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:

Copyright©D-WaveSystemsInc. 1

• IntroductiontoQuantumComputing• D-WaveBackground• D-WaveSystem• ProgrammingEnvironment• PotentialApplications

Topics


“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


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


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


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


ProgrammingEnvironment

• OperatesinahybridmodewithaHPCSystemorDataAnalyticEngineactingasaco-processororaccelerator

• D-Wavesystemis“front-ended”onanetworkbyastandardserver

• UserformulatesproblemasaseriesofQuantumMachineInstructions(QMIs)

• FrontendsendsQMItoquantumprocessor(QP)• QPstartstosamplefromthedistributionofbit-stringsdefinedbytheQMI

• Resultsarereturnedtothefront-endandontotheuser



Example:4-coloringCanada’sprovinces


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


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)


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


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


Task2:embedlogicaltophysicalqubits

Q QC

Q QC

C CC

C

logical

physical

B

G

R

Y


Task3:Intercellcouplersconstrainneighbors

BritishColumbia Alberta

B

G

R

Y

AlbertaBritishColumbia


Task4:Cloneregionsforplanarembedding

AlbertaBritishColumbia

NorthwestTerritories

BC AB

NT NT


Colorsencodedinunitcells


Scalingup...

• Wecannotfitallthestatesintounitcellsofthechip…• …soweadoptadivide-and-conquerstrategy

DividetheUSmapintochunks.Processthefirstchunkandgetvalidcoloringsforthefirstchunkofstates.Usethesecoloringstobiasthesecondchunk.Repeat.

chunk1 chunk2 chunk3


...andup...

254countiesinTexas


...andup3108UScounties


Implementationsofmapcoloring

QMI: weights strengths

C ToQ

Snippet(28of596LOC) entireprogram


• Algorithmsarebeingdiscoveredformappingapplicationstoadiabaticquantumcomputers

• Thesealgorithmsarebeingturnedintosoftwaretools

• ThisisgreatlyimprovingprogrammerproductivityintheAQCenvironment...

• ...andclosingthegapbetweenapplicationsandAQCpower


ThankYou

Questions?

DennyDahl

[email protected]

Documents

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: