Quantum computing provides an alternative computational model based on quantum mechanics. It utilizes quantum phenomena such as superposition and entanglement to perform computations using quantum logic gates on qubits. This allows quantum computers to potentially solve certain problems exponentially faster than classical computers. However, building large-scale quantum computers remains a challenge. In the meantime, smaller quantum systems are being developed and quantum algorithms are being experimentally tested on these devices. Researchers are also working on methods to efficiently simulate quantum computations on classical computers.
An overview of quantum computing, with its features, capabilities and types of problems it can solve. Also covers some current and future implementations of quantum computing, and a view of the patent landscape.
Quantum computes, Quantum computing, Bits and Qubits/Qbits (Binary bits and binary Quantum bits), Difference in processing between conventional and quantum computers, representation of data using superposition, History of quantum computers, demonstration on how a quantum computer will handle an algorithm, difference between processors.
Quantum Computers New Generation of Computers PART1 by Prof Lili SaghafiProfessor Lili Saghafi
This lecture is intended to introduce the concepts and terminology used in Quantum Computing, to provide an overview of what a Quantum Computer is, and why you would want to program one.
The material here is using very high level concepts and is designed to be accessible to both technical and non-technical audiences.
Some background in physics, mathematics and programming is useful to help understand the concepts presented.
Exploits Quantum Mechanical effects
Built around “Qubits” rather than “bits”
Operates in an extreme environment
Enables quantum algorithms to solve very hard problems
An overview of quantum computing, with its features, capabilities and types of problems it can solve. Also covers some current and future implementations of quantum computing, and a view of the patent landscape.
Quantum computes, Quantum computing, Bits and Qubits/Qbits (Binary bits and binary Quantum bits), Difference in processing between conventional and quantum computers, representation of data using superposition, History of quantum computers, demonstration on how a quantum computer will handle an algorithm, difference between processors.
Quantum Computers New Generation of Computers PART1 by Prof Lili SaghafiProfessor Lili Saghafi
This lecture is intended to introduce the concepts and terminology used in Quantum Computing, to provide an overview of what a Quantum Computer is, and why you would want to program one.
The material here is using very high level concepts and is designed to be accessible to both technical and non-technical audiences.
Some background in physics, mathematics and programming is useful to help understand the concepts presented.
Exploits Quantum Mechanical effects
Built around “Qubits” rather than “bits”
Operates in an extreme environment
Enables quantum algorithms to solve very hard problems
In this deck from the Argonne Training Program on Extreme-Scale Computing 2019, Jonathan Baker from the University of Chicago presents: Quantum Computing: The Why and How.
"Jonathan Baker is a second year Ph.D student at The University of Chicago advised by Fred Chong. He is studying quantum architectures, specifically how to map quantum algorithms more efficiently to near term devices. Additionally, he is interested in multivalued logic and taking advantage of quantum computing’s natural access to higher order states and using these states to make computation more efficient. Prior to beginning his Ph.D., he studied at the University of Notre Dame where he obtained a B.S. of Engineering in computer science and a B.S. in Chemistry and Mathematics."
Watch the video: https://wp.me/p3RLHQ-l1i
Learn more: https://extremecomputingtraining.anl.gov/
Sign up for our insideHPC Newsletter: http://insidehpc.com/newsletter
Quantum computers are designed to perform tasks much more accurately and efficiently than conventional computers, providing developers with a new tool for specific applications.
It is clear in the short-term that quantum computers will not replace their traditional counterparts; instead, they will require classical computers to support their specialized abilities, such as systems optimization.
The Presentation is about the quantum computers and quantum computing describing the quantum phenomena which makes the future computers 1000 times more powerful than the current computers .Also include an Artificial intelligence to tell the difference of computing power between the a conventional computer computing and a quantum computer computing.Quantum computers are still under research and development and not available for common peoples and businesses but major organization are investing highly on these future machine hardware especially U.S is spending billions of Dollars to make it happened for their future security purposes.
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
Quantum Computers new Generation of Computers part 7 by prof lili saghafi Qua...Professor Lili Saghafi
Quantum algorithm
algorithm for factoring, the general number field sieve
Optimization algorithm
deterministic quantum algorithm Deutsch-Jozsa algorithm
Entanglement
Enigma
Quantum Teleportation
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.
-It is a good ppt for a beginner to learn about Quantum
Computer.
-Quantum computer a solution for every present day computing
problems.
-Quantum computer a best solution for AI making
In this deck from the Argonne Training Program on Extreme-Scale Computing 2019, Jonathan Baker from the University of Chicago presents: Quantum Computing: The Why and How.
"Jonathan Baker is a second year Ph.D student at The University of Chicago advised by Fred Chong. He is studying quantum architectures, specifically how to map quantum algorithms more efficiently to near term devices. Additionally, he is interested in multivalued logic and taking advantage of quantum computing’s natural access to higher order states and using these states to make computation more efficient. Prior to beginning his Ph.D., he studied at the University of Notre Dame where he obtained a B.S. of Engineering in computer science and a B.S. in Chemistry and Mathematics."
Watch the video: https://wp.me/p3RLHQ-l1i
Learn more: https://extremecomputingtraining.anl.gov/
Sign up for our insideHPC Newsletter: http://insidehpc.com/newsletter
Quantum computers are designed to perform tasks much more accurately and efficiently than conventional computers, providing developers with a new tool for specific applications.
It is clear in the short-term that quantum computers will not replace their traditional counterparts; instead, they will require classical computers to support their specialized abilities, such as systems optimization.
The Presentation is about the quantum computers and quantum computing describing the quantum phenomena which makes the future computers 1000 times more powerful than the current computers .Also include an Artificial intelligence to tell the difference of computing power between the a conventional computer computing and a quantum computer computing.Quantum computers are still under research and development and not available for common peoples and businesses but major organization are investing highly on these future machine hardware especially U.S is spending billions of Dollars to make it happened for their future security purposes.
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
Quantum Computers new Generation of Computers part 7 by prof lili saghafi Qua...Professor Lili Saghafi
Quantum algorithm
algorithm for factoring, the general number field sieve
Optimization algorithm
deterministic quantum algorithm Deutsch-Jozsa algorithm
Entanglement
Enigma
Quantum Teleportation
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.
-It is a good ppt for a beginner to learn about Quantum
Computer.
-Quantum computer a solution for every present day computing
problems.
-Quantum computer a best solution for AI making
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
This presentation is about quantum computing.which going to be new technological concept for computer operating system.In this subject the research is going on.
As the making of transistors smaller and smaller is continued ,the width of a wire in a computer chip is no
longer than a size of a single atom. These are sizes for which rules of classical physics no longer apply. If the
transistors become much smaller, the strange effects of quantum mechanics will begin to hinder their
performance.
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.
Quantum Computing Quantum Internet 2020_unit 1 By: Prof. Lili SaghafiProfessor Lili Saghafi
The quantum internet is now in a similar stage as the classical internet in the 1960's.
In half a decade the internet gained a huge role in our daily life.
It is not a matter of science anymore: a large community has been and still is working on how we can use the internet in our daily communication.
Bringing a scientific concept from universities to society requires effort from academia and industry and now we see the first footsteps being made.
In 2020 it is aiming to have a small quantum node network, which might become the first quantum internet on earth.
A quantum internet enables us to send qubits from one node to another.
This allows us to create entanglement between any two points.
Entanglement is inherently private.
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 and Blockchain: Facts and Myths Ahmed Banafa
The biggest danger to Blockchain networks from quantum computing is its ability to break traditional encryption . Google sent shock waves around the internet when it was claimed, had built a quantum computer able to solve formerly impossible mathematical calculations–with some fearing crypto industry could be at risk . Google states that its experiment is the first experimental challenge against the extended Church-Turing thesis — also known as computability thesis — which claims that traditional computers can effectively carry out any “reasonable” model of computation
Machine Learning an Exploratory Tool: Key Conceptsachakracu
This was an Online Lecture Describing Key Concepts of Machine Learning Strategies inclusing Neural Networks
National Webinar On Education 4.0 “Ensuring Continuity in Learning and Innovation Through Digitization”
Organized By: Singhad Institute of Management, Pune in Association with Savitribai Phule Pune University
12th June 2020
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
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Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
1. Fundamentals of
Quantum Computing
Prof. Amlan Chakrabarti
Dean Faculty of Engineering and Technology
Director, A.K.Choudhury School of Information Technology
University of Calcutta
email: acakcs@caluniv.ac.in
Quantum Computing Knowledge Workshop, 12th
October 2018: Dept. of IT&E, Govt. of W.B.
2. Realizations are getting smaller (and faster) and reaching a point where
“classical” physics is no longer a sufficient model for the laws of physics
2
3. 3
MooreMoore’s Law’s Law
Courtesy:Quantum Computing and Communications- An Engineering
approach: Sandor Imre and Ferenc Balazs
Moore’s Law: the amount of information storable on a given amount of silicon has
roughly doubled every 18 months. At ~ 10nm. scale quantum effects will upset the
classical progression of Moore’s law..
4. 4
The Need of the ChangeThe Need of the Change
• The closer we are to the few-electron transistor disturbingThe closer we are to the few-electron transistor disturbing
quantum effects will appear more often and strongerquantum effects will appear more often and stronger
• Either we manage to find a new way of miniaturization or weEither we manage to find a new way of miniaturization or we
have to learn how to exploit the difficulties and strangeness ofhave to learn how to exploit the difficulties and strangeness of
quantum mechanicsquantum mechanics
• FeynmanFeynman’s Suggestion:’s Suggestion:
– Instead of regarding computers as devices working under theInstead of regarding computers as devices working under the
laws of classical physics which is common sense , let uslaws of classical physics which is common sense , let us
consider their operation as a special case of a more generalconsider their operation as a special case of a more general
theory governed by quantum mechanics.theory governed by quantum mechanics.
5. 5
Requirement of NewRequirement of New
Computational strategiesComputational strategies
• The way becomes open for the development of quantum hardware
• We have to study quantum mechanics from a computer science point of
view
• These software-related efforts are comprehended by quantum computing
• Top experts have experimentally validated quantum computing algorithms
which overcome the classical competitors
• Once we familiarized ourselves with quantum-faced computing why keep
communications away from the new chances
6. 6
WhyWhy Quantum Computing?Quantum Computing?
• It is,It is, apparentlyapparently, exponentially more time-, exponentially more time-
efficient thanefficient than any possibleany possible classical computingclassical computing
scheme at solvingscheme at solving somesome problems:problems:
– Factoring, discrete logarithms, related problemsFactoring, discrete logarithms, related problems
– Simulating quantum physical systems accuratelySimulating quantum physical systems accurately
• This application was the original motivation for quantumThis application was the original motivation for quantum
computing research first suggested by famous physicistcomputing research first suggested by famous physicist
Richard Feynman in the early 80Richard Feynman in the early 80’s’s
7. Quantum Computation
• A computation model based on quantum principles of
physics
• Ability to enter many parallel “states” and use
interference to recover important information
• Transformations must be unitary
8. Why Is This Helpful?
• Multiple computations simultaneously
• Computing power is exponential
11. Quantum Computing: Thrust Areas
● Quantum Technology
● Quantum Algorithms
● Quantum Modelling and Simulation
● Quantum Communication and Cryptography
11
12. 12
Status of Quantum ComputingStatus of Quantum Computing
• Computing giants Google and Microsoft recently hired a host of leading lights, and
have set challenging goals in QC (Nature news 2017)
• D-Wave 2000Q – the firm’s first 2,000 quantum bit (qubit) quantum computer
came to existence in 2017
– The quantum 2000Q is capable of outperforming “classical servers” by factors
of between 1,000 and 10,000
– IBM established a landmark in computing Friday, announcing a quantum
computer that handles 50 quantum bits, or qubits
– The company is also making a 20-qubit system available through its cloud
computing platform
– Scaling up to hundreds or thousands of quantum bits becomes a possibility
• Quantum Communication
– Teleportation, Entanglement and Zeno Effect has been successfully
implemented and tested
• Quantum Cryptography
– Quantum Key Exchange Protocols, BB84 etc.
• Quantum Machine Learning
– Quantum Clustering, Quantum Random Walk Algorithms for Heuristic Search
13. • Qubit vs. Bit:
Bit (Classical) degree of freedom that can take
only two possible values.
– Qubit
• Quantum observable whose spectrum contains two values
{0,1}.
• Minimal quantum physical system.
• The boolean observable of a qbit system is called a sharp
observable , as it can have only values 0 and 1.
• A qubit can have another observable which has an equal
probability of 1 and 0, individual probabilities summed will
results to unity.
• Qubit in reality:
– Electron spin (up or down)
– Photon polarization (horizontal/vertical)
– Spin of atomic nucleus
– Current in a super conducting loop
– Presence/absence of a particle
13
14. Quantum Phenomenon:
Superposition and Entanglement
● Superposition
○ Superposition is the ability of a quantum system to be in multiple
states at the same time.
● Entanglement
○ Multiple particles are associated in such a way that measurement
of one quantum state of one particle is determined by the
measurement of the state of another particle.
14
15. Computation with QubitsComputation with Qubits
How does the use of qubits affect computation?
Classical Computation
Data unit: bit
x = 0 x = 1
0
1
0
1
Valid states:
x = ‘0’ or ‘1’ |ψ〉 = c1|0〉 + c2|1〉
Quantum Computation
Data unit: qubit
Valid states:
|ψ〉 = |0〉 |ψ〉 = |1〉 |ψ〉 = (|0〉 + |1〉)/√2
=|1〉 =|0〉= ‘1’ = ‘0’
15
17. 17
Quantum Logic NetworksQuantum Logic Networks
• Invented by Deutsch (1989)Invented by Deutsch (1989)
– Analogous to classical Boolean logic networksAnalogous to classical Boolean logic networks
– Generalization of Fredkin-Toffoli reversible logic circuitsGeneralization of Fredkin-Toffoli reversible logic circuits
• System is divided into individual bits, orSystem is divided into individual bits, or qubitsqubits
– 2 orthogonal states of each qubit are designated as the2 orthogonal states of each qubit are designated as the
computationalcomputational basis statesbasis states,, “0” and “1”“0” and “1”
• Quantum logic gates:Quantum logic gates:
– Local unitary transforms that operate on only a few state bitsLocal unitary transforms that operate on only a few state bits
at a timeat a time
• Computation via predetermined sequence of gate applications toComputation via predetermined sequence of gate applications to
selected bitsselected bits
18. 18
Quantum Gates: NOTQuantum Gates: NOT
• All classical input-consuming reversible gates can beAll classical input-consuming reversible gates can be
represented as unitary transformations!represented as unitary transformations!
• E.g.E.g., input-consuming NOT gate (inverter), input-consuming NOT gate (inverter)
in out
in out
in out
0 1
1 0
1
0
10
≡
01
10:N 01
10
=
=
N
N
1
01
1
00
≡
≡
1
0:
0
1:
19. 19
Controlled-NOTControlled-NOT
• A.k.a. CNOT (or input-consuming XOR)A.k.a. CNOT (or input-consuming XOR)
A A’
B B’ = A⊕B
A A’
B
B’ = A⊕B
A B A’ B’
0 0 0 0
0 1 0 1
1 0 1 1
1 1 1 0
11
10
01
00
11100100
≡
0100
1000
0010
0001
:X 1110 =X
Example:
A B A B
Jadavpur University November 28, 2016
20. 20
Toffoli Gate (CCNOT)Toffoli Gate (CCNOT)
A B C A’ B’ C’
0 0 0 0 0 0
0 0 1 0 0 1
0 1 0 0 1 0
0 1 1 0 1 1
1 0 0 1 0 0
1 0 1 1 0 1
1 1 0 1 1 0
1 1 1 1 1 1
(XOR)
A
B
C
A’=A
B’=B
C’ = C⊕AB
A
B’B
C
A’
C’
111
110
101
100
011
010
001
000
111110101100011010001000
≡
01000000
10000000
00100000
00010000
00001000
00000100
00000010
00000001
:X Now, what happens if
the unitary matrix elements
are not always 0 or 1?
21. 21
The Hadamard TransformThe Hadamard Transform
• A randomizingA randomizing “square root of identity” gate.“square root of identity” gate.
• Used frequently in quantum logic networks.Used frequently in quantum logic networks.
1
0
10
−
≡
2
1
2
1
2
1
2
1
:H
==
10
01
2
2
IH
22. 22
• Quantum Logic CircuitsQuantum Logic Circuits
– Circuit behavior is governed explicitly by quantumCircuit behavior is governed explicitly by quantum
mechanicsmechanics
– Signal states are vectors interpreted as a superposition ofSignal states are vectors interpreted as a superposition of
binary “binary “qubitqubit”” vectors with complex-number coefficientsvectors with complex-number coefficients
– Operations are defined by linear algebra over Hilbert SpaceOperations are defined by linear algebra over Hilbert Space
and can be represented by unitary matrices with complexand can be represented by unitary matrices with complex
elementselements
– Severe restrictions exist on copying and measuring signalsSevere restrictions exist on copying and measuring signals
– Many universal gate sets exist but the best types are notMany universal gate sets exist but the best types are not
obviousobvious
Ψ = ci in −1in−1…i0
i = 0
2n
−1
∑
23. 23
• Unitary OperationsUnitary Operations
– Gates and circuits must be reversible (information-Gates and circuits must be reversible (information-
lossless)lossless)
• Number of output signal lines = Number of input signal linesNumber of output signal lines = Number of input signal lines
• The circuit function must be a bijection, implying that outputThe circuit function must be a bijection, implying that output
vectors are a permutation of the input vectorsvectors are a permutation of the input vectors
– Classical logic behavior can be represented byClassical logic behavior can be represented by
permutation matricespermutation matrices
– Non-classical logic behavior can be representedNon-classical logic behavior can be represented
including state sign (phase) and entanglementincluding state sign (phase) and entanglement
Quantum Circuit CharacteristicsQuantum Circuit Characteristics
24. 1/√21/√2
00
1/√21/√2
00
11
00
00
00
N
CNOT
|0〉 + |1〉
|0〉
Example Circuit
√2
______
1/√21/√2
00
1/√21/√2
00
1/√21/√2
00
00
1/√21/√2
00
00
00
11
|0〉 + |1〉
|0〉
√2
______
‘0’
‘0’
or
‘1’
‘1’
or
50% 50%
Separable state:
can be written as
tensor product
|Ψ〉 = |φ〉 ⊗ |χ〉
Entangled state:
cannot be written
as tensor product
|Ψ〉 ≠ |φ〉 ⊗ |χ〉
?
?
24
25. Some Interesting ConsequencesSome Interesting Consequences
No cloning theorem
It is impossible to exactly copy an unknown quantum state
|ψ〉
|0〉
|ψ〉
|ψ〉
Reversibility
Since quantum mechanics is reversible (dynamics are unitary),
quantum computation is reversible.
|00000000〉 |ψφβπµψ〉 |00000000〉
U.U†
= I
25
26. Grover’s Search Algorithm
The best a classical computer
can do on average is N/2 queries.
1 Oracle
No
...
2 Oracle
No
3 Oracle
Yes
Classical computer
Oracle
1+2+3+... No+No+Yes+No+...
Quantum computer
Using Grover’s algorithm, a quantum computer
can find the answer in √N queries!
Superposition over all N possible inputs.
27. Quantum Cryptography
● Provides for secure key exchange over physically
unprotected channels w. a guarantee of detection of any
eavesdropping of the key
● Physically impossible to compromise security (except @
endpoints) barring overthrow of physics!
● Probably secure under known laws
Experimentally verified to work perfectly over >48 km
distances (so far) (Hughes ‘99) via fiber-optic networks
27
28. 28
Typical Implementation MethodTypical Implementation Method
• AnyAny “flying qubit” will do.“flying qubit” will do.
– Most common method uses polarized photons.Most common method uses polarized photons.
(Bennett & Brassard(Bennett & Brassard ‘84)‘84)
θ
Arbitrarychoice
ofbasis:
“0”
“1”
↔+= θθ cossin
Diffraction grating
w. vertical slits
θ + π/4
“0”
“1”
)cos()sin( 44
ππ θθ +++=
Diffraction grating
w. diagonal slits
31. 31
Efficient QC SimulationsEfficient QC Simulations
• Task: Simulate anTask: Simulate an nn-qubit quantum computer.-qubit quantum computer.
• Maximally stupid approach:Maximally stupid approach:
– Store a 2Store a 2nn
-element vector-element vector
– Multiply it by a full 2Multiply it by a full 2nn
××22nn
matrix for each gate opmatrix for each gate op
• Some obvious optimizations:Some obvious optimizations:
– Never store whole matrix (compute dynamically)Never store whole matrix (compute dynamically)
– Store only nonzero elements of state vectorStore only nonzero elements of state vector
• Especially helpful when qubits are highly correlatedEspecially helpful when qubits are highly correlated
– Do only constant work per nonzero vector elementDo only constant work per nonzero vector element
• Scatter amplitude from each state to 1 or 2 successorsScatter amplitude from each state to 1 or 2 successors
– Drop small-probability-mass sets of statesDrop small-probability-mass sets of states
• Linearity of QM implies no chaotic growth of errorsLinearity of QM implies no chaotic growth of errors
32. 32
Simulating Quantum Computations
• Given:Given:
– AnyAny nn-qubit quantum computation, expressed as a-qubit quantum computation, expressed as a
sequence of 1-qubit gates and CNOT gates.sequence of 1-qubit gates and CNOT gates.
– An initial stateAn initial state ss00 which is just a basis state in thewhich is just a basis state in the
classical bitwise basis,classical bitwise basis, e.g.e.g. ||0000000000〉〉..
• Goal:Goal:
– Generate a final basis state stochastically with the sameGenerate a final basis state stochastically with the same
probability distribution as the quantum computer wouldprobability distribution as the quantum computer would
do.do.
U1
U3
U4
U2
33. 33
Matrix RepresentationMatrix Representation
• Consider each gate as rank-2Consider each gate as rank-2nn
unitary matrix:unitary matrix:
– Each CNOT application is a 0-1 (permutation)Each CNOT application is a 0-1 (permutation)
matrix - a classical reversible bit-operation.matrix - a classical reversible bit-operation.
– With appropriate row ordering, eachWith appropriate row ordering, each UUii gategate
application is block-diagonal, w. each 2×2 blockapplication is block-diagonal, w. each 2×2 block
equal toequal to UUii..
– We need never represent these full matrices!We need never represent these full matrices!
– The 1 or 2 nonzero entries in a given row can beThe 1 or 2 nonzero entries in a given row can be
located & computed immediately given the row idlocated & computed immediately given the row id
(bit string) and(bit string) and UUii..
36. QCADQCAD
• Motivation
– Circuit Synthesis for Quantum Algorithms
– Development of Quantum Module library (Technology Independent)
– Physical Machine Description (PMD) specific optimization and cost
estimation
– PMD specific cell library creation (Technology Dependent)
– Considering issues of FT-QC and Error coding
• Challenges
– Integration of Classical (Reversible) and Quantum Modules
– Handling larger circuit size in terms of qubits
– Appropriate Cost Estimation
– Optimization Issues
– Functional Verification
37. Quantum Algorithm DescriptionQuantum Algorithm Description
using QCLusing QCL
• QCL (Quantum Computation Language) is a high level, architecture independent
programming language for quantum computers (Omer,
http://tph.tuwien.ac.at/~oemer/qcl.html)
• Its syntax is similar to C programming language
• Both classical and quantum code can be combined in the same program
Quantum
Algorithm
in QCL
Input
State
Output
State
Quantum Algorithm Simulation
40. Automated Generation of QASMAutomated Generation of QASM
for Quantum & Reversiblefor Quantum & Reversible
ModulesModules
• Quantum & Reversible modulesQuantum & Reversible modules
considered at presentconsidered at present
– QFT/IQFTQFT/IQFT
– Bernstein-Vazirani Search (BVS)Bernstein-Vazirani Search (BVS)
– GroverGrover’s search’s search
– Arithmetic CircuitsArithmetic Circuits
• DraperDraper’s Adder’s Adder
• CuccaroCuccaro’s adder’s adder
• 4 qubit multiplier4 qubit multiplier
• modular adder (a+b)%Nmodular adder (a+b)%N
• modular subtractormodular subtractor
• Constant modular multiplierConstant modular multiplier
• Modular exponentiationModular exponentiation
Algorithm for generation of QFT Circuit
CC Lin, A. Chakrabarti and N.K.Jha, “QLib: Quantum Module Library”, ACM JETC 2014
41. PMD specific Synthesis
• Each PMD supports a set of primitive quantum operationsEach PMD supports a set of primitive quantum operations
• Quantum gate Library :Quantum gate Library : Rx(θ), Ry(θ), Rz(Rx(θ), Ry(θ), Rz(θ),θ), H, CNOT, CZ, ZENO, SWAP, CP(H, CNOT, CZ, ZENO, SWAP, CP(θ),θ), G(G(θ),θ), iSW (iSW (θ),θ), Toffoli,Toffoli,
Fredkin, and PeresFredkin, and Peres
• Gate implementations are optimized by identity rules, involving both one qubit andGate implementations are optimized by identity rules, involving both one qubit and
two-qubit operationstwo-qubit operations
PMD One-qubit operations Two-qbit
operations
QD Rx, Rz, σx, σz, S, T CZ
SC Rx, Ry, Rz, iSWAP, CP
IT Rxy, Rz, G
NA Rxy CZ
LP Rx, Ry, Rz, σx, σy, σz, S, T, H CNOT, CZ,
SWAP, ZENO
NP Asqu, Rx, Ry, Rz, H CNOT
43. Quantum CompilerQuantum Compiler
• SKA and STA can only compile one-qubit gatesSKA and STA can only compile one-qubit gates
• Conversion of non-FT two-qubit gates to FT two-qubit gates first and then all theConversion of non-FT two-qubit gates to FT two-qubit gates first and then all the
non-FT one-qubit gates to FT cascadesnon-FT one-qubit gates to FT cascades
Synthesis flow of non-FT one-qubit gates based on the FT table
CC Lin, A. Chakrabarti and N.K.Jha, “FTQLS: Fault-Tolerant Quantum Logic Synthesis”, IEEE TVLSI 2013
46. 46
Research work at School of I.T., CUResearch work at School of I.T., CU
• The present research activities in the area of quantum computing are as
follows :
– Quantum Machine Learning
– Designing of new quantum circuits for quantum algorithms
– New circuit optimization techniques
• Template based
• Heuristic based
– Development of CAD tools for quantum circuit design, optimization and
simulations
– Quantum Cryptography Multi-valued logic and quantum computing
• International Collaborations
– Department of Computer Engineering, Princeton University, USA
– Dept. of Computer Science & Engineering and Department of Physics, New
York State University at Buffalo, USA
– Iwate Prefecture University, Japan
– University of Bremen, Germany
– University Linz, Austria
– Nanyang Technological University, Singapore
47. Our Publications (Selected List)Our Publications (Selected List)
• K. Regan,K. Regan, A. ChakrabartiA. Chakrabarti, C. Guan, “Algebraic and Logical Emulations of Quantum Circuits”, C. Guan, “Algebraic and Logical Emulations of Quantum Circuits” Springer Trans. ComputationalSpringer Trans. Computational
ScienceScience 31: 41-76 (2018).31: 41-76 (2018).
• M. GhoshM. Ghosh, A. Chakrabarti, A. Chakrabarti, Niraj K. Jha, “Automated Quantum Circuit Synthesis and Cost Estimation for the Binary Welded Tree, Niraj K. Jha, “Automated Quantum Circuit Synthesis and Cost Estimation for the Binary Welded Tree
Oracle”Oracle” ACM Journal on Emerging Technologies in Computing Systems (JETC)ACM Journal on Emerging Technologies in Computing Systems (JETC)13(4): 51:1-51:14 (2017).13(4): 51:1-51:14 (2017).
• S. Guha Roy andS. Guha Roy and A. ChakrabartiA. Chakrabarti,, “Novel Graph Clustering Algorithm Based On Discrete Time Quantum Random Walk,” Book“Novel Graph Clustering Algorithm Based On Discrete Time Quantum Random Walk,” Book
Titled: Quantum Inspired Computational Intelligence: Research and Applications ,Titled: Quantum Inspired Computational Intelligence: Research and Applications , Morgan KaufmannMorgan Kaufmann 2017.2017.
• S. Basu, S. B. Mandal,S. Basu, S. B. Mandal, A. ChakrabartiA. Chakrabarti and Susmita Sur-Kolay, "An Efficient Synthesis Method for Ternary Reversible Logic",and Susmita Sur-Kolay, "An Efficient Synthesis Method for Ternary Reversible Logic",
Proc. of IEEE International Symposium on Circuits and Systems 2016 (ISCAS 2016)Proc. of IEEE International Symposium on Circuits and Systems 2016 (ISCAS 2016)..
• P.Niemann, S. Basu,P.Niemann, S. Basu, A. ChakrabartiA. Chakrabarti, Niraj K. Jha and Robert Wille, "Synthesis of Quantum Circuits for Dedicated Physical, Niraj K. Jha and Robert Wille, "Synthesis of Quantum Circuits for Dedicated Physical
Machine Descriptions,Machine Descriptions,"" Proc.of 7th Conference on Reversible ComputationProc.of 7th Conference on Reversible Computation ((RC 2015RC 2015))..
• S.B.Mondal,S.B.Mondal, A.Chakrabarti,A.Chakrabarti, and S.Sur-Kolay,and S.Sur-Kolay, “Quantum Ternary Circuit Synthesis Using Projection Operations,”“Quantum Ternary Circuit Synthesis Using Projection Operations,” Journal ofJournal of
Multiple-Valued Logic and Soft ComputingMultiple-Valued Logic and Soft Computing, Vol 21, Issue 1-4, pp. 73-92, January 2015., Vol 21, Issue 1-4, pp. 73-92, January 2015.
• C.C. Lin,C.C. Lin, A. ChakrabartiA. Chakrabarti, N. K. Jha,, N. K. Jha, “QLib: Quantum module library,”“QLib: Quantum module library,” ACM Journal on Emerging Technologies in ComputingACM Journal on Emerging Technologies in Computing
Systems (JETC)Systems (JETC), V. 11 Issue 1, Article No. 7, September 2014., V. 11 Issue 1, Article No. 7, September 2014.
• CC Lin,CC Lin, A. ChakrabartiA. Chakrabarti and N.K.Jha,and N.K.Jha, ““FTQLS: Fault-Tolerant Quantum Logic Synthesis,”““FTQLS: Fault-Tolerant Quantum Logic Synthesis,” IEEE Transactions on Very LargeIEEE Transactions on Very Large
Scale Integration (VLSI) SystemsScale Integration (VLSI) Systems, Vol. 22,No.6, pp. 1350-1363, June 2014., Vol. 22,No.6, pp. 1350-1363, June 2014.
• S.B.Mondal,S.B.Mondal, A.ChakrabartiA.Chakrabarti and S.Sur-Kolay,and S.Sur-Kolay, “Synthesis of Ternary Grover's Algorithm”“Synthesis of Ternary Grover's Algorithm”, Proc. of IEEE 441st International, Proc. of IEEE 441st International
Symposium on Multiple-Valued Logic (ISMVL 2014Symposium on Multiple-Valued Logic (ISMVL 2014)), Bremen Germany, 19-21 May 2014., Bremen Germany, 19-21 May 2014.
• C.C. Lin,C.C. Lin, A. ChakrabartiA. Chakrabarti, N. K. Jha,, N. K. Jha, “Optimized Quantum Gate Library for Various Physical Machine Descriptions,”“Optimized Quantum Gate Library for Various Physical Machine Descriptions,” IEEEIEEE
Transactions on Very Large Scale Integration (VLSI) SystemsTransactions on Very Large Scale Integration (VLSI) Systems, Vol. 21, No.11, pp. 2055-2068, Nov. 2013., Vol. 21, No.11, pp. 2055-2068, Nov. 2013. 47