introduction to quantum computing d-wave background d-wave ... · – 4 colors (blue, green, red,...
TRANSCRIPT
![Page 1: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/1.jpg)
Copyright©D-WaveSystemsInc. 1
• IntroductiontoQuantumComputing• D-WaveBackground• D-WaveSystem• ProgrammingEnvironment• PotentialApplications
Topics
![Page 2: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/2.jpg)
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
![Page 3: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/3.jpg)
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
![Page 4: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/4.jpg)
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
![Page 5: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/5.jpg)
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
![Page 6: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/6.jpg)
Copyright©D-WaveSystemsInc. 6
ProgrammingEnvironment
• OperatesinahybridmodewithaHPCSystemorDataAnalyticEngineactingasaco-processororaccelerator
• D-Wavesystemis“front-ended”onanetworkbyastandardserver
• UserformulatesproblemasaseriesofQuantumMachineInstructions(QMIs)
• FrontendsendsQMItoquantumprocessor(QP)• QPstartstosamplefromthedistributionofbit-stringsdefinedbytheQMI
• Resultsarereturnedtothefront-endandontotheuser
![Page 7: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/7.jpg)
Copyright©D-WaveSystemsInc. 7
![Page 8: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/8.jpg)
Copyright©D-WaveSystemsInc. 8
Example:4-coloringCanada’sprovinces
![Page 9: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/9.jpg)
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
![Page 10: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/10.jpg)
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)
![Page 11: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/11.jpg)
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
![Page 12: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/12.jpg)
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
![Page 13: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/13.jpg)
Copyright©D-WaveSystemsInc. 13
Task2:embedlogicaltophysicalqubits
Q QC
Q QC
C CC
C
logical
physical
B
G
R
Y
![Page 14: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/14.jpg)
Copyright©D-WaveSystemsInc. 14
Task3:Intercellcouplersconstrainneighbors
BritishColumbia Alberta
B
G
R
Y
AlbertaBritishColumbia
![Page 15: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/15.jpg)
Copyright©D-WaveSystemsInc. 15
Task4:Cloneregionsforplanarembedding
AlbertaBritishColumbia
NorthwestTerritories
BC AB
NT NT
![Page 16: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/16.jpg)
Copyright©D-WaveSystemsInc. 16
Colorsencodedinunitcells
![Page 17: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/17.jpg)
Copyright©D-WaveSystemsInc. 17
Scalingup...
• Wecannotfitallthestatesintounitcellsofthechip…• …soweadoptadivide-and-conquerstrategy
DividetheUSmapintochunks.Processthefirstchunkandgetvalidcoloringsforthefirstchunkofstates.Usethesecoloringstobiasthesecondchunk.Repeat.
chunk1 chunk2 chunk3
![Page 18: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/18.jpg)
Copyright©D-WaveSystemsInc. 18
...andup...
254countiesinTexas
![Page 19: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/19.jpg)
Copyright©D-WaveSystemsInc. 19
...andup3108UScounties
![Page 20: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/20.jpg)
Copyright©D-WaveSystemsInc. 20
Implementationsofmapcoloring
QMI: weights strengths
C ToQ
Snippet(28of596LOC) entireprogram
![Page 21: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/21.jpg)
Copyright©D-WaveSystemsInc. 21
• Algorithmsarebeingdiscoveredformappingapplicationstoadiabaticquantumcomputers
• Thesealgorithmsarebeingturnedintosoftwaretools
• ThisisgreatlyimprovingprogrammerproductivityintheAQCenvironment...
• ...andclosingthegapbetweenapplicationsandAQCpower
![Page 22: Introduction to Quantum Computing D-Wave Background D-Wave ... · – 4 colors (Blue, Green, Red, Yellow) – Create 13x4 = 52 logical qubits • Build QMI with these four tasks:](https://reader031.vdocuments.net/reader031/viewer/2022040716/5e1fe35d9368040b5531748a/html5/thumbnails/22.jpg)
Copyright©D-WaveSystemsInc. 22