Quantum Computers

1. Quantum Computers presented by Siva Desaraju Bindu Katragadda Manusri Edupuganti

2. Outline • Introduction • Quantum computation • Implementation • Quantum compiler • Error correction • Architecture • Classification • Fabrication • Challenges • Advantages over classical computers • Applications • Recent advances • Timeline • Conclusion

3. [2] Introduction • Quantum Mechanics • Why? – Moore’s law • Study of matter at atomic level (The power of atoms) • Classical physics laws do not apply • Superposition • Simultaneously possess two or more values • Entanglement • Quantum states of two atoms correlated even though spatially separated!!! • Albert Einstein baffled “spooky action at a distance”

4. [2] Bits n Qubits • Classical computers 0 or 1 (bits) • High/low voltage • Quantum computers 0 or 1 or 0 & 1 (Qubits) • Nuclear spin up/down 0 or 1 • Isolated atom spin up & down 0 & 1 • Represent more with less (n bits 2n states) ”To be or not to be. That is the question” – William Shakespeare The classic answers: ”to be” or ”not to be” The quantum answers: ”to be” or ”not to be” or a x (to be) + b x (not to be)

5. Quantum Computation • Prime factorization (Cryptography) • Peter Shor’s algorithm • Hard classical computation becomes easy quantum computation • Factor n bit integer in O(n3) • Search an unordered list • Lov Grover’s algorithm • Hard classical computation becomes less hard quantum computation • n elements in n1/2 queries

6. Implementation model Quantum unitary transforms (gates) Classical computation Quantum program Classical control flow decisions Quantum measurements Instruction stream Quantum compiler Classical bit instruction stream Early quantum computation - Circuit model(ASIC)

7. Quantum Compiler • Static precompiler • End-to-end error probability • Dynamic compiler • Accepts the precompiled binary code & produces an instruction stream

8. Error Correction • Localized errors on a few qubits can have global impact • Hamming code • Difficulty of error correcting quantum states • Classical computers – bit flip • Quantum computers – bit flip + phase flip • Difficulty in measurement (collapses superposition) • Quantum error correction code • [n,k] code uses n qubits to encode k qubits of data • Extra bits (n-k) are called ancilla bits • Ancilla bits are in initial state

9. Architecture • Aims of efficient architecture • Minimize error correction overhead • Support different algorithms & data sizes • Reliable data paths & efficient quantum memory • Major components • Quantum ALU • Quantum memory • Dynamic scheduler

10. Architecture contd… [1]

11. Quantum ALU • Sequence of transforms • the Hadamard (a radix-2, 1-qubit Fourier • transform) • identity (I, a quantum NOP) • bit flip (X, a quantum NOT) • phase flip (Z, which changes the signs of amplitudes) • bit and phase flip (Y) • rotation by π/4 (S) • rotation by π/8 (T) • controlled NOT (CNOT)

12. Quantum Memory • Reliable memory • Refresh units • Multiple memory banks

13. Quantum wires • Teleportation • Quantum swap gates • Cat state [1]

14. Dynamic Scheduler • Dynamic scheduler algorithm takes • Input - logical quantum operations, interleaved with classical control flow constructs • Output - physical individual qubit operations • Uses knowledge of data size & physical qubit error rates

15. Classification Quantum Computer Liquid Quantum Computer Solid Quantum Computer Si29 Doping Phosphorous Doping

16. Liquid Quantum Computers • NMR Technology • Disadvantages • Massive redundancy • Not scalable

17. Solid Quantum Computers • Why silicon • Chip design aims • Capturing & manipulating individual sub atomic particles • Harnessing, controlling & coordinating millions of particles at once

18. Si29 Doping • Need for Silicon 29 (Si29) doping • Fabrication • Advantages • Disadvantages [9]

19. Phosphorous doping [3]

20. Fabrication • STM technology to pluck individual atoms from hydrogen • PH3 used instead of P

21. Challenges • Decoherence • Chip fabrication • Error correction

22. Advantages over Classical computers • Encode more information • Powerful • Massively parallel • Easily crack secret codes • Fast in searching databases • Hard computational problems become tractable

23. Applications • Defense • Cryptography • Accurate weather forecasts • Efficient search • Teleportation • … • Unimaginable

24. Timeline • 2003 - A research team in Japan demonstrated the first solid state device needed to construct a viable quantum computer • 2001 - First working 7-qubit NMR computer demonstrated at IBM’s Almaden Research Center. First execution of Shor’s algorithm. • 2000 - First working 5-qubit NMR computer demonstrated at IBM's Almaden Research Center. First execution of order finding (part of Shor's algorithm). • 1999 - First working 3-qubit NMR computer demonstrated at IBM's Almaden Research Center. First execution of Grover's algorithm. • 1998- First working 2-qubit NMR computer demonstrated at University of California Berkeley. • 1997 - MIT published the first papers on quantum computers based on spin resonance & thermal ensembles. • 1996 - Lov Grover at Bell Labs invented the quantum database search algorithm • 1995 - Shor proposed the first scheme for quantum error correction

25. Conclusion…will this be ever true? • Millions into research • With a 100 qubit computer you can represent all atoms in the universe. • If you succeed, the world will be at your feet [6]

26. References [1] http://www.cs.washington.edu/homes/oskin/Oskin-A-Practical-Architecture-for-Reliable-Quantum-Computers.pdf [2] http://www.qubit.org [3] http://www.nature.com [4] http://www.wikipedia.com [5] http://www.howstuffworks.com [6] http://www.physicsweb.org/toc/world/11/3 [7] http://www.cs.ualberta.ca/~bulitko/qc/schedule/slides/QCSS-2002-06-18.ppt [8] http://physics.about.com/cs/quantumphysics/ [9] http://www.trnmag.com/Stories/2002/082102/Chip_ design_aims_for_quantum_leap_082102.html

27. Puzzled??? "I think I can safely say that nobody understands quantum mechanics."- Richard P. Feynman “Anybody who thinks they understand quantum physics is wrong."- Niels Bohr