Quantum Computing and D-Wave

Quantum Computing and D-Wave
May 2016

© 2016 D-Wave Systems Inc. All Rights Reserved | 2
Electronics April 19, 1965

Moore’s Law

But, Moore’s Law Seems to be Slowing Down
www.economist.com/technology-quarterly/2016-03-12/after-moores-law

Predictions for the End of Moore’s Law

“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

Richard Feynman
1960 1970 1980 1990 2000 2010 2020

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

Binary
Separable
Barriers
Characteristics of Classical Digital Systems

Quantum Effects on D-Wave Systems
Superposition
Entanglement
QuantumTunneling

QuantumTuring Machine
1950 1960 1970 1980 1990 2000 2010

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

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

Original Simulated Annealing Paper
1950 1960 1970 1980 1990 2000 2010

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

MIT Group Proposes Adiabatic QC
1960 1970 1980 1990 2000 2010 2020

Quantum Hamiltonian is an operator on Hilbert
space:
ℋ = ℰ + + Δ
Corresponding classical optimization problem:
Obj( , ; ) = +
Quantum Enhanced Optimization

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

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

Mission
To help solve the most challenging problems
in the multiverse:
• Optimization
• Machine Learning
• Monte Carlo/Sampling

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!

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

D-Wave Container -“SCIF-like” - No RF
Interference

System Shielding
• 16 Layers between the quantum chip
and the outside world
• Shielding preserves the quantum
calculation

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

D-Wave 2X Quantum Processor
Qubits within red boxes

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

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

D-Wave Software Environment

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
# ( , ; ) = +

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

Colors encoded in unit cells

Example: 4-coloring Canada’s provinces

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

Task 1: turn on one of four color qubits
Objective : # , $, %, & = + $ + % + & − (
)
≅
−(( + $ + % + &)
+)( $ + % + & + $ % + $ & + % &)
Blue qubit Green qubitQ QC
Yellow qubit Red qubitQ QC
C C
C
C

Task 2: embed logical to physical qubits
Q QC
Q QC
C C
C
C
logical
physical
B
G
R
Y

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

...and up...
254 counties inTexas

...and up
3108 US counties

Implementations of map coloring
QMI : weights strengths
C ToQ
Snippet (28 of 596 LOC) entire program

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

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

Sorting Networks forTSP
N=16 Bose-Nelson network:
65 qubits permute 16 inputs

Parallel update

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

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)!

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.

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

Quantum Computing and D-Wave

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