7/31/2019 quantum computing basic
1/24
KALYANI GOVT. ENGG. COLLEGE ECE DEPT.
PRESENTED BY * PARTHA PAUL
* SUBHAJIT MONDAL* SUDIPAN SINGHA
7/31/2019 quantum computing basic
2/24
OUTLINE
HistoryMotivationQuantum vs. ClassicalQuantum GatesQuantum Circuits
Physical Implementation
7/31/2019 quantum computing basic
3/24
HISTORY
Abacus
Gear Driven
Integrated Circuits
Over 200 million transistors
7/31/2019 quantum computing basic
4/24
computational LIMITS
Some important computational problemsseem to be permanently intractable
> Their complexity grows exponentially with
problem size, e.g. factoring largenumbers the basis for unbreakableInternet codes
Performance improvements in classical computer circuits may be approaching alimit > This is described by Moores Law
7/31/2019 quantum computing basic
5/24
Moores Law In 1965 Gordon Moore predicted that
number of transistors per square inchon integrated circuits had doubled
every year since the integrated circuitwas invented. Moore predicted thatthis trend would continue for theforeseeable future.
This has held true .. So far
http://www.webopedia.com/TERM/M/transistor.htmlhttp://www.webopedia.com/TERM/M/integrated_circuit_IC.htmlhttp://www.webopedia.com/TERM/M/integrated_circuit_IC.htmlhttp://www.webopedia.com/TERM/M/integrated_circuit_IC.htmlhttp://www.webopedia.com/TERM/M/integrated_circuit_IC.htmlhttp://www.webopedia.com/TERM/M/transistor.html7/31/2019 quantum computing basic
6/24
* In 1965 - Gordon Moore announced that his predictionwould not remain true for much longer because of modern
technology.The ability to put transistors on chips was approaching theatomic level.
* In 1982 - Feynman proposed the idea of creating machinesbased on the laws of quantum mechanics instead of the lawsof classical physics.
*In 1994 - Peter Shor came up with a quantum algorithm tofactor very large numbers in polynomial time.
* In 1997 - Lov Grover develops a quantum search algorithmwith O(N) complexity
7/31/2019 quantum computing basic
7/24
Quantum Computer
A quantum computer is a machine thatperforms calculations based on the laws ofquantum mechanics, which is the behaviorof particles at the sub-atomic level.
7/31/2019 quantum computing basic
8/24
Two States Are Better Than One !!
Digital Computers rely on Os and 1 s
Voltage produces high and lows
Can only have one state at a time
Quantum computers can have multiple states
Two places at once
7/31/2019 quantum computing basic
9/24
A single qubit can be forced intoa superposition of the twostates denoted by the additionof the state vectors:
1
Where 1 and are complex
numbers and | 1|^2 +| |^2 = 1
7/31/2019 quantum computing basic
10/24
Representation of Data -Superposition
Light pulse offrequency fortime interval t/2
State |0> + |1>
7/31/2019 quantum computing basic
11/24
Quantum Information
7/31/2019 quantum computing basic
12/24
Quantum Gates :
7/31/2019 quantum computing basic
13/24
Quantum Gates
X
X X
N0T MATRIX
7/31/2019 quantum computing basic
14/24
Quantum Gates - Hadamard :
Simplest gate involves one qubit and is called a Hadamard Gate ( also
known as a square-root of NOT gate.) Used to put qubits into superposition.
H H
StateI0>
StateI0>+I1>
StateI1>
Note: Two Hadamard gates used in succession can be used as a NOTgate
7/31/2019 quantum computing basic
15/24
Quantum Gates - Controlled NOT
A gate which operates on two qubits is called a Controlled-NOT (CN) Gate. If
the bit on the control line is 1, invert the bit on the target line.
A - Target
B - Control
A
B
A B A B
0 0
0 1
1 0
1 1
1 1
0 0
1 0
0 1Note: The CN gate has a similarbehavior to the XOR gate with someextra information to make it reversible.
7/31/2019 quantum computing basic
16/24
Quantum Logic Circuits A beam splitter
Half of the photons leaving the light source arrive at detector A;
the other half arrive at detector B.
7/31/2019 quantum computing basic
17/24
A beam-splitter0
1
0
1
%50
%50
Equal path lengths, rigid mirrors. Only one photon in the apparatus at a time. All photons leaving the source arrive at B. WHY?
7/31/2019 quantum computing basic
18/24
Quantum Circuits
A quantum (combinational) circuit is a sequence ofquantum gates, linked by wiresThe circuit has fixed width corresponding to thenumber of qubits being processedLogic design (classical and quantum) attempts tofind circuit structures for needed operations thatare
Functionally correctIndependent of physical technologyLow-cost, e.g., use the minimum number of qubits orgates
Quantum logic design is not well developed!
7/31/2019 quantum computing basic
19/24
Ad hoc designs known for many specific functions andgatesExample 1 illustrating a theorem by [Barenco et al.
1995]: Any C2
(U ) gate can be built from CNOTs, C( V ),and C( V ) gates, where V 2 = U
V V V
=
U
(1+i) (1-i)
(1-i) (1+i)(1-i) (1+i)
(1+i) (1-i)1/2
1/2
7/31/2019 quantum computing basic
20/24
Example 1 : Simulation
|0
|1
|x
|0
|1
|x
|0
|1
|x V V V
=
U
|0
|1
V |x
|0
|1
|0
|1
|x
|0
|1
|0
|1
|x
?
7/31/2019 quantum computing basic
21/24
Implementing a Half Adder
Problem: Implement the classical functions sum = x 1 x 0 and carry = x 1x 0
Generic design:
|x 1
U add |x 0 |y 1
|y 0
|x 1 |x 0 |y 1 carry
|y 0 sum
0001000000000000
0000100000000000
1000000000000000
0100000000000000
0000010000000000
0000100000000000
0000000100000000
0000001000000000
0000000001000000
0000000010000000
0000000000010000
0000000000100000
0000000000001000
0000000000000100
0000000000000010
0000000000000001
ADDU
Half Adder : Generic
design (contd.)
7/31/2019 quantum computing basic
22/24
Physical ImplementationMain Contenders
Nuclear magnetic resonance (NMR) Ion traps Semiconductor quantum dots Optical lattices etc.
Main Deficiency
Poor scalability
Chris Monroe,University ofMichigan
Ion traps
7/31/2019 quantum computing basic
23/24
Summary: State of the Art
Quantum circuits can solve some important problems withexponentially fewer operations than classical algorithms
Small quantum circuits have been demonstrated in thelab using various physical technologies
Quantum cryptography has been demonstrated over longdistances
Current technologies are fragile, and appear to be limitedto tens of qubits and hundreds of gates
Big gaps remain in our understanding of quantum circuitand algorithm design, as well as the necessaryimplementation techniques
7/31/2019 quantum computing basic
24/24