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Copyright©D-WaveSystemsInc. 1
• IntroductiontoQuantumComputing• D-WaveBackground• D-WaveSystem• ProgrammingEnvironment• PotentialApplications
Topics
Copyright©D-WaveSystemsInc. 2
“Virtual”QUBO
qbsolv
D-WaveSoftwareEnvironment
LANLAssembler
Environment/Libraries
1QbitSDK
JADE/QuellE…
QUBOINTERMEDIATE
REPRESENTATION
TARGET SYSTEM
HOST LIBRARY AND COMMAND
LINE INTERFACEC,C++,MATLABPython DW
SAPI SYSTEM INTERFACE AND
CONTROL
TRANSLATORSQSAGE
OptimizationConstraintSatisfaction
ToQ
SamplingSAT,ML
?l l l
QUANTUM MACHINE INSTRUCTIONQMI
APPLICATIONS
“QUORTRAN” COMPILERS“Q++”
PRODUCT PROTOTYPE CONCEPT
Copyright©D-WaveSystemsInc. 3
The systemsamples fromthe𝑞"thatminimizetheobjective
QUBIT 𝒒𝒊Quantum bitwhichparticipatesinannealingcycleandsettlesintooneoftwopossiblefinalstates: 0,1
COUPLER 𝒒𝒊𝒒)Physical devicethatallowsonequbit toinfluenceanotherqubit
WEIGHT 𝒂𝒊
Real-valued constantassociatedwitheachqubit,whichinfluencesthequbit’s tendencytocollapseintoitstwopossiblefinalstates;controlledbytheprogrammer
STRENGTH 𝒃𝒊𝒋Real-valuedconstantassociatedwitheachcoupler, whichcontrolstheinfluenceexertedbyonequbit onanother;controlledbytheprogrammer
OBJECTIVE 𝑂𝑏𝑗Real-valuedfunctionwhichisminimizedduringtheannealingcycle
𝑶𝒃𝒋(𝒂𝒊,𝒃𝒊𝒋; 𝒒𝒊) =5𝒂𝒊𝒊
𝒒𝒊 +5𝒃𝒊𝒋𝒒𝒊𝒊𝒋
𝒒𝒋
Copyright©D-WaveSystemsInc. 4
Weights- 𝑎"Strengths- 𝑏"8
QuantumProcessor
Qubits- 𝑞"
QuantumMachineInstruction(QMI)
TheQMIforthe1000-qubitchiphas(nominally):
TotalsizeoftheQMIis1152+2304+1056=4412parameters
Eachparametercanbespecified toabout4-5bitsofprecision
qubit weights intracell couplerstrengths intercell couplerstrengths
8percellx 12x12 16percellx12x12 2directionsx4x 12x11
1152 2304 1056
Qubits- 𝑞"Qubits- 𝑞"Qubits- 𝑞"AnnealingCycles
Copyright©D-WaveSystemsInc. 5
Generation L,M,N Qubits Couplers QMIcoefficients
Simulator 4,4,4 128 352 480
Rainier 4,4,4 128 352 480
Vesuvius 4,8,8 512 1472 1984
W1K 4,12,12 1K 3K 4K
W2K 4,16,16 2K 6K 8K
Chimera L,M,N 2𝐿𝑀𝑁 𝐿=𝑀𝑁 + 𝐿 𝑀− 1 𝑁+𝐿𝑀(𝑁 − 1)
2𝐿𝑀𝑁+ 𝐿=𝑀𝑁+𝐿 𝑀 − 1 𝑁+ 𝐿𝑀(𝑁 − 1)
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
M
N
UnitCellL L
column cross
Copyright©D-WaveSystemsInc. 6
ProgrammingEnvironment
• OperatesinahybridmodewithaHPCSystemorDataAnalyticEngineactingasaco-processororaccelerator
• D-Wavesystemis“front-ended”onanetworkbyastandardserver
• UserformulatesproblemasaseriesofQuantumMachineInstructions(QMIs)
• FrontendsendsQMItoquantumprocessor(QP)• QPstartstosamplefromthedistributionofbit-stringsdefinedbytheQMI
• Resultsarereturnedtothefront-endandontotheuser
Copyright©D-WaveSystemsInc. 7
Copyright©D-WaveSystemsInc. 8
Example:4-coloringCanada’sprovinces
Copyright©D-WaveSystemsInc. 9
Canadarepresentedasagraph
AB AlbertaBC British ColumbiaMB ManitobaNB New BrunswickNL Newfoundland and LabradorNS Nova ScotiaNT Northwest TerritoriesNU NunavutON OntarioPE Prince Edward IslandQC QuebecSK SaskatchewanYT Yukon
NU MB ON QC NL
NS
PE
BC AB
NBSKYTNT
Copyright©D-WaveSystemsInc. 10
Needle&Haystack:ColoringCanada
#ofcolors Needle Haystack N/H
3 1728 3@A = 1.6x10E 0.0011
4 653184 4@A = 6.7x10H 0.0097
(nottoscale)
Copyright©D-WaveSystemsInc. 11
Encodecolorsandprovincesviaqubits
• Pickunaryencodingforsimplicity:– 13regions
– 4colors(Blue,Green,Red,Yellow)
– Create13x4=52logicalqubits
• BuildQMIwiththesefourtasks:1. Turnonexactlyoneofthefourcolorqubits foreachregion
2. Maplogicalcolorqubits foraregiontophysicalqubits ofaunitcell
3. Useintercell couplerstoenforceneighborconstraints
4. Cloneregionsasnecessary sothatCanadacanembedintoaplanargrid
• EachtaskcontributesaportionofthefinalQMI• AddindividualcontributionstogetthetotalQMI
Copyright©D-WaveSystemsInc. 12
Task1:turnononeoffourcolorqubits
Objective:𝑶 𝒒𝒃,𝒒𝒈,𝒒𝒓, 𝒒𝒚 = 𝒒𝒃 + 𝒒𝒈 + 𝒒𝒓 + 𝒒𝒚 − 𝟏 𝟐 ≅−𝟏(𝒒𝒃 + 𝒒𝒈 + 𝒒𝒓 + 𝒒𝒚)
+𝟐(𝒒𝒃𝒒𝒈 + 𝒒𝒃𝒒𝒓 + 𝒒𝒃𝒒𝒚 + 𝒒𝒈𝒒𝒓 + 𝒒𝒈𝒒𝒚 + 𝒒𝒓𝒒𝒚)
Bluequbit GreenqubitQ QC
Yellowqubit RedqubitQ QC
C CC
C
Copyright©D-WaveSystemsInc. 13
Task2:embedlogicaltophysicalqubits
Q QC
Q QC
C CC
C
logical
physical
B
G
R
Y
Copyright©D-WaveSystemsInc. 14
Task3:Intercellcouplersconstrainneighbors
BritishColumbia Alberta
B
G
R
Y
AlbertaBritishColumbia
Copyright©D-WaveSystemsInc. 15
Task4:Cloneregionsforplanarembedding
AlbertaBritishColumbia
NorthwestTerritories
BC AB
NT NT
Copyright©D-WaveSystemsInc. 16
Colorsencodedinunitcells
Copyright©D-WaveSystemsInc. 17
Scalingup...
• Wecannotfitallthestatesintounitcellsofthechip…• …soweadoptadivide-and-conquerstrategy
DividetheUSmapintochunks.Processthefirstchunkandgetvalidcoloringsforthefirstchunkofstates.Usethesecoloringstobiasthesecondchunk.Repeat.
chunk1 chunk2 chunk3
Copyright©D-WaveSystemsInc. 18
...andup...
254countiesinTexas
Copyright©D-WaveSystemsInc. 19
...andup3108UScounties
Copyright©D-WaveSystemsInc. 20
Implementationsofmapcoloring
QMI: weights strengths
C ToQ
Snippet(28of596LOC) entireprogram
Copyright©D-WaveSystemsInc. 21
• Algorithmsarebeingdiscoveredformappingapplicationstoadiabaticquantumcomputers
• Thesealgorithmsarebeingturnedintosoftwaretools
• ThisisgreatlyimprovingprogrammerproductivityintheAQCenvironment...
• ...andclosingthegapbetweenapplicationsandAQCpower
Copyright©D-WaveSystemsInc. 22
ThankYou
Questions?
DennyDahl
ddahl@dwavesys.com
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