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Quantum Computing and D-Wave
May 2016
© 2016 D-Wave Systems Inc. All Rights Reserved | 2
Electronics April 19, 1965
© 2016 D-Wave Systems Inc. All Rights Reserved | 3
Moore’s Law
© 2016 D-Wave Systems Inc. All Rights Reserved | 4
But, Moore’s Law Seems to be Slowing Down
www.economist.com/technology-...
© 2016 D-Wave Systems Inc. All Rights Reserved | 5
Predictions for the End of Moore’s Law
© 2016 D-Wave Systems Inc. All Rights Reserved | 6
“The number of people predicting the death
of Moore’s law doubles every...
© 2016 D-Wave Systems Inc. All Rights Reserved | 7
© 2016 D-Wave Systems Inc. All Rights Reserved | 8
Richard Feynman
1960 1970 1980 1990 2000 2010 2020
© 2016 D-Wave Systems Inc. All Rights Reserved | 9
What is a Quantum Computer?
• Exploits quantum mechanical effects
• Bui...
© 2016 D-Wave Systems Inc. All Rights Reserved | 10
Binary
Separable
Barriers
Characteristics of Classical Digital Systems
© 2016 D-Wave Systems Inc. All Rights Reserved | 11
Quantum Effects on D-Wave Systems
Superposition
Entanglement
QuantumTu...
© 2016 D-Wave Systems Inc. All Rights Reserved | 12
QuantumTuring Machine
1950 1960 1970 1980 1990 2000 2010
© 2016 D-Wave Systems Inc. All Rights Reserved | 13
Algorithms
• David Deutsch (1992): Determine whether f: {0,1}n→
{0,1} ...
© 2016 D-Wave Systems Inc. All Rights Reserved | 14
Quantum Information Science
Quantum
Computing
Gate Model
Adiabatic
Top...
© 2016 D-Wave Systems Inc. All Rights Reserved | 15
Original Simulated Annealing Paper
1950 1960 1970 1980 1990 2000 2010
© 2016 D-Wave Systems Inc. All Rights Reserved | 16
QuantumAnnealingOutlined byTokyoTech
PHYSICAL REVIEW E VOLUME 58, NUMB...
© 2016 D-Wave Systems Inc. All Rights Reserved | 17
MIT Group Proposes Adiabatic QC
1960 1970 1980 1990 2000 2010 2020
© 2016 D-Wave Systems Inc. All Rights Reserved | 18
Quantum Hamiltonian is an operator on Hilbert
space:
ℋ = ℰ + + Δ
Corre...
© 2016 D-Wave Systems Inc. All Rights Reserved | 19
Energy Landscape
• Space of solutions
defines an energy
landscape & be...
© 2016 D-Wave Systems Inc. All Rights Reserved | 20
Company Background
• Founded in 1999
• World’s first quantum computing...
© 2016 D-Wave Systems Inc. All Rights Reserved | 21
Mission
To help solve the most challenging problems
in the multiverse:...
© 2016 D-Wave Systems Inc. All Rights Reserved | 22
Intel 64 D-Wave
Performance (GFLOPS) ~20 (12 cores) 0
Precision (bits)...
1000+ qubits
Performance: up to 600X
Synthetic cases –
100,000,000X
Power: <25 kW
Three orders:
Google/NASA
LANL
Lockheed ...
© 2016 D-Wave Systems Inc. All Rights Reserved | 24
D-Wave Container -“SCIF-like” - No RF
Interference
© 2016 D-Wave Systems Inc. All Rights Reserved | 25
System Shielding
• 16 Layers between the quantum chip
and the outside ...
© 2016 D-Wave Systems Inc. All Rights Reserved | 26
Processor Environment
• Cooled to 0.015 Kelvin, 175x colder
than inter...
© 2016 D-Wave Systems Inc. All Rights Reserved | 27
D-Wave 2X Quantum Processor
Qubits within red boxes
© 2016 D-Wave Systems Inc. All Rights Reserved | 28
Processing Using D-Wave
• A lattice of superconducting loops (qubits)
...
© 2016 D-Wave Systems Inc. All Rights Reserved | 29
Programming Environment
• Operates in a hybrid mode with a HPC System ...
© 2016 D-Wave Systems Inc. All Rights Reserved | 30
D-Wave Software Environment
© 2016 D-Wave Systems Inc. All Rights Reserved | 31
Programming Model
The system samples from the 	that minimize the objec...
© 2016 D-Wave Systems Inc. All Rights Reserved | 32
Size and shape of a QMI
Weights -
Strengths -
Quantum
Processor
Qubits...
© 2016 D-Wave Systems Inc. All Rights Reserved | 33
Colors encoded in unit cells
© 2016 D-Wave Systems Inc. All Rights Reserved | 34
Example: 4-coloring Canada’s provinces
© 2016 D-Wave Systems Inc. All Rights Reserved | 35
Canada represented as a graph
AB Alberta
BC British Columbia
MB Manito...
© 2016 D-Wave Systems Inc. All Rights Reserved | 36
Task 1: turn on one of four color qubits
Objective : # , $, %, & = + $...
© 2016 D-Wave Systems Inc. All Rights Reserved | 37
Task 2: embed logical to physical qubits
Q QC
Q QC
C C
C
C
logical
phy...
© 2016 D-Wave Systems Inc. All Rights Reserved | 38
Scaling up...
• We cannot fit all the states into unit cells of the
ch...
© 2016 D-Wave Systems Inc. All Rights Reserved | 39
...and up...
254 counties inTexas
© 2016 D-Wave Systems Inc. All Rights Reserved | 40
...and up
3108 US counties
© 2016 D-Wave Systems Inc. All Rights Reserved | 41
Implementations of map coloring
QMI : weights strengths
C ToQ
Snippet ...
© 2016 D-Wave Systems Inc. All Rights Reserved | 42
Traveling Salesman Problem
Approaches:
1.Direct embedding of QUBO
i. E...
© 2016 D-Wave Systems Inc. All Rights Reserved | 43
Direct Embedding: four cities
• Associate a qubit with each of the six...
© 2016 D-Wave Systems Inc. All Rights Reserved | 44
Sorting Networks forTSP
N=16 Bose-Nelson network:
65 qubits permute 16...
© 2016 D-Wave Systems Inc. All Rights Reserved | 45
Parallel update
© 2016 D-Wave Systems Inc. All Rights Reserved | 46
Discrete Combinatorial Optimization Benchmarks
MedianTime to Find Best...
© 2016 D-Wave Systems Inc. All Rights Reserved | 47
Machine Learning: Binary Classification
• Traditional algorithm
recogn...
© 2016 D-Wave Systems Inc. All Rights Reserved | 48
Google Blog December 8, 2015
http://googleresearch.blogspot.ca/2015/12...
© 2016 D-Wave Systems Inc. All Rights Reserved | 49
The Most Advanced Quantum Computer
in theWorld
Number
of
Qubits
2004 2...
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Quantum Computing and D-Wave

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The presentation slide of D-Wave systems for the conference
"RCO Study Night 「D-Waveが切り開く、量子コンピュータを活用する未来」"
- https://atnd.org/events/76931

Published in: Technology
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Quantum Computing and D-Wave

  1. 1. Quantum Computing and D-Wave May 2016
  2. 2. © 2016 D-Wave Systems Inc. All Rights Reserved | 2 Electronics April 19, 1965
  3. 3. © 2016 D-Wave Systems Inc. All Rights Reserved | 3 Moore’s Law
  4. 4. © 2016 D-Wave Systems Inc. All Rights Reserved | 4 But, Moore’s Law Seems to be Slowing Down www.economist.com/technology-quarterly/2016-03-12/after-moores-law
  5. 5. © 2016 D-Wave Systems Inc. All Rights Reserved | 5 Predictions for the End of Moore’s Law
  6. 6. © 2016 D-Wave Systems Inc. All Rights Reserved | 6 “The number of people predicting the death of Moore’s law doubles every two years.” Peter Lee, a vice-president at Microsoft Research Moore’s Law’s Law
  7. 7. © 2016 D-Wave Systems Inc. All Rights Reserved | 7
  8. 8. © 2016 D-Wave Systems Inc. All Rights Reserved | 8 Richard Feynman 1960 1970 1980 1990 2000 2010 2020
  9. 9. © 2016 D-Wave Systems Inc. All Rights Reserved | 9 What is a Quantum Computer? • Exploits quantum mechanical effects • Built with “qubits” rather than “bits” • Operates in an extreme environment • Enables quantum algorithms to solve very hard problems Quantum Processor
  10. 10. © 2016 D-Wave Systems Inc. All Rights Reserved | 10 Binary Separable Barriers Characteristics of Classical Digital Systems
  11. 11. © 2016 D-Wave Systems Inc. All Rights Reserved | 11 Quantum Effects on D-Wave Systems Superposition Entanglement QuantumTunneling
  12. 12. © 2016 D-Wave Systems Inc. All Rights Reserved | 12 QuantumTuring Machine 1950 1960 1970 1980 1990 2000 2010
  13. 13. © 2016 D-Wave Systems Inc. All Rights Reserved | 13 Algorithms • David Deutsch (1992): Determine whether f: {0,1}n→ {0,1} is constant or balanced using a quantum computer • Daniel Simon (1994): Special case of the abelian hidden subgroup problem • Peter Shor (1994): Given an integer N, find its prime factors • Lov Grover (1996): Search an unsorted database with N entries in O(N1/2) time 1960 1970 1980 1990 2000 2010 2020
  14. 14. © 2016 D-Wave Systems Inc. All Rights Reserved | 14 Quantum Information Science Quantum Computing Gate Model Adiabatic Topological One-way/ cluster state Quantum Cryptography Quantum key distribution Quantum Sensor Quantum information processing Quantum CommunicationEmerging Emerging
  15. 15. © 2016 D-Wave Systems Inc. All Rights Reserved | 15 Original Simulated Annealing Paper 1950 1960 1970 1980 1990 2000 2010
  16. 16. © 2016 D-Wave Systems Inc. All Rights Reserved | 16 QuantumAnnealingOutlined byTokyoTech PHYSICAL REVIEW E VOLUME 58, NUMBER 5 NOVEMBER 1998 Quantum annealing in the transverse Ising model Tadashi Kadowaki and Hidetoshi Nishimori Department of Physics,Tokyo Institute ofTechnology, Oh-okayama, Meguro-ku, Tokyo 152- 8551, Japan (Received 30 April 1998) We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach.The idea is tested by the transverse Ising model, in which the transverse field is a function of time similar to the temperature in the conventional method.The goal is to find the ground state of the diagonal part of the Hamiltonian with high accuracy as quickly as possible.We have solved the time-dependent Schrödinger equation numerically for small size systems with various exchange interactions.Comparison with the results of the corresponding classical (thermal) method reveals that the quantum annealing leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule. [S1063-651X~98!02910-9] 1960 1970 1980 1990 2000 2010 2020
  17. 17. © 2016 D-Wave Systems Inc. All Rights Reserved | 17 MIT Group Proposes Adiabatic QC 1960 1970 1980 1990 2000 2010 2020
  18. 18. © 2016 D-Wave Systems Inc. All Rights Reserved | 18 Quantum Hamiltonian is an operator on Hilbert space: ℋ = ℰ + + Δ Corresponding classical optimization problem: Obj( , ; ) = + Quantum Enhanced Optimization
  19. 19. © 2016 D-Wave Systems Inc. All Rights Reserved | 19 Energy Landscape • Space of solutions defines an energy landscape & best solution is lowest valley • Classical algorithms must walk over this landscape • Quantum annealing uses quantum effects to go through the mountains
  20. 20. © 2016 D-Wave Systems Inc. All Rights Reserved | 20 Company Background • Founded in 1999 • World’s first quantum computing company • Public customers: – Lockheed Martin/USC – Google/NASA Ames – Los Alamos National Lab • Other customer projects done via cloud access to systems in D-Wave’s facilities • 120+ U.S. patents
  21. 21. © 2016 D-Wave Systems Inc. All Rights Reserved | 21 Mission To help solve the most challenging problems in the multiverse: • Optimization • Machine Learning • Monte Carlo/Sampling
  22. 22. © 2016 D-Wave Systems Inc. All Rights Reserved | 22 Intel 64 D-Wave Performance (GFLOPS) ~20 (12 cores) 0 Precision (bits) 64 4-5 MIPS ~12,000 (12 cores) 0.01 Instructions 245+ (A-M) 251+ (N-Z) 1 OperatingTemp. 67.9° C -273° C Power Cons. 100 w +/- ~0 Devices 4B+ transistors 1000 qubits Maturity 1945-2016 ~1950’s But, It Is Fundamentally DifferentThan AnythingYou’ve Ever Done Before!
  23. 23. 1000+ qubits Performance: up to 600X Synthetic cases – 100,000,000X Power: <25 kW Three orders: Google/NASA LANL Lockheed Martin/USC The D-Wave 2X
  24. 24. © 2016 D-Wave Systems Inc. All Rights Reserved | 24 D-Wave Container -“SCIF-like” - No RF Interference
  25. 25. © 2016 D-Wave Systems Inc. All Rights Reserved | 25 System Shielding • 16 Layers between the quantum chip and the outside world • Shielding preserves the quantum calculation
  26. 26. © 2016 D-Wave Systems Inc. All Rights Reserved | 26 Processor Environment • Cooled to 0.015 Kelvin, 175x colder than interstellar space • Shielded to 50,000× less than Earth’s magnetic field • In a high vacuum: pressure is 10 billion times lower than atmospheric pressure • On low vibration floor • <25 kW total power consumption – for the next few generations 15mK
  27. 27. © 2016 D-Wave Systems Inc. All Rights Reserved | 27 D-Wave 2X Quantum Processor Qubits within red boxes
  28. 28. © 2016 D-Wave Systems Inc. All Rights Reserved | 28 Processing Using D-Wave • A lattice of superconducting loops (qubits) • Chilled near absolute zero to quiet noise • User maps a problem into search for “lowest point in a vast landscape” which corresponds to the best possible outcome • Processor considers all possibilities simultaneously to satisfy the network of relationships with the lowest energy • The final state of the qubits yields the answer
  29. 29. © 2016 D-Wave Systems Inc. All Rights Reserved | 29 Programming Environment • Operates in a hybrid mode with a HPC System or Data Analytic Engine acting as a co-processor or accelerator • D-Wave system is “front-ended” on a network by a standard server (Host) • User formulates problem as a series of Quantum Machine Instructions (QMIs) • Host sends QMI to quantum processor (QP) • QP samples from the distribution of bit-strings defined by the QMI • Results are returned to the Host and back to the user
  30. 30. © 2016 D-Wave Systems Inc. All Rights Reserved | 30 D-Wave Software Environment
  31. 31. © 2016 D-Wave Systems Inc. All Rights Reserved | 31 Programming Model The system samples from the that minimize the objective QUBIT Quantum bit which participates in annealing cycle and settles into one of two possible final states: 0,1 COUPLER Physical device that allows one qubit to influence another qubit WEIGHT Real-valued constant associated with each qubit, which influences the qubit’s tendency to collapse into its two possible final states; controlled by the programmer STRENGTH Real-valued constant associated with each coupler, which controls the influence exerted by one qubit on another; controlled by the programmer OBJECTIVE ! " Real-valued function which is minimized during the annealing cycle # ( , ; ) = +
  32. 32. © 2016 D-Wave Systems Inc. All Rights Reserved | 32 Size and shape of a QMI Weights - Strengths - Quantum Processor Qubits - Quantum Machine Instruction (QMI) The QMI for the 1000-qubit chip has (nominally): 1152 qubit weights + 3360 coupler strengths = 4512 parameters Each parameter can be specified to about 3-5% precision Qubits - Qubits - Qubits - Annealing Cycles
  33. 33. © 2016 D-Wave Systems Inc. All Rights Reserved | 33 Colors encoded in unit cells
  34. 34. © 2016 D-Wave Systems Inc. All Rights Reserved | 34 Example: 4-coloring Canada’s provinces
  35. 35. © 2016 D-Wave Systems Inc. All Rights Reserved | 35 Canada represented as a graph AB Alberta BC British Columbia MB Manitoba NB New Brunswick NL Newfoundland and Labrador NS Nova Scotia NT Northwest Territories NU Nunavut ON Ontario PE Prince Edward Island QC Quebec SK Saskatchewan YT Yukon NU MB ON QC NL NS PE BC AB NBSKYT NT
  36. 36. © 2016 D-Wave Systems Inc. All Rights Reserved | 36 Task 1: turn on one of four color qubits Objective : # , $, %, & = + $ + % + & − ( ) ≅ −(( + $ + % + &) +)( $ + % + & + $ % + $ & + % &) Blue qubit Green qubitQ QC Yellow qubit Red qubitQ QC C C C C
  37. 37. © 2016 D-Wave Systems Inc. All Rights Reserved | 37 Task 2: embed logical to physical qubits Q QC Q QC C C C C logical physical B G R Y
  38. 38. © 2016 D-Wave Systems Inc. All Rights Reserved | 38 Scaling up... • We cannot fit all the states into unit cells of the chip… • …so we adopt a divide-and-conquer strategy Divide the US map into chunks. Process the first chunk and get valid colorings for the first chunk of states. Use these colorings to bias the second chunk. Repeat. chunk 1 chunk 2 chunk 3
  39. 39. © 2016 D-Wave Systems Inc. All Rights Reserved | 39 ...and up... 254 counties inTexas
  40. 40. © 2016 D-Wave Systems Inc. All Rights Reserved | 40 ...and up 3108 US counties
  41. 41. © 2016 D-Wave Systems Inc. All Rights Reserved | 41 Implementations of map coloring QMI : weights strengths C ToQ Snippet (28 of 596 LOC) entire program
  42. 42. © 2016 D-Wave Systems Inc. All Rights Reserved | 42 Traveling Salesman Problem Approaches: 1.Direct embedding of QUBO i. Edge variables ii. Permutation matrix 2.Sorting network 3.Perturbation method i. Serial update ii. Parallel update
  43. 43. © 2016 D-Wave Systems Inc. All Rights Reserved | 43 Direct Embedding: four cities • Associate a qubit with each of the six legs • Include a constraint term in the objective to make sure exactly two of the three legs connecting to a city are turned on • Add distance terms to the objective B C DA city 1 city 2 mileage qubit # Albuquerque Boston 2264 1 Albuquerque Charlotte 1628 2 Albuquerque Detroit 1596 3 Boston Charlotte 563 4 Boston Detroit 814 5 Charlotte Detroit 645 6
  44. 44. © 2016 D-Wave Systems Inc. All Rights Reserved | 44 Sorting Networks forTSP N=16 Bose-Nelson network: 65 qubits permute 16 inputs
  45. 45. © 2016 D-Wave Systems Inc. All Rights Reserved | 45 Parallel update
  46. 46. © 2016 D-Wave Systems Inc. All Rights Reserved | 46 Discrete Combinatorial Optimization Benchmarks MedianTime to Find Best Solution 0.001 0.01 0.1 1 10 100 1000 10000 0 100 200 300 400 500 Mediantimetobestsolution(s) Problem size (number of qubits) CPLEX METSTABU AKMAXSAT VESUVIUS 11000 x Timing Benchmark – Smaller is Better D-WAVE II
  47. 47. © 2016 D-Wave Systems Inc. All Rights Reserved | 47 Machine Learning: Binary Classification • Traditional algorithm recognized car about 84% of the time • Google/D-Wave Qboost algorithm implemented to recognize a car (cars have big shadows!) • “Quantum Classifier” was more accurate (94%) and more efficient • Ported quantum classifier back to traditional computer, more accurate and fewer CPU cycles (less power)!
  48. 48. © 2016 D-Wave Systems Inc. All Rights Reserved | 48 Google Blog December 8, 2015 http://googleresearch.blogspot.ca/2015/12/when-can-quantum-annealing-win.html When can Quantum Annealing win? Tuesday, December 08, 2015 Posted by Hartmut Neven, Director of Engineering - During the last two years, the Google Quantum AI team has made progress in understanding the physics governing quantum annealers. We recently applied these new insights to construct proof-of-principle optimization problems and programmed these into the D-Wave 2X quantum annealer that Google operates jointly with NASA. The problems were designed to demonstrate that quantum annealing can offer runtime advantages for hard optimization problems characterized by rugged energy landscapes We found that for problem instances involving nearly 1000 binary variables, quantum annealing significantly outperforms its classical counterpart, simulated annealing. It is more than 108 times faster than simulated annealing running on a single core.
  49. 49. © 2016 D-Wave Systems Inc. All Rights Reserved | 49 The Most Advanced Quantum Computer in theWorld Number of Qubits 2004 2008 2012 2016 D-Wave One 128 qubit D-WaveTwo 512 qubit 28 qubit 16 qubit 4 qubit D-Wave 2X 1000+ qubit 1 10 100 1,000 10,000

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