1. 1 © Copyright 2007 D-Wave Systems, Inc. Progress in Quantum Computing panel presentation slides Supercomputing 2007 Reno, Nevada November 15 th, 2007 1:30pm—3:00pm Image matching with a 28-qubit superconducting quantum computer

2. 2 © Copyright 2007 D-Wave Systems, Inc. Image matching technical leads Image matching algorithms and applications Dr. Hartmut Neven, Technical Lead Manager neven@google.com Quantum computing algorithms and hardware Dr. Geordie Rose, Chief Technology Officer rose@dwavesys.com

3. 3 © Copyright 2007 D-Wave Systems, Inc. Prologue: D-Wave Only pure play company in two categories: quantum computation and superconducting computing systems Best financed & largest effort in both categories More granted US QC patents than all other corporations (IBM, Microsoft, HP, NEC, …) combined Empirical high-throughput philosophy; Eight full processor design cycles completed so far in 2007 Core technical team TRW, NASA, JPL, MDA, Kodak, Electronic Arts, LSI Logic, top computer science & physics research scientists

4. 4 © Copyright 2007 D-Wave Systems, Inc. Overview Our system: The problem we solve How superconducting AQCs work: Some physics Case study: Solving image matching problems with a D-Wave quantum computing system

5. 5 © Copyright 2007 D-Wave Systems, Inc. Demo system is a web services QUBO solver Quadratic Unconstrained Binary Optimization: Minimize E over binary variables x i ; h i & J ij  

6. 6 © Copyright 2007 D-Wave Systems, Inc. High-level systems architecture User data Local solver engineQuantum computer QUBO out Solution returned

7. 7 © Copyright 2007 D-Wave Systems, Inc. Under the Hood: D-Wave quantum processors

8. 8 © Copyright 2007 D-Wave Systems, Inc. A problem with a split personality QUBO is equivalent to the two-dimensional Ising model in a magnetic field (2DIMM) problem

9. 9 © Copyright 2007 D-Wave Systems, Inc. What this problem means to a computer scientist QUBO is NP-hard ; the decision version is NP-complete Few technical terms have gained such rapid notoriety as the appellation “NP-complete”. In the short time since its introduction in the early 1970s, this term has come to symbolize the abyss of inherent intractability that algorithm designers increasingly face as they seek to solve larger and more complex problems. Computers and Intractability: A Guide to the Theory of NP-Completeness Michael R. Garey and David S. Johnson

10. 10 © Copyright 2007 D-Wave Systems, Inc. The Ising model tries to imitate behaviour in which individual elements (e.g., atoms, animals, protein folds, biological membrane, social behavior, etc.) modify their behavior so as to conform to the behavior of other individuals in their vicinity… More than 12,000 papers have been published between 1969 and 1997 using the Ising model. http://scienceworld.wolfram.com/physics/IsingModel.html What this problem means to a physicist Model for describing real physical systems

11. 11 © Copyright 2007 D-Wave Systems, Inc. Core concept: Use (quantum) physics to do math Deep connection between hard math problem and fundamental laws of nature Build an “analog computer” at the ultimate limits of what is possible… any computer that could do better would violate the laws of physics Math Physics

12. 12 © Copyright 2007 D-Wave Systems, Inc. Our approach: Superconducting adiabatic quantum computer Extremely fast: Special purpose processor; superconducting electronics are naturally fast (700+ GHz) Extremely low power: In principle reversible (zero heat generation); in practice power consumption & heat generation drastically reduced (factors of millions) At the limits of physics: Universal quantum computer… can’t do better

13. 13 © Copyright 2007 D-Wave Systems, Inc. Device schematic: Niobium CJJ RF-SQUID flux qubit Qubit loop Compound Josephson junction (CJJ) loop Two currents in One current out

14. 14 © Copyright 2007 D-Wave Systems, Inc.

15. 15 © Copyright 2007 D-Wave Systems, Inc. Potential energy: cosine + parabola Device physics: The Hamiltonian

16. 16 © Copyright 2007 D-Wave Systems, Inc. Potential energy can be programmed by user E

17. 17 © Copyright 2007 D-Wave Systems, Inc. Qubit manipulation:  c modulates barrier height

18. 18 © Copyright 2007 D-Wave Systems, Inc. Qubit manipulation:  x tilts double well

19. 19 © Copyright 2007 D-Wave Systems, Inc. |0> |1> Readout basis: Direction of circulating current

20. 20 © Copyright 2007 D-Wave Systems, Inc. Device schematic: Symmetric bipolar coupler

21. 21 © Copyright 2007 D-Wave Systems, Inc.

22. 22 © Copyright 2007 D-Wave Systems, Inc. Models of computation:\\adiabatic quantum computation Computer initialized in “easy to reach” (convex) ground state Answer encoded in final state All currents adjusted slowly enough so that system remains in ground state at all times AQC can be universal for QC AQC is exact by definition

23. 23 © Copyright 2007 D-Wave Systems, Inc. Models of computation:\\quantum annealing Computer initialized in ground state Answer encoded in final state All currents adjusted over period of time fixed by user QA is a heuristic algorithm

24. 24 © Copyright 2007 D-Wave Systems, Inc. Processor designed to enable AQC/QA

25. 25 © Copyright 2007 D-Wave Systems, Inc. Problem Hamiltonian = desired QUBO

26. 26 © Copyright 2007 D-Wave Systems, Inc. A simple operating prescription 1.Set CJJ biases to maximally lower barriers 2.Raise {h,J} biases to target values 3.Ramp CJJ biases to large barriers 4.Read out qubits

27. 27 © Copyright 2007 D-Wave Systems, Inc. Image matching This is hard: Automated object recognition is a foundational artificial intelligence problem known to be very difficult for designed (as opposed to evolved) computers

28. 28 © Copyright 2007 D-Wave Systems, Inc. Image matching Given two images

29. 29 © Copyright 2007 D-Wave Systems, Inc. Image matching Identify interest points in each image

30. 30 © Copyright 2007 D-Wave Systems, Inc. Image matching Generate local description of all interest points (local wavelet transform  feature vectors) j

31. 31 © Copyright 2007 D-Wave Systems, Inc. Image matching Define point-wise similarity between interest point j in image 1 and interest point  in image 2 to be inner product of feature vectors j 

32. 32 © Copyright 2007 D-Wave Systems, Inc. Image matching Generate relational description of all pairs of interest points j k

33. 33 © Copyright 2007 D-Wave Systems, Inc. Image matching Define relational compatibility of a pair (j,k) from first image and a pair ( ,  ) from second image

34. 34 © Copyright 2007 D-Wave Systems, Inc. Image matching as a QUBO Quadratic Unconstrained Binary Optimization problem: Minimize E over binary variables x [ i,  ] The set of all pairs {i  G 1,  G 2 } where x [ i,  ] =1 gives the region and size of maximum overlap Favors point-wise similarityFavors relational compatibility

35. 35 © Copyright 2007 D-Wave Systems, Inc. Show Demo

36. 36 © Copyright 2007 D-Wave Systems, Inc. Summary of preliminary results A set of progressively more powerful superconducting quantum processors have been built Next generation Q3/2008 targets competition with incumbent QUBO solver methods (500+ qubits) Web services architecture operational at several levels of abstraction from hardware; APIs documented and available