in the representable state of data, and new solutions to problems that are infeasible using today's classical computers. This session assumes no prior knowledge of quantum technology and presents a introduction to the field of quantum computing, including an introduction to the quantum bit, the types of problem suited to quantum computing, a demo of running algorithms on IBM's quantum machines, and a peek into the future of quantum computers.
Lecture of Professor Amlan Chakrabarti, University of Calcutta on : Fundamentals of Quantum Computing, presented at the Quantum Conference organized by the Dept. of IT, Govt. of West Bengal, India on 12th October 2018
What is Quantum Computing
What is Quantum bits (Qubit)
What is Reversible Logic gates and Logic Circuits
What is Quantum Neuron (Quron)
What are the methods of implementing ANN using Quantum computing
Quantum computing - A Compilation of ConceptsGokul Alex
Excerpts of the Talk Delivered at the 'Bio-Inspired Computing' Workshop conducted by Department of Computational Biology and Bioinformatics, University of Kerala.
A Shore Introduction to Quantum Computer and the computation of ( Quantum Mechanics),
Nowadays we work on classical computer that work with bits which is either 0s or 1s, but Quantum Computer work with qubits which is either 0s or 1s or 0 and 1 in the same time.
The Extraordinary World of Quantum ComputingTim Ellison
Originally presented at QCon London - 6 March-2018.
The classical computer on your lap or housed in your data centre manipulates data represented with a binary encoding -- quantum computers are different. They use atomic level mechanics to represent multiple data states simultaneously, leading to a phenomenal exponential increase in the representable state of data, and new solutions to problems that are infeasible using today's classical computers. This session assumes no prior knowledge of quantum technology and presents a introduction to the field of quantum computing, including an introduction to the quantum bit, the types of problem suited to quantum computing, a demo of running algorithms on IBM's quantum machines, and a peek into the future of quantum computers.
Lecture of Professor Amlan Chakrabarti, University of Calcutta on : Fundamentals of Quantum Computing, presented at the Quantum Conference organized by the Dept. of IT, Govt. of West Bengal, India on 12th October 2018
In the last decades, a new model of computation based on quantum mechanics has gained attention in the computer science community. We give an introduction to this model starting from the basics, with no prerequisites. Then, with the help of some simple examples, we see why quantum computers outperform standard ones in certain tasks. We then move to the topic of quantum entanglement and show how sharing quantum information can create a strong provable correlation among distant parties. With this basic understanding of quantum computation and quantum entanglement, we can already illustrate two interesting cryptographic protocols: quantum key distribution and position verification. Both perform classically impossible tasks: the first allows to detect an intruder intercepting a secret communication, while the second allows certifying somebody's GPS location.
Quantum computers are incredibly powerful machines that take a new approach to processing information. Built on the principles of quantum mechanics, they exploit complex and fascinating laws of nature that are always there, but usually remain hidden from view. By harnessing such natural behavior, quantum computing can run new types of algorithms to process information more holistically. They may one day lead to revolutionary breakthroughs in materials and drug discovery, the optimization of complex manmade systems, and artificial intelligence. We expect them to open doors that we once thought would remain locked indefinitely. Acquaint yourself with the strange and exciting world of quantum computing.
An introduction to quantum computing, its history and evolution from concept to commercial quantum computer, and an overview of relevant use in biomedical informatics and medice
In this deck from the HPC User Forum in Tucson, John Martinis from Google presents: Quantum Computing and Quantum Supremacy.
Google recently announced that the company has developed a new 72-Qbit quantum processor called Bristlecone.
"The goal of the Google Quantum AI lab is to build a quantum computer that can be used to solve real-world problems. Our strategy is to explore near-term applications using systems that are forward compatible to a large-scale universal error-corrected quantum computer. In order for a quantum processor to be able to run algorithms beyond the scope of classical simulations, it requires not only a large number of qubits. Crucially, the processor must also have low error rates on readout and logical operations, such as single and two-qubit gates."
Watch the video: https://wp.me/p3RLHQ-ipZ
Learn more: https://research.googleblog.com/2018/03/a-preview-of-bristlecone-googles-new.html
and
htttp://hpcuserforum.com
La présentation introduira les principes de fonctionnement des ordinateurs quantiques, la conception de portes logiques et d'algorithmes quantiques simples puis leur exécution sur une véritable puce quantique optoélectronique de l'université de Bristol. Les premiers ordinateurs quantiques sont donc une réalité. Plusieurs attaques et leurs impacts sur les cryptosystèmes symétriques et asymétriques actuels sont analysés et différentes alternatives sont proposées pour être utilisées dans le futur. Les participants sont encouragés à participer avec leur ordinateur portable pour mettre en pratique les exemples abordés.
Quantum computing is an emerging new theory of computation based on the principles of quantum mechanics. It is the basis for a fundamentally new information processing model that is garnering increasing attention in the media and from commercial information technology companies. In certain computing tasks, it can theoretically arrive at a solution more efficiently than classical computers. In this session, we explore the basic principles behind quantum computing, including qubit superposition and entanglement -- the basis for quantum parallelism. We explore quantum logic gates as an abstracted representation of underlying hardware and discuss a simple quantum gate circuit that demonstrates parallelism. We also review the current state of the technology and what has been demonstrated compared to what is theoretically predicted. Current trends in the quantum computing industry will be presented along with proposed possible uses in biomedical informatics.
Quantum Computing - A History in the Making Gokul Alex
Please find my key note lecture on Quantum Computing presented at the RedTeam Security Summit 2019 in North Kerala at Malabar in Calicut City. This session is a survey on the history of Quantum Computing from early 1960's to the recent Quantum Supremacy experiment done by Google along with University of Santa Barbara. It captures the history from conjugate coding to sycamore processor succinctly. It also captures the essence of post quantum cryptography and quantum algorithms.
In the last decades, a new model of computation based on quantum mechanics has gained attention in the computer science community. We give an introduction to this model starting from the basics, with no prerequisites. Then, with the help of some simple examples, we see why quantum computers outperform standard ones in certain tasks. We then move to the topic of quantum entanglement and show how sharing quantum information can create a strong provable correlation among distant parties. With this basic understanding of quantum computation and quantum entanglement, we can already illustrate two interesting cryptographic protocols: quantum key distribution and position verification. Both perform classically impossible tasks: the first allows to detect an intruder intercepting a secret communication, while the second allows certifying somebody's GPS location.
Quantum computers are incredibly powerful machines that take a new approach to processing information. Built on the principles of quantum mechanics, they exploit complex and fascinating laws of nature that are always there, but usually remain hidden from view. By harnessing such natural behavior, quantum computing can run new types of algorithms to process information more holistically. They may one day lead to revolutionary breakthroughs in materials and drug discovery, the optimization of complex manmade systems, and artificial intelligence. We expect them to open doors that we once thought would remain locked indefinitely. Acquaint yourself with the strange and exciting world of quantum computing.
An introduction to quantum computing, its history and evolution from concept to commercial quantum computer, and an overview of relevant use in biomedical informatics and medice
In this deck from the HPC User Forum in Tucson, John Martinis from Google presents: Quantum Computing and Quantum Supremacy.
Google recently announced that the company has developed a new 72-Qbit quantum processor called Bristlecone.
"The goal of the Google Quantum AI lab is to build a quantum computer that can be used to solve real-world problems. Our strategy is to explore near-term applications using systems that are forward compatible to a large-scale universal error-corrected quantum computer. In order for a quantum processor to be able to run algorithms beyond the scope of classical simulations, it requires not only a large number of qubits. Crucially, the processor must also have low error rates on readout and logical operations, such as single and two-qubit gates."
Watch the video: https://wp.me/p3RLHQ-ipZ
Learn more: https://research.googleblog.com/2018/03/a-preview-of-bristlecone-googles-new.html
and
htttp://hpcuserforum.com
La présentation introduira les principes de fonctionnement des ordinateurs quantiques, la conception de portes logiques et d'algorithmes quantiques simples puis leur exécution sur une véritable puce quantique optoélectronique de l'université de Bristol. Les premiers ordinateurs quantiques sont donc une réalité. Plusieurs attaques et leurs impacts sur les cryptosystèmes symétriques et asymétriques actuels sont analysés et différentes alternatives sont proposées pour être utilisées dans le futur. Les participants sont encouragés à participer avec leur ordinateur portable pour mettre en pratique les exemples abordés.
Quantum computing is an emerging new theory of computation based on the principles of quantum mechanics. It is the basis for a fundamentally new information processing model that is garnering increasing attention in the media and from commercial information technology companies. In certain computing tasks, it can theoretically arrive at a solution more efficiently than classical computers. In this session, we explore the basic principles behind quantum computing, including qubit superposition and entanglement -- the basis for quantum parallelism. We explore quantum logic gates as an abstracted representation of underlying hardware and discuss a simple quantum gate circuit that demonstrates parallelism. We also review the current state of the technology and what has been demonstrated compared to what is theoretically predicted. Current trends in the quantum computing industry will be presented along with proposed possible uses in biomedical informatics.
Quantum Computing - A History in the Making Gokul Alex
Please find my key note lecture on Quantum Computing presented at the RedTeam Security Summit 2019 in North Kerala at Malabar in Calicut City. This session is a survey on the history of Quantum Computing from early 1960's to the recent Quantum Supremacy experiment done by Google along with University of Santa Barbara. It captures the history from conjugate coding to sycamore processor succinctly. It also captures the essence of post quantum cryptography and quantum algorithms.
This is a seminar on Quantum Computing given on 9th march 2017 at CIME, Bhubaneswar by me(2nd year MCA).
Video at - https://youtu.be/vguxg0RYg7M
PDF at - http://www.slideshare.net/deepankarsandhibigraha/quantum-computing-73031375
Implementation of Stopwatch using QCA based Carry Select AdderIJTET Journal
As transistor size reduces and more of them can be accommodated in a single die, thus rising chip computational capabilities. However, transistors cannot get smaller than their current size. The quantum-dot cellular automata (QCA) approach represents one of the possible solutions in overcoming this physical limit. The design of adders on quantum-dot cellular automata has been of recent interest. This paper presents an efficient QCA design for the Carry Select Adder (CSA). The QCA based CSA has better performance in terms of area and delay than the existing RCA. The application of this QCA based Carry Select Adder in stopwatch also designed.
Study of Logic Gates Using Quantum Cellular Automataidescitation
The power consumption of MOS technology device
can be reduced by scaling the devices. The technology also
tries to improve speed by working on the already existing
technology. The need for new technology is fast approaching
as Moore’s law cannot hold good for next few years. For the
same purpose we should turn to quantum logic and quantum
cells. Quantum cellular automaton is one such technology.
Though the technology is in its primitive stage, many people
are working in this field. After a breakthrough in the physical
implementation of the basic quantum cell the new technology
is mainly focused on implementing digital designs. This article
is trying to review and implement the basic gates in quantum
cellular automata. Implementation is done in QCA Designer
provided by University of British Columbia.
All optical XOR, CNOT gates with initial insight for quantum computation usin...omarshehab
The design for an all optical XOR gate is proposed. The basic idea is to split the input beams and let them cancel or strengthen each other selectively or flip the encoded information based on their polarization properties. The information is encoded in terms of polarization of the beam. Polarization of a light beam is well understood hence the design should be feasible to implement. The truth table of the optical circuit is worked out and compared with the expected truth table. Then it is demonstrated that the design complies with the linear behavior of the XOR function. In the next section, based on a similar idea, the design of an all optical CNOT gate is proposed. The truth table for the gate is verified. Then, it is discussed how this approach can be used for Linear Optics Quantum Computation (LOQC). It is shown that with a Hadamard gate and a rotation gate, the CNOT gate makes up a universal set of quantum gates based on linear optics. This novel approach requires no additional power supply, extra input beam or ancilla photon to operate. It also doesn\'t require the expensive and complex single photon source and detector. Only narrowband laser sources are required to operate these gates.
QCA’s home base is comparative sociology/comparative politics, where there is
a strong tradition of case-oriented work alongside an extensive and growing body
of quantitative cross-national research.
QCA is a method that bridges qualitative and quantitative analysis
Quantum computation uses the quantistic physics principles to store and to process information on computational devices.
Presentation for a workshop during the event "SUPER, Salone delle Startup e Imprese Innovative"
This is a seminar on Quantum Computing given on 9th march 2017 at CIME, Bhubaneswar by me(2nd year MCA).
Video at - https://youtu.be/vguxg0RYg7M
ppt at - http://www.slideshare.net/deepankarsandhibigraha/quantum-computing-73031661
What is a thing of the IoT? Aspiration of things narrated by a 'Thing Interpr...Pratik Desai, PhD
The vision of connecting every networked computer with each other created the Internet we use today from a research project, which got possible because of the open Internet standard and a tangible architecture. In the chaos of buzzwords and marketing campaigns, the Interoperating between connected devices, Things, has been compromise, suffocating the growth of the Internet of Things domain. The interoperability between wearable devices and other IoT components can lead to development of high intelligence applications enabling non-hardware entities to be part of the wearable domain. We propose a semantic web assisted IoT architecture, which implements standard data models described in relationship graphs. The graph based data structure enables reasoning and intelligence at the machine level laying down road for innovations.
Quantum entanglement is one of the most intriguing and counterintuitive pheno...NishaJaiswal34
Quantum entanglement is one of the most intriguing and counterintuitive phenomena in the realm of quantum mechanics. It describes a peculiar correlation that can exist between particles, where the properties of one particle instantly affect the properties of another, regardless of the distance separating them.
At the heart of quantum entanglement is the principle of superposition, which states that particles can exist in multiple states simultaneously until measured or observed. When two or more particles become entangled, their quantum states become intertwined in such a way that the state of one particle is directly linked to the state of the other(s).
One of the remarkable features of quantum entanglement is that the entangled particles can be separated by vast distances, yet changes to one particle's state will instantaneously influence the state of the other particle, seemingly defying the constraints of space and time. This phenomenon famously led Albert Einstein to refer to it as "spooky action at a distance," as it challenges our classical understanding of causality and locality.
a ppt on based on quantum computing and in very short manner and all the basic areas are covered
and Logical gates are also included
and observation and conclusion also
this will lead you to get a brief knowledge about quantum computers and its explanation
The second quantum revolution: the world beyond binary 0 and 1Bruno Fedrici, PhD
Our active application of quantum
mechanics has previously been constrained by our
ability to engineer and control systems at the small
scales where quantum effects predominate. This has
now changed. Scientists have reached first base on a
set of enabling technologies that allow us to
routinely manipulate atoms of matter and photons of
light at individual level. This has unlocked our ability
to create a new generation of devices that deliver
unique capabilities directly tied to properties of quantum mechanics such as superposition and entanglement.
Jack Tuszynski From Quantum Physics to Quantum Biology in 100 Years. How long...Kim Solez ,
Jack Tuszynski presents "From Quantum Physics to Quantum Biology in 100 Years. How long to Quantum Medicine?" March 17 and 22, 2016 University of Alberta, Edmonton, Canada.
Quantum computing is the computing which uses the laws of quantum mechanics to process information. Quantum computer works on qubits, which stands for "Quantum Bits".
With quantum computers, factoring of prime numbers are possible.
Quantum computers is a machine that performs calculations based on the laws of quantum mechanics which is the behaviour of particles at the subatomic level.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
2. Contents
I.
Computing and the Laws of Physics
II. A Happy Marriage; Quantum Mechanics &
Computers
III. Qubits and Quantum Gates
IV. Quantum Parallelism
V. Summary
3. Technological limits
For the past two decades we have enjoyed Gordon Moore’s
law. But all good things may come to an end…
We are limited in our ability to increase
the density and
the speed of a computing engine.
Reliability will also be affected
to increase the speed we need increasingly smaller circuits (light
needs 1 ns to travel 30 cm in vacuum)
smaller circuits systems consisting only of a few particles subject
to Heissenberg uncertainty
4. Power dissipation, circuit density, and speed
In 1992 Ralph Merkle from Xerox PARC calculated that a 1
GHz computer operating at room temperature, with 1018
gates packed in a volume of about 1 cm3 would dissipate 3
MW of power.
A small city with 1,000 homes each using 3 KW would require the
same amount of power;
A 500 MW nuclear reactor could only power some 166 such
circuits.
5. Talking about the heat…
The heat produced by a super dense computing engine is
proportional with the number of elementary computing circuits,
thus, with the volume of the engine. The heat dissipated grows as
the cube of the radius of the device.
To prevent the destruction of the engine we have to remove the
heat through a surface surrounding the device. Henceforth, our
ability to remove heat increases as the square of the radius while
the amount of heat increases with the cube of the size of the
computing engine.
6. Contents
I.
Computing and the Laws of Physics
II. A Happy Marriage; Quantum Mechanics &
Computers
III. Qubits and Quantum Gates
IV. Quantum Parallelism
V. Summary
7. A happy marriage…
The two greatest discoveries of the 20-th century
quantum mechanics
stored program computers
produced quantum computing and quantum information
theory
8. Quantum; Quantum mechanics
Quantum is a Latin word meaning some quantity. In physics it is
used with the same meaning as the word discrete in mathematics,
i.e., some quantity or variable that can take only sharply defined
values as opposed to a continuously varying quantity. The
concepts continuum and continuous are known from geometry
and calculus
smallest possible discrete unit of any physical
property
Quantum mechanics is a mathematical model of the physical
world
9. Heissenberg uncertainty principle
Heisenberg uncertainty principle says we cannot determine both
the position and the momentum of a quantum particle with
arbitrary precision.
In his Nobel prize lecture on December 11, 1954 Max Born says
about this fundamental principle of Quantum Mechanics : ``... It
shows that not only the determinism of classical physics must be
abandoned, but also the naive concept of reality which looked
upon atomic particles as if they were very small grains of sand.
At every instant a grain of sand has a definite position and
velocity. This is not the case with an electron. If the position is
determined with increasing accuracy, the possibility of
ascertaining its velocity becomes less and vice versa.''
10. A revolutionary approach to computing and
communication
We need to consider a revolutionary rather than an
evolutionary approach to computing.
Quantum theory does not play only a supporting role by
prescribing the limitations of physical systems used for
computing and communication.
Quantum properties such as
uncertainty,
interference, and
entanglement
form the foundation of a new brand of theory, the quantum
information theory where computational and
communication processes rest upon fundamental physics.
12. A mathematical model to describe the state of a
quantum system
ψ = α 0 0 + α1 1
| α 0 , α1 |
are complex numbers
| α 0 | + | α1 | = 1
2
2
13. Superposition and uncertainty
In this model a state
ψ = α 0 0 + α1 1
is a superposition of two basis states, “0” and “1”
This state is unknown before we make a measurement.
After we perform a measurement the system is no longer in an
uncertain state but it is in one of the two basis states.
2 is the probability of observing the outcome “1”
|α0 |
2 is the probability of observing the outcome “0”
|α |
1
| α 0 |2 + | α 1 |2 = 1
14. The superposition probability rule
If an event may occur in two or more indistinguishable ways then
the probability amplitude of the event is the sum of the probability
amplitudes of each case considered separately (sometimes known
as Feynmann rule).
15. Quantum computers
In quantum systems the amount of parallelism increases
exponentially with the size of the system, thus with the
number of qubits. This means that the price to pay for an
exponential increase in the power of a quantum
computer is a linear increase in the amount of matter
and space needed to build the larger quantum computing
engine.
A quantum computer will enable us to solve problems
with a very large state space.
16. Contents
I.
Computing and the Laws of Physics
II. A Happy Marriage; Quantum Mechanics &
Computers
III. Qubits and Quantum Gates
IV. Quantum Parallelism
V. Summary
17. A bit versus a qubit
A bit
Can be in two distinct states, 0 and 1
A measurement does not affect the state
A qubit
= 0 0 + 1
ψ
can be in state
α
α1
| 0〉 or in state| 1〉 or in any other state that is a
linear combination of the basis state
When we measure the qubit we find it
in state
in state
| 0〉 with probability
| 1〉with probability
| α0 |2
| α1 |2
20. The Boch sphere representation of one
qubit
A qubit in a superposition state is represented as a vector
connecting the center of the Bloch sphere with a point on its
periphery.
The two probability amplitudes can be expressed using Euler
angles.
21.
22.
23. Two qubits
Represented as vectors in a 2-dimensional Hilbert space
with four basis vectors
00 , 01 , 10 , 11
When we measure a pair of qubits we decide that the
system it is in one of four states
00 , 01 , 10 , 11
with probabilities
| α 00 | , | α 01 | , | α10 | , | α11 |
2
2
2
2
25. Measuring two qubits
Before a measurement the state of the system consisting of
two qubits is uncertain (it is given by the previous equation
and the corresponding probabilities).
After the measurement the state is certain, it is
00, 01, 10, or 11 like in the case of a classical two bit
system.
26. Measuring two qubits (cont’d)
What if we observe only the first qubit, what conclusions
can we draw?
We expect that the system to be left in an uncertain sate,
because we did not measure the second qubit that can still
be in a continuum of states. The first qubit can be
0 with probability
1 with probability
| α 00 |2 + | α 01 |2
| α10 |2 + | α11 |2
27. Measuring two qubits (cont’d)
Call
ψ
I
0
the post-measurement state when we measure
the first qubit and find it to be 0.
I
Call ψ 1 the post-measurement state when we measure
the first qubit and find it to be 1.
ψ
I
0
=
α 00 00 + α 01 01
| α 00 | + | α 01 |
2
2
ψ
I
1
=
α10 1 0 + α11 11
| α10 | + | α11 |
2
2
28. Measuring two qubits (cont’d)
Call
ψ
II
0
the post-measurement state when we measure
the second qubit and find it to be 0.
II
Call ψ 1 the post-measurement state when we measure
the second qubit and find it to be 1.
ψ 0II =
α 0 0 00 + α10 10
| α 00 | + | α10 |
2
2
ψ
II
1
=
α 01 01 + α11 11
| α 01 | + | α11 |
2
2
29. Bell states - a special state of a pair of
qubits
If
1
α 00 = α11 =
and
2
α 01 = α10 = 0
When we measure the first qubit we get the post
I
I
measurement state
ψ =| 11〉
ψ 0 =| 00〉
1
When we measure the second qubit we get the post
mesutrement state
II
ψ II =| 11〉
ψ 0 =| 00〉
1
30. This is an amazing result!
The two measurements are correlated, once we
measure the first qubit we get exactly the same result as
when we measure the second one.
The two qubits need not be physically constrained to be
at the same location and yet, because of the strong
coupling between them, measurements performed on
the second one allow us to determine the state of the
first.
31. Entanglement
Entanglement is an elegant, almost exact translation of the
German term Verschrankung used by Schrodinger who was
the first to recognize this quantum effect.
An entangled pair is a single quantum system in a
superposition of equally possible states. The entangled state
contains no information about the individual particles, only
that they are in opposite states.
The important property of an entangled pair is that the
measurement of one particle influences the state of the
other particle. Einstein called that “Spooky action at a
distance".
32. The spin
In quantum mechanics the intrinsic angular moment, the
spin, is quantized and the values it may take are multiples of
the rationalized Planck constant.
The spin of an atom or of a particle is characterized by the
spin quantum number s , which may assume integer and halfinteger values. For a given value of s the projection of the
spin on any axis may assume 2s + 1 values ranging from - s
to $ + s by unit steps, in other words the spin is quantized.
33. More about the spin
There are two classes of quantum particles
fermions - spin one-half particles such as the electrons. The
spin quantum numbers of fermions can be
s=+1/2 and
s=-1/2
bosons - spin one particles. The spin quantum numbers of
bosons can be
s=+1,
s=0, and
s=-1
34. The spin of the electron
The electron has spin s = 1 /2 and the spin projection can
assume the values + ½ referred to as spin up, and -1/2 referred
to as spin down.
35. Light and photons
Light is a form of electromagnetic radiation; the wavelength of
the radiation in the visible spectrum varies from red to violet.
Light can be filtered by selectively absorbing some color ranges
and passing through others.
A polarization filter is a partially transparent material that
transmits light of a particular polarization.
36. Photons
Photons differ from the spin 1/2 electrons in two ways:
(1) they are massless and
(2) have spin $1$.
A photon is characterized by its
vector momentum (the vector momentum determines the frequency)
and
polarization.
In the classical theory light is described as having an electric
field which oscillates either vertically, the light is x-polarized,
or horizontally, the light is y-polarized in a plane perpendicular
to the direction of propagation, the z-axis.
The two basis vectors are |h> and |v>
37. Classical gates
Implement Boolean functions.
Are not reversible (invertible). We cannot recover the input
knowing the output.
This means that there is an iretriviable loss of information
38.
39. One qubit gates
Transform an input qubit into an output qubit
Characterized by a 2 x 2 matrix with complex coefficients
41. One qubit gates
I identity gate; leaves a qubit unchanged.
X or NOT gate transposes the components of an input
qubit.
Y gate.
Z gate flips the sign of a qubit.
H the Hadamard gate.
42. One qubit gates
g11
G =
g
21
g12
g 22
g11
G =
g
12
T
*
*
g11 g11 + g 21 g 21
G +G = *
g g + g* g
22 21
12 11
g 21
g 22
*
g11
+
G = *
g
12
g g + g g 22
=I
g g + g g 22
*
11 12
*
12 12
*
21
*
22
*
g 21
*
g 22
44. CNOT a two qubit gate
Two inputs
Control
Target
The control qubit is transferred to the output as is.
The target qubit
Unaltered if the control qubit is 0
Flipped if the control qubit is 1.
49. Final comments on the CNOT gate
CNOT preserves the control qubit (the first and the
second component of the input vector are replicated in
the output vector) and flips the target qubit (the third and
fourth component of the input vector become the fourth
and respectively the third component of the output
vector).
WCNOT = α 0 0 ( β 0 0 + β1 01 ) + α1 1 ( β1 0 + β 0 1 )
The CNOT gate is reversible. The control qubit is
replicated at the output and knowing it we can reconstruct
the target input qubit.
50. Fredkin gate
Three input and three output qubits
One control
Two target
When the control qubit is
0 the target qubits are replicated to the output
1 the target qubits are swapped
51.
52. Toffoli gate
Three input and three output qubits
Two control
One target
When both control qubit
are 1 the target qubit is flipped
otherwise the target qubit is not changed.
53. Toffoli gate is universal. It may
emulate an AND and a NOT gate
57. Contents
I.
Computing and the Laws of Physics
II. A Happy Marriage; Quantum Mechanics &
Computers
III. Qubits and Quantum Gates
IV. Quantum Parallelism
V. Summary
58. A quantum circuit
Given a function f(x) we can construct a reversible quantum
circuit consisting of Fredking gates only, capable of
transforming two qubits as follows
The function f(x) is hardwired in the circuit
59. A quantum circuit (cont’d)
If the second input is zero then the transformation done by
the circuit is
60. A quantum circuit (cont’d)
Now apply the first qubit through a Hadamad gate.
0 +1
2
0
The resulting sate of the circuit is
0 f(
0 +1
)
f (0) + 1 f (1)
2
2
The output state contains information about f(0) and f(1).
61.
62. Quantum parallelism
The output of the quantum circuit contains information about
both f(0) and f(1). This property of quantum circuits is called
quantum parallelism.
Quantum parallelism allows us to construct the entire truth
table of a quantum gate array having 2n entries at once. In a
classical system we can compute the truth table in one time step
with 2n gate arrays running in parallel, or we need 2n time steps
with a single gate array.
We start with n qubits, each in state |0> and we apply a WelshHadamard transformation.
63. Advantages
• Much more powerful
• Faster
• Smaller
• Improvements to science
• Can improve on practical personal electronics
65. Difficulties
• Hard to control quantum particles
• Lots of heat
• Expensive
• Difficult to build
• Not enough is known about quantum mechanics
66. Future Work
• Silicon Quantum Computer
• It may become technology sooner than we expect
• New algorithms and communication
• Maximum exploitation
• Simulate other quantum systems.
67. Contents
I.
Computing and the Laws of Physics
II. A Happy Marriage; Quantum Mechanics &
Computers
III. Qubits and Quantum Gates
IV. Quantum Parallelism
V. Summary
68. Final remarks
A tremendous progress has been made in the area of
quantum computing and quantum information theory
during the past decade. Thousands of research papers, a
few solid reference books, and many popular-science
books have been published in recent years in this area.
The growing interest in quantum computing and
quantum information theory is motivated by the
incredible impact this discipline could have on how we
store, process, and transmit data and knowledge in this
information age.
69. Final remarks (cont’d)
Computer and communication systems using quantum effects
have remarkable properties.
Quantum computers enable efficient simulation of the most complex
physical systems we can envision.
Quantum algorithms allow efficient factoring of large integers with
applications to cryptography.
Quantum search algorithms speedup considerably the process of
identifying patterns in apparently random data.
We can guarantee the security of our quantum communication systems
because eavesdropping on a quantum communication channel can always
be detected.
70. Final remarks (cont’d)
Building a quantum computer faces tremendous
technological and theoretical challenges.
At the same time, we witness a faster rate of progress in
quantum information theory where applications of quantum
cryptography seem ready for commercialization. Recently, a
successful quantum key distribution experiment over a
distance of some 100 km has been announced.