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Doing this for Oracles implementing all four possible search functions f and averaging the obtained results in each case over many identical runs of the algorithm, we obtain the success probabilities of the different implementations of the search algorithm.

- 1. Andreas Dewes Acknowledgements go to "Quantronics Group", CEA Saclay. R. Lauro, Y. Kubo, F. Ong, A. Palacios-Laloy, V. Schmitt PhD Advisors: Denis Vion, Patrice Bertet, Daniel Esteve Let's Build a Quantum Computer! 31C3 29/12/2014
- 2. Motivation
- 3. Outline Quantum Computing What is it & why do we want it Quantum Algorithms Cracking passwords with quantum computers Building A Simple Quantum Processor Superconductors, Resonators, Microwaves Recent Progress in Quantum Computing Architectures, Error Correction, Hybrid Systems
- 4. Why Quantum Computing? Quantum physics cannot be simulated efficiently with a classical computer.1) A computer that makes use of quantum mechanics can do it. It can also be faster for some other mathematical problems. 1) http://www.cs.berkeley.edu/~christos/classics/Feynman.pdf
- 5. Classical Computing http://commons.wikimedia.org/wiki/File:Abacus_1_(PSF).png
- 6. Bits 0 1
- 7. Bit Registers InA 0 … 00, 0 … 01, … , 1 … 11 ... InB In.. n bits 𝑁 = 2 𝑛 states
- 8. Logic Gates InA InB Out f
- 9. Logic Gates InA InB Out f InA InB Out 0 0 1 0 1 1 1 0 1 1 1 0 NAND-Gate
- 10. A problem: Password cracking ************ Launch Missile Forgot your pasword?
- 11. A Password Checking Function InA InB Out fj 𝑓 = 0 𝑖 ≠ 𝑗 1 𝑖 = 𝑗 𝑖, 𝑗 ∈ 00 … 000,00 … 001, … , 11 … 111 In.. ... 𝑁=2𝑛possibilities
- 12. A Cracking Algorithm 1. Set register state to i = 00000...0 2. Calculate f(i) 3. If f(i)= 1, return i as solution 4. If not, increment i by 1 and go to (2)
- 13. Time Complexity of our Algorithm search space size - N numberofevaluationsoff
- 14. Quantum Computing
- 15. Quantum Bit / Qubit |0> Qubit Two-Level Atom |1>
- 16. Quantum Superposition |0> |1> |𝜓 = 𝑎|0 + 1 − 𝑎 ∙ 𝑒 𝑖𝜑 |1
- 17. How to imagine superposition http://en.wikipedia.org/wiki/Double-slit_experiment#mediaviewer/File:Doubleslit3Dspectrum.gif
- 18. Quantum Measurements |0> |1> |𝜓 = 𝑎|0 + 1 − 𝑎 ∙ 𝑒 𝑖𝜑 |1 0 1
- 19. Quantum Measurements 0 1 |0> |𝜓 =|0 ; probability = a
- 20. Quantum Measurements 0 1 |1> |𝜓 =|1 ; probability = 1-a
- 21. QuBit Registers ... |𝐴 |𝐵 |𝑍 |𝐴 |𝐵 … |𝑍
- 22. QuBit Registers ... |𝐴 |𝐵 |𝑍 |𝐴𝐵 … 𝑍
- 23. Multi-Qubit Superpositions ... 0.51/2 |0 + |1 0.51/2 |0 + |1 0.51/2 |0 + |1 0.5 𝑛/2 |0 + |1 … |0 + |1 n times
- 24. Multi-Qubit Superpositions ... 0.51/2 |0 + |1 0.51/2 |0 + |1 0.51/2 |0 + |1 𝑁 = 2 𝑛 states in superposition 0.5 𝑛/2 |00 … 0 + ⋯ + |11 … 1
- 25. Multi-Qubit Superpositions omitting normalizations ... |0 + |1 |0 + |1 |0 + |1 |00 … 0 + ⋯ + |11 … 1
- 26. Quantum Gates 𝑓 ... |0 … 00 ∙ 𝑓(0 … 00) + |0 … 01 ∙ 𝑓(0 … 01) +… + |1 … 11 ∙ 𝑓(1 … 11) |0 + |1 |0 + |1 |0 + |1
- 27. Quantum Entanglement 0 1 |0 |01 + |10 𝑓 𝑓(|01 ) = |01 + |10 |1 |0|1
- 28. Summary: Qubits Quantum-mechanical two-level system Can be in a superposition state |𝟎 + |𝟏 A measurement will yield either 0 or 1 and project the qubit into the respective state Can become entangled with other qubits
- 29. Back to business... ************ Launch Missile Wrong password!
- 30. Quantum Searching our Password |0 … 000 + |0 … 010 +|01 … 10𝟏 + |1 … 110 𝑓𝑗 ... |0 + |1 |0 + |1 |0 + |1
- 31. But how we get the solution? 𝑟𝑒𝑠𝑢𝑙𝑡 = 01 … 10𝟏 𝑝 = 1 𝑁 ∗∗ ⋯ ∗∗ 𝟎 𝑝 = 1 − 1 𝑁 fj ... |0 + |1 |0 + |1 |0 + |1 0 1 0 1 0 1 0 1
- 32. |0 + |1 |0 + |1 |0 + |1 Solution: Grover Algorithm fj Grover Operator ... 0 1 0 1 0 1 0 1 repeat 𝑁 times 𝑟𝑒𝑠𝑢𝑙𝑡 = 01 … 10𝟏 𝑝 ≈ 1 ∗∗ ⋯ ∗∗ 𝟎 𝑝 ≈ 0 Grover L.K.: A fast quantum mechanical algorithm for database search, Proceedings, 28th Annual ACM Symposium on the Theory of Computing, 1996
- 33. Efficiency of Grover Search (for 10 qubits) N = 1024 25 iterations required
- 34. Time Complexity Revisited search space size – N numberofevaluationsoff quantum speed-up
- 35. Number Factorization: Shor Alg. problem size – n (number of bits) Runtime 𝑟 = 𝑞 ∙ 𝑠; q,s prime numbers
- 36. How to Build a Quantum Processor?
- 37. photo not CC-licensed photo not CC-licensed University of Innsbruck (http://www.quantumoptics.at/) University of Santa Barbara (http://web.physics.ucsb.edu/~martinisgroup/) ...and many more technologies: Nuclar magnetic resonance, photonic qubits, quantum dots, electrons on superfluid helium, Bose-Einstein condensates... Ion Trap Quantum Processors Superconducting Quantum Processors
- 38. a) 100 m 1 mm A Simple Two-Qubit Processor Using superconducting qubits (Transmons - Wallraff et al., Nature 431 (2004) ) 1m 38 Dewes et al. Phys. Rev. Lett. 108, 057002 (2012)
- 39. thermally anchor and shield from EM fields mount on microwave PCB and wirebond 39 * 20 mK putindilutioncryostat
- 40. |0> |0> Y/2 Y/2 iSWAP Z-/2 Z-/2 iSWAP X/2 X/2 Readout 0 1 0 1 Y(/2) readout 50 100 150 200 ns f01[f(t)],a(t) 0 iSWAP iSWAP Z(/2) X(/2) Running Grover-Search for 2 Qubits Calculate fj Apply Grover operator 40 Prepare superposition
- 41. Dewes et. al., PRB Rapid Comm 85 (2012) |0> |0> Y/2 Y/2 iSWAP Z±/2 Z±/2 iSWAP X/2 X/2 0 1 0 1 67 % 55 % 62 % 52 % f00 f01 f10 f11 Single-Run Success Probability 41 classical benchmark (with "I'm feeling lucky" bonus) ReadoutCalculate fj Apply Grover operatorPrepare superposition
- 42. Challenges Decoherence Environment measures and manipulates the qubit and destroys its quantum state. Gate Fidelity & Qubit-Qubit Coupling Difficult to reliably switch on & off qubit-qubit coupling with high precision for many qubits And some more: High-Fidelity state measurement, qubit reset, ...
- 43. Recent Trends in Superconducting Quantum Computing
- 44. Better Qubit Architectures Better Qubits and Resonators Quantum Error Correction Hybrid Quantum Systems (photos not included since not CC-BY licensed)
- 45. Moore's Law: Quantum Edition (for superconducting qubits) 1 10 100 1000 10000 100000 1000000 1998 2000 2002 2004 2006 2008 2010 2012 2014 coherencetime-ns year Superconducting Qubits: Reported Coherence Time (T) Cooper pair box Quantronium Circuit QED 3D Cavities
- 46. Summary Quantum computers are coming! ...but still there are many engineering challenges to overcome... Bad News Likely that governments and big corporations will be in control of QC in the short term.
- 47. Thanks! More "quantum information": Diamonds are a quantum computer’s best friend – Tomorrow, 30.12 at 12:45h in Hall 6 by Nicolas Wöhrl Get in touch with me: ich@andreas-dewes.de // @japh44

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