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Let's Build a Quantum Computer!

Dive into the world of quantum computing to understand its significance, quantum algorithms, building processors, and recent advancements in architectures and error correction. Learn about quantum bits, superposition, measurements, entanglement, and algorithms like Grover and Shor. Exploring quantum processor technologies, challenges, trends, and the future of quantum computing. Exciting possibilities await as quantum computers revolutionize computation.

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Let's Build a Quantum Computer!

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  1. Let's Build a Quantum Computer! 31C3 29/12/2014 Andreas Dewes Acknowledgementsgoto "Quantronics Group", CEA Saclay. R. Lauro, Y. Kubo, F. Ong, A. Palacios-Laloy, V. Schmitt PhDAdvisors: Denis Vion, Patrice Bertet, Daniel Esteve

  2. Motivation

  3. Outline Quantum Computing Whatisit & why do wewantit Quantum Algorithms Crackingpasswordswithquantumcomputers Building A Simple Quantum Processor Superconductors, Resonators, Microwaves Recent Progress in Quantum Computing Architectures, Error Correction, Hybrid Systems

  4. Why Quantum Computing? Quantum physicscannotbesimulatedefficientlywith a classical computer.1) A computerthatmakesuseofquantummechanicscan do it. Itcan also befasterforsomeothermathematicalproblems. 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 0 V 5 V

  7. Bit Registers InA InB nbits ... In.. states

  8. Logic Gates InA f InB Out

  9. Logic Gates NAND-Gate InA f InB Out

  10. A problem: Password cracking ************ Launch Missile Forgotyourpasword?

  11. A Password CheckingFunction InA fj InB possibilities ... In.. Out

  12. A CrackingAlgorithm Set registerstatetoi = 00000...0 Calculatef(i) Iff(i)= 1, returniassolution If not, incrementiby1andgoto (2)

  13. Time ComplexityofourAlgorithm O(N) numberofevaluationsoff searchspacesize - N

  14. Quantum Computing

  15. Quantum Bit / Qubit |1> |0> QubitTwo-Level Atom

  16. Quantum Superposition |1> |0>  =

  17. Howtoimaginesuperposition http://en.wikipedia.org/wiki/Double-slit_experiment#mediaviewer/File:Doubleslit3Dspectrum.gif

  18. Quantum Measurements 0 1 |1> |0> =

  19. Quantum Measurements 0 1 |0> = ; probability = a

  20. Quantum Measurements 0 1 |1> = ; probability = 1-a

  21. QuBit Registers ...

  22. QuBit Registers ...

  23. Multi-QubitSuperpositions ... n times

  24. Multi-QubitSuperpositions ... states in superposition

  25. Multi-QubitSuperpositionsomittingnormalizations ...

  26. Quantum Gates ... +

  27. Quantum Entanglement 0 1

  28. Summary: Qubits Quantum-mechanicaltwo-level system Can be in a superpositionstate A measurement will yieldeither0or1andprojectthequbitintotherespectivestate Can becomeentangledwithotherqubits

  29. Back tobusiness... ************ Launch Missile Wrongpassword!

  30. Quantum Searchingour Password ... +

  31. But howwegetthesolution? 0 0 0 0 1 1 1 1 fj ... 

  32. Solution: GroverAlgorithm repeat times 0 0 0 0 1 1 1 1 Grover Operator fj ...  Grover L.K.: A fast quantummechanicalalgorithmfordatabasesearch, Proceedings, 28th Annual ACM Symposium on theTheoryof Computing, 1996

  33. Efficiency ofGrover Search(for 10 qubits)  25iterations required N = 1024

  34. Time ComplexityRevisited classicalalgorithm - O numberofevaluationsoff quantum speed-up O GroverAlgorithm searchspacesize – N

  35. NumberFactorization: Shor Alg. q,sprime numbers classicalalgorithm – exp(1.9log[N]1/3log[log[n]]2/3) Runtime Shoralgorithm – log(n)3 problemsize – n (numberofbits)

  36. HowtoBuild a Quantum Processor?

  37. photo not CC-licensed photo not CC-licensed University of Innsbruck (http://www.quantumoptics.at/) University ofSanta Barbara (http://web.physics.ucsb.edu/~martinisgroup/) Ion Trap Quantum Processors Superconducting Quantum Processors ...andmanymoretechnologies: Nuclarmagneticresonance, photonicqubits, quantumdots, electrons on superfluid helium, Bose-Einstein condensates...

  38. 38 A Simple Two-QubitProcessorUsingsuperconductingqubits (Transmons -Wallraffet al., Nature 431 (2004) ) a) 1 mm 100 m 1m Deweset al. Phys. Rev. Lett. 108, 057002 (2012)

  39. 39 mount on microwave PCB andwirebond put in dilutioncryostat * 20 mK thermallyanchorand shieldfrom EM fields

  40. 40 RunningGrover-Search for 2 Qubits Preparesuperposition Calculatefj ApplyGroveroperator Readout 0 0 1 1 Y/2 iSWAP Z-/2 iSWAP X/2 |0> |0> Y/2 Z-/2 X/2 readout Z(p/2) Y(p/2) iSWAP iSWAP X(p/2) f01[f(t)],a(t) 50 100 150 200 ns 0

  41. 41 Single-Run SuccessProbability Preparesuperposition Calculatefj ApplyGroveroperator Readout 0 0 1 1 Y/2 iSWAP Z±/2 iSWAP X/2 |0> 67 % |0> Y/2 Z±/2 X/2 f00 f01 f10 f11 62 % 55 % 52 % classical benchmark (with "I'm feeling lucky" bonus) Dewes et. al.,PRB RapidComm85 (2012)

  42. Challenges Decoherence Environment measuresandmanipulatesthequbitanddestroysitsquantumstate. Gate Fidelity & Qubit-QubitCoupling Difficulttoreliablyswitch on & off qubit-qubitcouplingwith high precisionformanyqubits Andsomemore: High-Fidelitystatemeasurement, qubitreset, ...

  43. Recent Trends in SuperconductingQuantum Computing

  44. BetterQubitArchitectures BetterQubitsand Resonators Quantum Error Correction Hybrid Quantum Systems (photos not includedsince not CC-BY licensed)

  45. Moore's Law: Quantum Edition(forsuperconductingqubits) 3D Cavities Circuit QED Quantronium Cooper pair box

  46. Summary Quantum computersarecoming! ...but still therearemanyengineeringchallengestoovercome... Bad News Likelythatgovernmentsandbigcorporations will be in controlof QC in theshortterm.

  47. Thanks! More "quantuminformation": Diamonds are a quantum computer’s best friend – Tomorrow, 30.12 at 12:45h in Hall 6 by Nicolas Wöhrl Get in touchwithme: ich@andreas-dewes.de // @japh44

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