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Quantum computation
Based on nanotechnology




            By:
            M.Revanth kumar
            T.Sri kanth
Speed of computation:

    Vaccum tubes

    Transistors

     Devices that perform
     quantum computing
Quantum mechanics

Physical phenomena at
  microscopic scales

Completely different from
  classical mechanics
Quantum computing
   Theoretical study of
    quantum systems

   Those systems are
    applied to make a
    quantum computer

   Uses “QUBITS”
Bits       (classical computing)
   A bit can exist only in one
    state

    Either 0 or 1

   Information behaviour : one
    single direction

   Logic gates are irreversible
Qubits
   Can exist as 0 or 1 or
    coherent superposition of
    both

   Operation on a qubit
    effectively acts on both
    values at a same time

   An exist in both values
    simultaneously
Bloch’s sphere:
                  |1>




                  |0>
Ket notation:
                q= a l0> + b l1>


       Qubit system       No. of
       (n)                operations


       2                  4
       3                  8
       4                  16
Representation of Data -
Qubits
   Light pulse of
   frequency  for time
   interval t




      |0>                  |1>
Physical interpretation
   Light pulse of frequency  for
   time interval t/2




    State |0>                       State |0> + |1>
Representation of Data -
Superposition
    A single qubit can be forced into a superposition
     of the two states denoted by the addition of the
     state vectors:

                |> =  |0> +  |1>


    Where  and  are complex numbers and | |
     + | | =1
Processors


  Classical processors      Quantum processors

Each processor perform    Single processor can
  one computation,while      perform multiple
  other processors do        computations on its own
  other computations         simultaneously
As increase in no.of Qubits

   Increase in quantum parallelism
                                      Solve
Quantum parallelism               problems in
        +                          fraction of
     Algorithm                        time
GATES:
Can achieve reversible operations by using quantum
gates

Ex.

The AND Gate
                        A   B     C


                        0   0     0

                        0   1     0

                        1   0     0

                        1   1     1
Reversible operations


 For a computer to run fast
 Inputs can be correctly deduced from
  outputs
 Irreversible computation involve loss of
  information
Taffoli gate:
It’s a reversible gate
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

              State          State           State
              |0>            |0> +           |1>
                             |1>



  Note: Two Hadamard gates used in
  succession can be used as a NOT gate
Quantum computer

 Use direct use of quantum mechanical
  phenomena
 Utilizes quantum properties to represent data
 Could solve certain problems much faster
Shor’s algorithm

 Allows extremely quick factoring
 To factor a 1000 digit number
 For a classical computer it take 10
  million billion years
 For a quantum computer its just 20 min
Building a quantum computer

   It can’t be from transistor and diodes

   A new type of technology is needed

   A technology that enables qubits to exist
    as coherent superposition of 0 and 1
Why Nanotechnology is applied?
References
   Text books: 1. Palanisamy
    2. A quantum revolution for computing. Julian
    Brown, New Scientist 24/9/94
 Wikipedia.org
 Videos on quantum computation by
  “centre for quantum computation and
  communication technology”
Queries
          ?
What ever may be the technology we
come up with, should able to reach a
          common man.

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Quantum computing

  • 1. Quantum computation Based on nanotechnology By: M.Revanth kumar T.Sri kanth
  • 2. Speed of computation:  Vaccum tubes  Transistors  Devices that perform quantum computing
  • 3. Quantum mechanics Physical phenomena at microscopic scales Completely different from classical mechanics
  • 4. Quantum computing  Theoretical study of quantum systems  Those systems are applied to make a quantum computer  Uses “QUBITS”
  • 5. Bits (classical computing)  A bit can exist only in one state Either 0 or 1  Information behaviour : one single direction  Logic gates are irreversible
  • 6. Qubits  Can exist as 0 or 1 or coherent superposition of both  Operation on a qubit effectively acts on both values at a same time  An exist in both values simultaneously
  • 8. Ket notation: q= a l0> + b l1> Qubit system No. of (n) operations 2 4 3 8 4 16
  • 9. Representation of Data - Qubits Light pulse of frequency  for time interval t |0> |1>
  • 10. Physical interpretation Light pulse of frequency  for time interval t/2 State |0> State |0> + |1>
  • 11. Representation of Data - Superposition  A single qubit can be forced into a superposition of the two states denoted by the addition of the state vectors: |> =  |0> +  |1>  Where  and  are complex numbers and | | + | | =1
  • 12. Processors Classical processors Quantum processors Each processor perform Single processor can one computation,while perform multiple other processors do computations on its own other computations simultaneously
  • 13. As increase in no.of Qubits  Increase in quantum parallelism Solve Quantum parallelism problems in + fraction of Algorithm time
  • 14. GATES: Can achieve reversible operations by using quantum gates Ex. The AND Gate A B C 0 0 0 0 1 0 1 0 0 1 1 1
  • 15. Reversible operations  For a computer to run fast  Inputs can be correctly deduced from outputs  Irreversible computation involve loss of information
  • 16. Taffoli gate: It’s a reversible gate
  • 17. 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 State State State |0> |0> + |1> |1> Note: Two Hadamard gates used in succession can be used as a NOT gate
  • 18. Quantum computer  Use direct use of quantum mechanical phenomena  Utilizes quantum properties to represent data  Could solve certain problems much faster
  • 19. Shor’s algorithm  Allows extremely quick factoring  To factor a 1000 digit number  For a classical computer it take 10 million billion years  For a quantum computer its just 20 min
  • 20. Building a quantum computer  It can’t be from transistor and diodes  A new type of technology is needed  A technology that enables qubits to exist as coherent superposition of 0 and 1
  • 22.
  • 23. References  Text books: 1. Palanisamy 2. A quantum revolution for computing. Julian Brown, New Scientist 24/9/94  Wikipedia.org  Videos on quantum computation by “centre for quantum computation and communication technology”
  • 24. Queries ?
  • 25. What ever may be the technology we come up with, should able to reach a common man.