QuantumTechnology101:OverviewofQuantumComputing

andQuantumCybersecurityWarnerA.Miller*

DepartmentofPhysics&CenterforCryptographyandInformationSecurityFloridaAtlanticUniversity

HudsonInstitute'sConferenceon“TheComingQuantumRevolution:SecurityandPolicyImplications,”17Oct17

NSFCAE-R

* SupportfromAFOSR/AOARDunderintelligentConvergenceCyberSecuritySystems(iC2S2)contractFA2386-17-1-4070

Outline(QuantumInformationScience)

• Quantum101

• QuantumComputing101

• QuantumCryptography101

JohnArchibaldWheelerRichardP.Feynman

TheProblemIhaveastheSpeakerToday• Ifsomebodysaysthattheycanthinkaboutquantumphysicswithoutbecomingdizzy,thatshowsonlythattheyhavenotunderstoodanythingwhateveraboutit.NielsBohr

• Neverexpressyourselfmoreclearlythanyouthink.NielsBohr

DelayedChoiceExperiment

W.A.Miller&J.A.Wheeler,“Delayed-ChoiceExperimentsandBohr'sElementaryQuantumPhenomenon,"Proc.Int.Symp.FoundationsofQuantumMechanics,ed.S.Kamefuchi,Tokyo,(1984)140-152.

DelayedChoiceonaCosmicScale

ESA/Hubble, NASA, Suyu et al. :HE0435-1223 Miller & Wheeler

Quantum:Observer-ParticipatoryUniverse

Quantummechanicspromotesthemere“observerofreality”to“participatorinthedefiningofreality.JohnArchibaldWheeler

TheQuantumState:DistinguishabilityandComplementarity

Qubit,HilbertSpace&SuperpositionPrinciple

| i = ↵v| li+ ↵h| $i= ↵0|0i+ ↵1|1i

P1 = |↵1|2

|�i

|li

|.%i

QuantumComputersScaleExponentiallyToo:Inthenumberofqubitsnotinyears

Classical DRAM Quantum Bits

64 KB 1064 MB 2064 GB 30

......

64 Exabyte 60|000i

|111i

|100i| {z }3 qubit state

QuantumSupremacy

ThePowerofQuantumEntanglement

EntangledQuantumStateofTwoPhotons

| i = 1p2(|00i+ |11i) 6= | 1i ⌦ | 2i

0

1

210 +

210 -

0

1

210 +

210 -

ConventionalvsQuantumComputing

Quantum Computer

Single quantum input:superposition of many

classical-like states

Quantum Computation:Interference (Entanglement) of many states

2

1100 + 01 + 10 +=ψ → φ→

Measurement:classical-like

resultMany singledistinguishableclassical inputs

Conventional Parallel Computer

0 0 →

Classicalresult

0 1 →

1 0 →

1 1 →

x2 x1→

Quantum Parallelism

vsConventional Parallelism – n qubits(physicalsystems)canhold2n classicalbits ofinfo

– 250 ~1015 bits~100TB(10XLibraryofCongress),2100 ~1030 bits~1017 TB

Quantum Information(i) Information encoded in the physical states of atomic-level systems (qubits)(ii) Superposition state: system can be in many states simultaneously

(iv) Exponentially larger state space of information

(iii) Input state into quantum computer = all classical inputs simultaneously

Classes of Quantum Algorithms• Quadratic speedup: exhaustive search , optimization, k-Sat• Exponential speedup: uncover hidden structure using the Quantum Fourier Transform; f(x) where A x = b (Lloyd)

Quantum Computers: Current Status• Theoretical Foundations: established/sound• Decoherence (environmental noise)• Currently: dozens

Dennardscalingcomestoanend

Moore’sLaw

Problem:transistorgatestoothinat~100nm;currentleaksintosubstrate

Thechallenge:classicalchipshitawall

(Powerdensityconstantas#transistorsdoubles)

Dr. Daniel Lidar, ISI/USC

|OUT � = bUQC |IN�

2N ⇥ 2NN � partite

QuantumCircuit&TimelessnessoftheQuantum• DavidDiVincenzo Criteria

• Ascalablephysicalsystemwithwellcharacterizedqubits

• Theabilitytoinitializethestateofqubitstoasimplefiducialstate

• Longdecoherence timesrelativetothetimeofgateoperations

• Auniversalsetofgateoperations• Aqubit-specificmeasurementcapability

QuantumComputing:ManyChoicesforqubits

“Ablueprintforbuildingaquantumcomputer,” R.V.Meter&C.Horsman,Comm.oftheACM56,84(2013)

QuantumInformationProcessingLevels

• QuantumAnnealing• Quantumtunnelingtominimum

• QuantumSimulation• Partialqubitcontrol

• UniversalQuantumComputing• Fullcontrolofeveryqubit• Faulttolerantcomputing(quantumerrorcorrection)

DavidDeutsch

PeterShore

Wojciech H.Zurek

Decoherence andQuantumErrorcorrection

⌧D ⇡ ⌧R

✓~

�x

p2mkbT

◆2

W.H.Zurek,arXiv:quant-ph/0306072

Classicalerrorcorrectionmakesuseofredundancy,i.e.cloning.Noquantumcloning.

Quantumstatescantbecloned;however,P.Shorutilizedentanglementtorevealerrorsandnotdestroyingthesuperposition.

NoCloningaQuantumState

|li =) |lli

|$i =) |$$i

|.%i = | li+ |$i|p2

=) | lli+ |$$i|p2

|.%i =) |.%.%i ==

✓| li+ |$i|p

2

◆⌦

✓| li+ |$i|p

2

◆=

|lli+ |l$i+ |$li+ |$$i2

Zurek&Wootters6=

MutuallyUnbiasedBases

0

1

0

1 2

n=2 HorizontalVertical

Right CircularLeft Circular

|.%i = | li+ |$i|p2

|-&i = | li � |$i|p2

Rigt DiagonalLeft Diagonal

|�i = | li+ i |$i|p2

| i = | li � i |$i|p2

|li = |0i

|$i = |1i

1

n

✓n

n+ 1

◆

QuantumKeyDistributionandBitErrorRate

If Bob gets correct result with probability BER<BERT, then Eve can be marginalized at the expense of bandwidth using classical privacy amplification

Eve’schanceofpickingcorrectsorterjforthestate

BobgetscorrectresultbutEveknows

Can’tcloneEvesendswrongstate

BobgetscorrectresultfromEve’swrongchoice

0

1

0

1 2

n=2

10

n=3

0

1

2

2 3

BER Threshold:

BERT =n� 1

n+ 1=

⇢33% for n = 267% for n = 5

1

n+ 11

n+ 1

n

n+ 1