NetOSSeminar

QC for QCs

Jon Crowcroft

http://www.cl.cam.ac.uk/~jac22

LayintrotoQuantumCompu3ng

•  Apieceofmymind?– PenrosetheoryJ

•  CanIdoitjus3ce?–  Intendedaudiencee.g.lawyers

QuantumMechanics•  UltravioletCatastrophe•  Planck/Blackbodyradia3on&infiniteenergy..

•  Con3nuous(waves&par3cles)•  Young’sslitsexperiment

•  Wave“selfinterferes”•  Butifweseewhichslitpar3clegoesthrough

•  Doesn’tanymore!

•  Copenhagenprobabilty/Feynmnpathintegral•  Uncertainty•  Heisenberg–observereffect

•  Spooky(ac3onatdistance/entanglement)•  Einstein

Superposi3on

•  Morethanjustsetofstates– Supersetofstates– Phase&normalisa3on

Ametaphor

QKD

•  Isathingbutisn’tQC•  Justusesonequantumproperty•  Tamperevidence•  Alsousedinquantumblockchain,forexample

•  AlsooneofthethingsthatwillsaveusfromQC/Shor

QCresources

•  Qubitsv.classicalbits– Entangledstory

•  QCprograms/circuitsv.ALUs–  Itera3onissequenceofsuperposedstates– Unitarygatesoperateonwholestate– Circuitsquiteproblemspecific

•  Outputisthechallenge– Measurementprojectsvector/superposedstate–  ontoorthonormalbasis– Finalvalueprobablyok

Contrastwithclassical

•  Memory&processorsamebinarygates– Eckart/vonNeumannstoredprogramcomputer

•  CPU/ALU:Circuitsforcommoninstruc3ons– Arithmen3c,logic,sequence/control– Sequen3alinstruc3onfetch&execute(mostly)– Withrecursion/itera3on– Verygeneral(turingmachinesJ)

StoredProgramv.SwitchedProgram

•  QCismorelikeoneoftheearliestcomputers– Bletchley’sColussus–SwitchedProgram–  Insteadofcode&datainstore,– datainputtoasequenceofswitchconfigura3ons

•  QC“program”=circuitmadeofgatetypes•  QC“data”=sequenceofQubitdistribu3ons

QC“programming”

•  IsmorelikeCPUdesign•  programsarelikeprobablis3cprogramming•  See(e.g.)anglican

hbp://www.robots.ox.ac.uk/~fwood/anglican/language/•  Run3mereminiscentofMCMC

hbps://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo

– Quantum“pathintegral”equivalenttothemul3-dimensionalintegral

– Quantumcircuitequivalenttosamplingmechanisminmcmc

Some“algorithms”then

•  Grover–  databasesearch

•  Shor– Fasterfactoriser

•  Deutsch–Jozsa– Exactoracle

•  QCemula3on– mcmc

Grover

Contrastwithclassical

•  Findarecordwithkey=valueinalist•  Iterate-complexityO(n)•  Think–findabookinapileofbooksnotinorder

Shor

Contrastwithclassical

•  FindprimefactorsofalargenumberN– e.g.inrange1to2^256(10^90)–  Isn’tknowninpolynomial3me–  i.e.asrangeofgetsbigger,3megetslonger,fasterthann^kforanykatall…(asfarasweknow)

– Don’ttrythisathome– Sieve/search

Deutchse-Jozsa

Exactoracle

•  Determinis3calgorithmtocompute:–  Iff(x)isconstantorbalancedforallx,–  Inoneitera3on

•  Classically,–  needs2nitera3onsoff(x)ifxisnbits

D-Wave

•  100q-bit,butonlyforquantumannealing

•  Findsminimumofafunc3onbyqunatumflucta3ons–morelikeanalogcompu3ng

Uncertainty

•  Decoherence•  Affordability•  Algorithmically•  Intractability

Whatmightthismean…

•  IfQCisrealized…andaffordable1.  Iscryptodead?–Notreallyc.f.hbps://

www.ncsc.gov.uk/whitepaper/quantum-safe-cryptography2.  Areimpossibleproblemsthentractable?Not

really3.  Aresomeproblemsmoreprac3cal?Yes

•  WhenmightweexpectaQC(QCWorld)?–  Hardtosay,asitisn’tjustanengineeringpb.

hbps://spectrum.ieee.org/compu3ng/hardware/the-case-against-quantum-compu3ng

ConsequenceofQC

•  IfwereplacePKIwithQKD,mayneedtodevisenewmechanismforsignatures

•  SomedirectQCimplementa3onofprobabilis3cprogramingorbayesmodelinferencingmaybecomemuchmoreefficient

QC&A

•  Ques3ons….?•  Peaceofmind?

•  Acknowledgementsto–  AnujDewar(Cambridge)forslideware– Wikipediaforgraphicalmaterials