Quantum computing uses quantum mechanical phenomena like superposition and entanglement to perform computations. It has the potential to solve certain problems like factoring large numbers and simulating quantum systems much faster than classical computers. The basic unit of quantum information is the qubit, which can exist in superpositions of states. Quantum algorithms like Deutsch's algorithm and Shor's algorithm demonstrate quantum speedups using techniques like interference and parallelism. Physical implementations of quantum computers face challenges like controlling and measuring qubits while preventing decoherence. Significant progress has been made in developing algorithms and implementing small qubit systems, but scaling to larger, fully functional quantum computers remains an ongoing challenge.
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.
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.
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
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.
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.
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 basics of quantum computing, associated mathematics, DJ algorithms and coding details are covered.
These slides are used in my videos https://youtu.be/6o2jh25lrmI, https://youtu.be/Wj73E4pObRk, https://youtu.be/OkFkSXfGawQ and https://youtu.be/OkFkSXfGawQ
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.
Quantum computing description in short. History about quantum computers. Hero's of quantum computers,. introductions abstract what are quantum computers
Descripcion about IBM quantum experience. In this presentation I introduce the IBM Tools for quantum programming. Also it serves as a general introduction to Quantum Computing
COMPUTATIONAL PERFORMANCE OF QUANTUM PHASE ESTIMATION ALGORITHMcsitconf
A quantum computation problem is discussed in this paper. Many new features that make
quantum computation superior to classical computation can be attributed to quantum coherence
effect, which depends on the phase of quantum coherent state. Quantum Fourier transform
algorithm, the most commonly used algorithm, is introduced. And one of its most important
applications, phase estimation of quantum state based on quantum Fourier transform, is
presented in details. The flow of phase estimation algorithm and the quantum circuit model are
shown. And the error of the output phase value, as well as the probability of measurement, is
analysed. The probability distribution of the measuring result of phase value is presented and
the computational efficiency is discussed.
The basics of quantum computing, associated mathematics, DJ algorithms and coding details are covered.
These slides are used in my videos https://youtu.be/6o2jh25lrmI, https://youtu.be/Wj73E4pObRk, https://youtu.be/OkFkSXfGawQ and https://youtu.be/OkFkSXfGawQ
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.
Quantum computing description in short. History about quantum computers. Hero's of quantum computers,. introductions abstract what are quantum computers
Descripcion about IBM quantum experience. In this presentation I introduce the IBM Tools for quantum programming. Also it serves as a general introduction to Quantum Computing
COMPUTATIONAL PERFORMANCE OF QUANTUM PHASE ESTIMATION ALGORITHMcsitconf
A quantum computation problem is discussed in this paper. Many new features that make
quantum computation superior to classical computation can be attributed to quantum coherence
effect, which depends on the phase of quantum coherent state. Quantum Fourier transform
algorithm, the most commonly used algorithm, is introduced. And one of its most important
applications, phase estimation of quantum state based on quantum Fourier transform, is
presented in details. The flow of phase estimation algorithm and the quantum circuit model are
shown. And the error of the output phase value, as well as the probability of measurement, is
analysed. The probability distribution of the measuring result of phase value is presented and
the computational efficiency is discussed.
2. Outline
Introduction:
What is quantum computing?
What use is quantum computing?
Overview of Quantum Systems
Dirac notation & wave functions
Two level systems
Classical Computation
Turing machine model
3. Outline (cont.)
Circuit model
Quantum Computation
Qubits
Circuit model of quantum computation
Deutsch's algorithm, Shor's algorithm
Physical implementation
Summary
Works Cited
5. What is Quantum Computing?
A quantum computer is any device that uses
quantum mechanical phenomena to perform
calculations and manipulate data.
6. Why Quantum Computers?
More efficient algorithms
Quantum Parallelism
Cryptography (breaking
codes & securing data)
Simulating quantum
systems
7. Cryptography
RSA public key encryption relies on the difficulty of
factoring large integers
It is conjectured that factorization is impossible to
do efficiently with a classical computer.
Shor's factoring algorithm for quantum computers
would render this encryption method useless
8. An Inevitability?
Moore's Law: The
number of transistor's
on a silicon chip
doubles every two
years
Atomic size is a
fundamentally limit to
the size of possible
transistors.
10. Schrödinger's Equation
Quantum systems are described by a wave
function (ψ)
For a given potential (V(x)), we find all solutions
to Schrödinger's equation.
These solutions form a basis of a vector space
called a Hilbert space.
11. Dirac (Bra-ket) Notation
Notation introduced by
Dirac to represent
objects in Hilbert
space.
Bra – row vector
Ket – column vector
Bra-kets – inner
products
12. Wave Functions
Hilbert spaces have an
orthogonal basis.
A wave function is a
linear combination of
the basis vectors
Wave functions should
be normalizable.
13. Useful Wave Function Properties
Interference
Like classical waves, the wave function can exhibit
constructive/destructive interference
Exploited in quantum algorithms (Deutsch's)
Entanglement
Multiple particle's wave functions may become
“entangled”
Measuring or manipulating one particle will
necessarily affect the other.
14. Born (statistical) Interpretation
A quantum system can in a superposition of the
allowed states until a measurement is done.
When a measurement is performed, the wave
function accepts one of the allowed states.
You cannot know which state the system will
be in before the measurement, only the
probability of it being in a given state.
16. Useful Wave Function Properties
Interference
Like classical waves, the wave function can exhibit
constructive/destructive interference
Exploited in some quantum algorithms
Entanglement
Multiple particle's wave functions may become
“entangled”
Measuring or manipulating one particle will
necessarily affect the other.
19. 2 Level Systems
A system with two basis
states.
Examples:
Nuclear spin (up, down)
Polarization of a photon
(left, right)
Qubits (|1>, |0>)
20. Bits
A bit is an elementary unit
of information.
A bit has two possible
states: 1 or 0.
A bit is unambiguous,
never in a superposition
of states.
21. Qubits
A qubit is the
elementary unit of
quantum information.
A qubit has two allowed
states: |1>, |0>.
A qubit can be in a
superposition of the
states of a bit.
23. Classical Computation
Computation is done by means of an algorithm,
which can be thought of as a set of instructions
for solving a specific problem.
The mathematician Alan Turing (1912-1954)
devised a hypothetical machine that could
execute any algorithm called a Turing
Machine.
24. Turing Machine
Tape – infinite number of
cells, every cell is blank or
contains a letter in a finite
alphabet
Control Head – has a finite
number of states and a
halting state
Read/Write – reads and
writes or erases a letter in
a given cell then moves
left or right.
25. Operation of a Turing Machine
Programs are defined by a set of instructions (a function)
An instruction can be written as T:(s,a) → (s',a',d)
s is the current state and s' is the final state of the head.
a is the letter in the cell, a' is the letter to be written.
d is the direction the head will move
26. Input of a Turing Machine
The input is the initial state of the Turing machine.
a finite number of non-blank cells
the read/write head in an initial position
the control head in an initial state.
a set of instructions for every preceding state
27. Output of a Turing Machine
The output of a Turing machine is the final state
of the Turing machine, if any.
Control head reaches the halting state (H)
Finite length of non-blank cells
For a Turing machine it is impossible to know for
all inputs whether the control head will reach a
halting state or not. This is the known as the
halting problem.
28. Example: Unary Addition
Top: A table listing the
instructions for
mapping each state of
the Turing machine
(s,a) to a sucessive
state (s',a',d).
Bottom: Initial and Final
state of the Turing
Machine.
s a s' a' d
s1 b s2 b l
s2 b s3 b l
s2 1 s2 1 l
s3 b H b 0
s3 1 s4 b r
s4 b s2 1 l
29. Circuit Model of Computation
Circuits are made of wires and gates.
Each wire carries one bit of information
Gates perform logical operations on one or more
wires.
In any computation, a circuit can be represented
as mapping a n-bit input to a m-bit output.
30. Logic Gates
AND –
outputs 1 iff both inputs
are 1
OR -
outputs 0 iff both inputs
are 0
NOT -
outputs 1 iff input is 0
outputs 0 iff input is 1
31. Logic Gates
FANOUT -
outputs two bits
identical to input.
AND,OR,NOT, and
FANOUT constitute a
universal set of gates.
That is, any n-bit to
m-bit function can be
represented by them.
32. Gates as Linear Operators
Consider the NOT gate,
which returns the
opposite of the input.
We may represent this
gate as a 2x2 matrix.
36. Qubits
2 level system in a
superposition of bit
states.
We will manipulate
qubits in a manner
analogous to the
circuit model of
classical computation.
37. Representing a Two-Qubit Input
Given two wires going
into a gate, you can
represent both bits as
the tensor product of
the two bit.
Two 2-dimensional
vectors becomes one
4-dimensional vector.
38. Representing Two Qubits
We can write a basis for a two qubit system as
the tensor products of the individual qubit's
basis vectors
39. Entanglement of Two Qubits
A two-qubit state is separable if it can be written
as the tensor product of two one-qubit states.
A two-qubit state is entangled otherwise.
40. n-Qubit Quantum Register
A quantum computer may be thought of as a collection
of n-qubits called a quantum register.
A n-qubit quantum register has a basis of 2n
allowed
states, and any state of the quantum computer is in a
superposition of these states.
41. Prerequisites for Quantum
Computation
Be able to prepare system
in a well defined initial
state.
Be able to manipulate the
wave function via unitary
transformations.
Be able to measure the
final states of each qubit.
42. Hadamard Gate (Single Qubit)
Changes the basis to a superposition of the
computation basis.
Hadamard gate is a Hermitian operator.
43. Controlled Gates (CNOT)
The first qubit acts as
the control qubit.
The second qubit acts
as the target qubit.
Flips the state of the
target qubit if the first
qubit is found in a
certain state. ( |1>)
44. Quantum CNOT Gate
Can be used to introduce entangled state into a
two-qubit system.
CNOT along with some of its variants form a
universal set of quantum logic gates.
45. Deutsch's Algorithm (1992)
Acts on a boolean function
Is the function balanced?
Is the function constant?
Can determine whether the
function is balanced or
constant in one step!
Classical computers require
two runs!
x f1 f2 f3 f4
0 0 1 0 1
1 0 0 1 1
46. Deutsch's Algorithm (1992)
Start with |01> state
Apply Hadamard gates
to both qubits.
Apply U, then another
Hadamard gate on
the first bit.
Measure the first bit.
|0> => f is constant.
47. Shor's Algorithm (1994)
A hybrid algorithm that is able to a factor a large integer
n in polynomial time.
We want to factor a large composite integer n.
Find the periodicity of F(a) = xa
(mod n) for x relatively
prime to n.
Test all the exponents 'a' up to a power of two between
n2
and 2n2
using quantum parallelism.
Given this period we can more easily determine possible
factors.
48. Other Curiosities
Grover's sorting algorithm (1996)
Searching through an unsorted database
Best classical algorithm is brute force
Universal quantum simulator
Proposed by Richard Feynman (1982)
Quantum simulation requires exponential resources
classically
Can be done efficiently with a quantum computer.
(Seth Lloyd - 1996)
49. Implementation
Quantum logic gate implemented (1995 - NIST)
C-NOT gate using trapped ions
Quantum algorithm – 7 qubits (2001 - IBM)
Used Shor's algorithm to factor 15
Largest qubit register – 12 qubits (2006 ICQ)
Benchmarked a 12 qubit register
Decoherence – the bane of quantum computing
50. Summary
Quantum computing is promising field
Efficient solutions to classically difficult problems
Inevitable conclusion of Moore's law
Decryption & Encryption
Computer modeling of quantum mechanics
Physical implementation requires solving or
bypassing the problem of decoherence.
51. Works Cited
“Principle of Quantum Computation and Information” - Benenti, et
al.
“An Introduction to Quantum Computing” - Kaye, et al.
“Quantum Computing and Shor's Algorithm” - Hayward (
http://alumni.imsa.edu/~matth/quant/299/paper/)
Images from Wikipedia (http://en.wikipedia.org/*)
Slide 1 – Bloch Sphere; Slide 6 – BQP; Slide 8 – Moore's Law;
Slide 24 – Turing Machine; Slides 31/32 – Logic Gates;
Actual Turing machine from (http://aturingmachine.com)
LaTeX by the Online LaTeX Generator: (http://codecogs.com/)