Welcome to the presentation on Computational Capabilities with Quantum Computer

1. Welcome to the presentation onComputational Capabilities with Quantum Computer By Anil Kumar Javali

2. Agenda • Introduction • Quantum Parallelism • Quantum Algorithms • NMR for Quantum Computer ( Q.C. ) • CNOT Gate for Q. C • Obstacles • References

3. Introduction • What is a Q.C.

4. Classical Computer (C.C) vs. Q.C. bit qubit

5. Power & Potential of Q.C 500 • A system with 500 qubits => 2 states • Each state = single list of 500 0’s & 1’s • 99 & 100th qubit • Best know encryption method RSA, will no longer be the best

6. Quantum Interference

7. Quantum Interference (contd)

8. CC vs QC 1/3 2/3 2/3 • Best know algorithm for classical computer runs in O(exp[(64/3) (ln N) (ln ln N) ]) steps • For ex, in 1994, 129 digit number, factorized, 1600 workstations, 8 months. • Similarly, 800,000 years to factor a 250 digit number & 10 years to factor a 1000 digit number 25

9. CC vs QC (cont.) 2+E • Where as, Q.C takes O((log N) ) steps • 1000 digit number would take only a few million steps. • Public key cryptosystems based on factoring may be breakable

10. Quantum Algorithms • Shor’s Algorithm • Grover’s Algorithm

11. Shor’s Algorithm • Finds factors of a very large number • For ex; N = 91, • Choose a co-prime of 91 which is 729 • i.e., 729 = 1 (mod 91) • => 28 x 26 = 0 (mod 91) • => either gcd(28,91) or gcd(26,91) will give the factors of 91 • Here, both gives different factors, those are 7 & 13 • 91 = 7 x 13

12. Physical Implementation of Q.C • NMR (nuclear magnetic resonance)-Based Q.C • Heteropolymer-Based Q.C • Ion Trap Based Q.C • Cavity QED-Based Q.C

13. NMR for Q.C

14. How NMR works • Takes pulse signal as input • Acts on the qubit molecules • Qubit changes its state • Measure the density of the qubit to know its new state

15. How NMR works (cont.) • Qubits initial state is represented by its density which is represented in the form of matrix ( ‘a’ ) • When input pulse signal ‘x’ acts on ‘a’ • Density of qubit changes to final state ‘b’ • We can represent the above operation symbolically as ‘a’ X ‘x’ = ‘b’

16. Genetic Algorithm (G.A) to find the pulse signal • Using GA, find the pulse signal ‘x’ • Train the network using GA for different test cases • Test the network for new values

17. My contribution towards NMR QC • Implementing GA to find the pulse signal

18. Basic gates for C.C • AND, OR, NOT • Original 2 inputs can’t be restored • Electronic circuits are not reversible

19. Basic Gates for Q.C • There are AND, OR and NOT gates for Q.C • They are not the smallest units for Q.C • Where as CNOT ( controlled NOT ) is • CNOT represent AND, OR & NOT operations

20. 0 1 0 1 X Universal CNOT gate for Q.C CONTROL CONNECTION TARGET

21. How CNOT works

22. Obstacles • There are many obstacles to be resolved to make Q.C a reality like, • Quantum Entanglement • Quantum Teleportation • Quantum Error Correction

23. References • Isaac L Chuang, M A Nielsen, Quantum Computation and Information, Dec 2000 • Center for Quantum Computation, http://www.qubit.com/ • Jacob West, The Quantum Computer, http://www.cs.caltech.edu/~westside/quantum-intro.html April 28, 2000 • Samuel L. Braunstein, Quantum Computation, http://www.informatics.bangor.ac.uk/~schmuel/comp/comp.html Aug 23, 1995

24. Questions ?