quantum information a glimpse at the strange and intriguing future of information dan c. marinescu...

Quantum Information Quantum Information A Glimpse at the Strange and A Glimpse at the Strange and

Intriguing Future of InformationIntriguing Future of Information

Dan C. MarinescuDan C. Marinescu

School of Computer Science School of Computer Science

University of Central FloridaUniversity of Central Florida

Orlando, Florida 32816Orlando, Florida 32816, , USAUSA

[email protected]@cs.ucf.edu

Boole Lecture - February 15, 2006Boole Lecture - February 15, 2006 22


AcknowledgmentsAcknowledgments

The material presented is based on the booksThe material presented is based on the books

Approaching Quantum ComputingApproaching Quantum Computing

ISBN 013145224X, Prentice Hall, March 2004ISBN 013145224X, Prentice Hall, March 2004

Approaching Quantum Information Approaching Quantum Information Theory Theory

(in preparation)(in preparation)

by Dan C. Marinescu and Gabriela M. Marinescuby Dan C. Marinescu and Gabriela M. Marinescu

Work supported by National Science Work supported by National Science Foundation grants MCB9527131, Foundation grants MCB9527131, DBI0296107,ACI0296035, and EIA0296179.DBI0296107,ACI0296035, and EIA0296179.


InformationInformation

• 2,450,000,000 Google hits for the word 2,450,000,000 Google hits for the word “information”.“information”.

• The earliest historical meaning of the word The earliest historical meaning of the word informationinformation in English was related to the act of in English was related to the act of informinginforming, or giving form or shape to the mind, as in , or giving form or shape to the mind, as in education, instruction, or training. A quote from education, instruction, or training. A quote from 1387: "1387: "Five books come down from heaven for Five books come down from heaven for information of mankindinformation of mankind." (Oxford English ." (Oxford English Dictionary)…..Dictionary)…..Amazon.com was established later….Amazon.com was established later….

•2667?2667? ( Japanese imperial year based on the mythical founding of Japan by Emperor Jimmu in 660 BC)( Japanese imperial year based on the mythical founding of Japan by Emperor Jimmu in 660 BC)


Information (cont’d)Information (cont’d)

• Information is a primitive concept (like matter or Information is a primitive concept (like matter or energy). energy).

• Information abstracts properties of and allows us to Information abstracts properties of and allows us to distinguish distinguish objects/entities/phenomena.objects/entities/phenomena.

• There is a common expression of information, There is a common expression of information, strings strings of bits,of bits, regardless of the object/entity/process it regardless of the object/entity/process it describes. Bits are describes. Bits are independentindependent of their physical of their physical embodiment.embodiment.

• Information is transformed using logic operations. Information is transformed using logic operations. GatesGates implement logic operations and allow for implement logic operations and allow for automatic processing of information. The usefulness automatic processing of information. The usefulness of information increases if the physical embodiments of information increases if the physical embodiments of of bits and gates become smallerbits and gates become smaller and we need less and we need less energy to process, store, and transmit information.energy to process, store, and transmit information.


Classical InformationClassical Information

• Can be copiedCan be copied without altering it. without altering it.

• DeterministicDeterministic; the result of measuring/observing ; the result of measuring/observing it is deterministic (unless affected by noise).it is deterministic (unless affected by noise).

• Cannot travel faster than light or backward in Cannot travel faster than light or backward in time.time.

• It is processed by conventional computers using It is processed by conventional computers using irreversible gatesirreversible gates. During processing we . During processing we experience an irretrievable loss of information.experience an irretrievable loss of information.

• Information TheoryInformation Theory was developed by Shannon was developed by Shannon for macroscopic bodies at a time when for macroscopic bodies at a time when microscopic systems carrying information were microscopic systems carrying information were not known. not known.


Matter

Information

Energy

E = m c2

Landauer’s Principle (Thermodinamics)

The erasure of one bit produces at least kB T log 2 Joules of heat and increases the thermodynamic entropy by at least kB log 2

Laws ofQuantum

Mechanics


MICROPROCESSORS1980s

WORLD WIDE WEB1990s

GOOGLE, YouTube2000s

FIBER OPTICS1990s

WIRELESS2000s

SENSORSDIGITAL CAMERAS

2000s

COLLECT

PROCESS

STORE

DISSEMINATE

COMMUNICATE

OPTICAL STORAGEHIGH DENSITY SOLID-STATE

1990sSPINTRONICS

2000s

MILESTONES OF INFORMATIONPROCESSING1850 – 2007

BOOLEAN ALGEBRA1854

DIGITAL COMPUTERS

1940s

QUANTUM COMPUTING

QUANTUM COMMUNICATION


MicroprocessoMicroprocessorr

YearYear # transistors# transistors

40044004 19711971 2,2502,250

80088008 19721972 2,5002,500

80808080 19741974 5,0005,000

80868086 19781978 29,00029,000

286286 19821982 120,000120,000

386386 19851985 275,000275,000

486486 19891989 1,180,0001,180,000

PentiumPentium 19931993 3,100,0003,100,000

Pentium IIPentium II 19971997 7,500,0007,500,000

Pentium IVPentium IV 20002000 42,000,00042,000,000

ItaniumItanium 20022002 220,000,000220,000,000

Itanium IIItanium II 20032003 410,000,000410,000,000

Moore’s LawMoore’s Law


Limits of Solid-State TechnologyLimits of Solid-State Technology

• To increase the clock rateTo increase the clock rate we have we have to pack to pack transistors as densely as possible because transistors as densely as possible because the speed the speed of light is finiteof light is finite..

• The power dissipation increases with the cube of the The power dissipation increases with the cube of the clock rate. When we double the speed of a device its clock rate. When we double the speed of a device its power dissipation increases 8 (eight) foldpower dissipation increases 8 (eight) fold..

• The computer technology vintage year 2000 The computer technology vintage year 2000 requires some requires some 3 x 103 x 10-18-18 Joules/elementary operation. Joules/elementary operation.


The heat generated by densely packed solid-state devices in a sphere of radius R is proportional to the volume thus to R3; the heat can be removed

trough the surface of the sphere, proportional to R2


Hitting a Wall…Hitting a Wall…

• An exponential growth cannot be sustained An exponential growth cannot be sustained indefinitely; sooner or later one will hit a wall.indefinitely; sooner or later one will hit a wall.

• Revolutionary rather than evolutionary approach Revolutionary rather than evolutionary approach to information processing and to communication:to information processing and to communication:– Quantum computing and communication Quantum computing and communication quantum quantum

information.information.– DNA Computing DNA Computing biological information. biological information.


Quantum Information Processing Quantum Information Processing

A happy marriage between two of the greatest A happy marriage between two of the greatest scientific achievements of the 20th century:scientific achievements of the 20th century:

quantum mechanicsquantum mechanics stored program computersstored program computers..

In 1985 Richard Feynman wrote: “In 1985 Richard Feynman wrote: “..it seems that the ..it seems that the laws of physics present no barrier to reducing the laws of physics present no barrier to reducing the size of computers until bits are the size of atoms size of computers until bits are the size of atoms and quantum behavior holds sway.and quantum behavior holds sway.””

Quantum information Quantum information Information encoded as Information encoded as the state of atomic or sub-atomic particles.the state of atomic or sub-atomic particles.


I think I can fairly say that nobody

understands QuantumMechanics

Richard Feynman


LightLight

• Light Light electromagnetic radiation. electromagnetic radiation.

• The electric and magnetic field The electric and magnetic field – oscillate in a plane perpendicular to the direction of oscillate in a plane perpendicular to the direction of

propagation and propagation and – are perpendicular to each other.are perpendicular to each other.

• The dual, wave and corpuscular, nature of light:The dual, wave and corpuscular, nature of light:– Diffraction phenomenaDiffraction phenomena wave-like behaviorwave-like behavior– Photoelectric effectPhotoelectric effect corpuscular/granularcorpuscular/granular The The

light consists of light consists of quantum “particles” called photonsquantum “particles” called photons..


PolarizationPolarization of Light of Light

Polarization is given by the electric field vectorPolarization is given by the electric field vector– Linearly polarized Linearly polarized (vertical/horizontal) (vertical/horizontal) the tip of the the tip of the

electric field vector oscillates along any straight line in a electric field vector oscillates along any straight line in a plane perpendicular to the direction of propagation.plane perpendicular to the direction of propagation.

– Circularly polarizedCircularly polarized (right- /left-hand) (right- /left-hand) the tip of the the tip of the electric field vector moves along a circle in a plane electric field vector moves along a circle in a plane perpendicular to the direction of propagation:perpendicular to the direction of propagation:

– Elliptically polarizedElliptically polarized light light the tip of the electric field the tip of the electric field vector moves along an ellipse in a plane perpendicular to vector moves along an ellipse in a plane perpendicular to the direction of propagation.the direction of propagation.

• In a beam of linearly polarized light each photon has In a beam of linearly polarized light each photon has a random orientation of the polarization vector.a random orientation of the polarization vector.


The Spin of Atoms and Sub-atomic The Spin of Atoms and Sub-atomic ParticlesParticles

• Spin Spin the intrinsic angular momentum; it takes the intrinsic angular momentum; it takes discrete values (the discrete values (the spin quantum number s.)spin quantum number s.)

• Two classes of quantum particles:Two classes of quantum particles:– fermionsfermions - - spin one-halfspin one-half (e.g., electrons). (e.g., electrons).

•s=+1/2 and s=+1/2 and

•s=-1/2s=-1/2– bosonsbosons - - spin onespin one particles (e.g., photons). particles (e.g., photons).

•s=+1, s=+1,

•s=0, and s=0, and

•s=-1s=-1


Sz

12

h

12

h-

Rn(0)

Rn(180)

(a) (b)

The spin of the electron: The spin of the electron: + ½ + ½ spin upspin up,, - ½ - ½ spin downspin down..


Quantum MechanicsQuantum Mechanics

Quantum mechanics Quantum mechanics mathematical model of mathematical model of the physical worldthe physical world..

Quantum concepts such as: Quantum concepts such as: – Uncertainty, Uncertainty, – Superposition, Superposition, – Entanglement,Entanglement,– No-cloning,No-cloning,

do not have a correspondent in classical do not have a correspondent in classical physicsphysics. .


Heisenberg's Uncertainty PrincipleHeisenberg's Uncertainty Principle

The position and the momentum of a quantum particle The position and the momentum of a quantum particle cannot be determined with arbitrary precision.cannot be determined with arbitrary precision.

• h=6.6262 x 10h=6.6262 x 10-34-34 Joule x second Joule x second Planck’s constant Planck’s constant

• Non-determinism Non-determinism basic tenet of quantum basic tenet of quantum mechanics.mechanics.

4/hPX X


Max Born’s Nobel Prize Lecture, Dec. 11, Max Born’s Nobel Prize Lecture, Dec. 11, 19541954

““... Quantum Mechanics shows that not only ... Quantum Mechanics shows that not only the determinism of classical physics must be the determinism of classical physics must be abandoned, but also the naive concept of abandoned, but also the naive concept of reality which looked upon atomic particles as reality which looked upon atomic particles as if they were very small grains of sand. At if they were very small grains of sand. At every instant a grain of sand has a definite every instant a grain of sand has a definite position and velocity. This is not the case position and velocity. This is not the case with an electron. with an electron. If the position is determined If the position is determined with increasing accuracy, the possibility of with increasing accuracy, the possibility of ascertaining its velocity becomes less and ascertaining its velocity becomes less and vice versa.vice versa.””


“Liebe Gott würfelt nicht”(Dear God does not play dice)

- Albert Einstein


Superposition PrincipleSuperposition Principle

States of a quantum system:States of a quantum system:- - OrthogonalOrthogonal..- - Non-orthogonalNon-orthogonal..- - SuperpositionSuperposition – a weighted sum (some – a weighted sum (some

elements appear with a – sign because the elements appear with a – sign because the phases are negative). Schrödinger’s cat.phases are negative). Schrödinger’s cat.

In a quantum system, in addition to reliably In a quantum system, in addition to reliably distinguishable states there are states that distinguishable states there are states that cannot be reliably distinguishable. cannot be reliably distinguishable.

Incomplete distinguishability is one of the Incomplete distinguishability is one of the tenets of quantum mechanics.tenets of quantum mechanics.


From Lewis Carroll to…. Incomplete From Lewis Carroll to…. Incomplete Distinguishability in Quantum PhysicsDistinguishability in Quantum Physics

““I have a very long and sad I have a very long and sad taletale’’ said the Mouse.’’ said the Mouse.

““I see that your I see that your tailtail is long, but why do you say it is long, but why do you say it is sad?’’ askedis sad?’’ asked

Alice.Alice.


(a) Orthogonal states of a photon can be reliably distinguished from one another: V (vertical) from H (horizontal); 135 deg from 45 deg.

V H 135 45

-

(b) Non-orthogonal states of a photon cannot be reliably distinguished from one another: V (vertical) from 45 deg.

=+

2=

2

(c) Superposition states.


Entanglement (Vërschränkung)Entanglement (Vërschränkung)

• Discovered by Schrödinger.Discovered by Schrödinger.

• An An entangled pairentangled pair is a single quantum is a single quantum system in a superposition of equally possible system in a superposition of equally possible states. states.

• The entangled state contains no information The entangled state contains no information about the individual particles, only that they about the individual particles, only that they are in opposite states.are in opposite states.

• Einstein called entanglement “Einstein called entanglement “Spooky action Spooky action at a distance.at a distance.””


EPR (Einstein, Podolski,Rosen) EffectEPR (Einstein, Podolski,Rosen) Effect

• A source generates A source generates two entangled particlestwo entangled particles e.g., two photons entangled in polarization.e.g., two photons entangled in polarization.

• A A measurement of one of themmeasurement of one of them, say using a V-, say using a V-H basis, produces a random result (V) or (H) H basis, produces a random result (V) or (H) and at the same time and at the same time forces the other particle forces the other particle to enter the same state.to enter the same state.

Source

Measurement


No Cloning Principle No Cloning Principle Monogamy of EntanglementMonogamy of Entanglement

Quantum states cannot be cloned. Cloning Quantum states cannot be cloned. Cloning

- would increase distinguishability of - would increase distinguishability of states,states,

- it is a non-linear transformation- it is a non-linear transformation..

Quantum Copy Machine

A

A

A’

B


Charles Bennett and Peter Shor: “Charles Bennett and Peter Shor: “classical classical

information can be copied freely, but can only be information can be copied freely, but can only be transmitted forward in time to a receiver in the transmitted forward in time to a receiver in the sender's forward light cone. Entanglement, by sender's forward light cone. Entanglement, by contrast cannot be copied, but can connect any contrast cannot be copied, but can connect any two points in space-time. Conventional data-two points in space-time. Conventional data-processing operations destroy entanglement, but processing operations destroy entanglement, but quantum operations can create it, preserve it and quantum operations can create it, preserve it and use it for various purposes, notably speeding up use it for various purposes, notably speeding up certain computations and assisting in the certain computations and assisting in the transmission of classical data or intact quantum transmission of classical data or intact quantum states (teleportation) from a sender to a receiverstates (teleportation) from a sender to a receiver..””


Quantum InformationQuantum Information

• Embodied by the Embodied by the statestate of atomic or sub-atomic of atomic or sub-atomic particles. particles.

• SuperpositionSuperposition - we cannot reliably recognize - we cannot reliably recognize differences between the states of a quantum differences between the states of a quantum system except under special conditions.system except under special conditions.

• The state of a quantum system cannot be The state of a quantum system cannot be measured or copiedmeasured or copied without disturbing it. without disturbing it.

• Quantum state can be Quantum state can be entangled. Two or more entangled. Two or more systems have a definite state though neither has systems have a definite state though neither has an identifiable state of its own. an identifiable state of its own.

• QubitsQubits – elementary units of quantum – elementary units of quantum information.information.


Classical Information

Quantum Information


QuantumInformation

ClassicalInformationMeasurement


Classical versus Quantum InformationClassical versus Quantum Information

Classical information is Classical information is information written in information written in stonestone……

Quantum information is more like the Quantum information is more like the information in a dream.information in a dream. Recalling a dream Recalling a dream inevitably changes your memory of it. Eventually inevitably changes your memory of it. Eventually you remember only your own description, not you remember only your own description, not the original dream. the original dream.

Charles Bennett at QIPP workshop, 2002Charles Bennett at QIPP workshop, 2002


EntropyEntropy

• ThermodynamicThermodynamic:: the number of the number of

microstatesmicrostates

• Informational, Shannon’sInformational, Shannon’s:: X is a random variableX is a random variable ppXi Xi -probability of outcome X-probability of outcome Xii

• Quantum, von Neumann’sQuantum, von Neumann’s:: is the density matrix is the density matrix

logBkS

ii Xi

X ppH log

)log()( TrS


0

1

0

1

(a) One bit (b) One qubit

Superposition states

Basis (logical) state 1

Basis (logical) state 0

A Bit Versus a QubitA Bit Versus a Qubit


Qubit MeasurementQubit Measurement0

1

Possible states of one qubit beforethe measurement

The state of the qubit afterthe measurement

p1

p0


Quantum GatesQuantum Gates

• One-qubit gates One-qubit gates X - transposes the components X - transposes the components of a qubit; Z - flips the sign of a qubit; Hadamard - of a qubit; Z - flips the sign of a qubit; Hadamard - creates a superposition state.creates a superposition state.

• Two-qubit gates Two-qubit gates CNOT CNOT

• Three-qubit gates Three-qubit gates Toffoli Toffoli

• Quantum gates are reversibleQuantum gates are reversible in principle no in principle no power dissipation.power dissipation.


Universal Quantum GatesUniversal Quantum Gates

• Any Boolean expression can be written as a Any Boolean expression can be written as a sum (logical OR) of products (logical AND) of sum (logical OR) of products (logical AND) of Boolean variables and/or negation of Boolean variables and/or negation of Boolean variables. Thus, any classical logic Boolean variables. Thus, any classical logic circuit can be implemented using only AND, circuit can be implemented using only AND, OR, and NOT gates.OR, and NOT gates.

• NAND and NOR are NAND and NOR are classical universal gatesclassical universal gates..

• Similarly, we can Similarly, we can simulate any complex n-simulate any complex n-qubit quantum circuit using a small set of qubit quantum circuit using a small set of

one-qubit and CNOT gatesone-qubit and CNOT gates..


DecoherenceDecoherence

Decoherence Decoherence randomization of the internal state randomization of the internal state of a quantum computer due to interactions with the of a quantum computer due to interactions with the environmentenvironment..

Conceptually decoherence can be prevented using:Conceptually decoherence can be prevented using: - Quantum fault-tolerant circuits.- Quantum fault-tolerant circuits. - Quantum Error Correcting Codes.- Quantum Error Correcting Codes. - Entanglement Purification and Distillation - Entanglement Purification and Distillation

extract aextract a subset of states of high entanglement and high subset of states of high entanglement and high

purity purity from a large set of less entangled states.from a large set of less entangled states.


Di Vicenzo’s Criteria for Physical Di Vicenzo’s Criteria for Physical Implementation of a Quantum ComputerImplementation of a Quantum Computer

1.1. Scalable physical system with well characterized Scalable physical system with well characterized qubits.qubits.

2.2. Initialize the qubits state as |000…00>.Initialize the qubits state as |000…00>.3.3. Long decoherence times.Long decoherence times.4.4. Universal set of quantum gates (operations).Universal set of quantum gates (operations).5.5. Qubit specific measurementsQubit specific measurements


Entering the Quantum Wonderland ….Entering the Quantum Wonderland ….

• We now have: We now have: – quantum gates and quantum circuitsquantum gates and quantum circuits– quantum communication channels.quantum communication channels.

• What should we be excited about?What should we be excited about?– Quantum parallelismQuantum parallelism– Quantum teleportationQuantum teleportation– Communication with entangled particlesCommunication with entangled particles– Quantum key distributionQuantum key distribution


Quantum ParallelismQuantum Parallelism

• In quantum systems In quantum systems the amount of parallelism the amount of parallelism increases exponentially with the size of the systemincreases exponentially with the size of the system, , thus with the number of qubits. For example, a 21-thus with the number of qubits. For example, a 21-qubit quantum computer is twice as powerful as as a qubit quantum computer is twice as powerful as as a 20-qubit one. 20-qubit one.

• An exponential increase in the power of a quantum An exponential increase in the power of a quantum

computer requires linear increase in the amount of computer requires linear increase in the amount of matter and space needed to build the larger matter and space needed to build the larger quantum computing engine.quantum computing engine.

• A quantum computer will enable us to solve A quantum computer will enable us to solve problems with a very large state space.problems with a very large state space.


Bush

Bush Kerry

Bush

KerryBush

Balanced function f(0) = f(1)

Kerry

Bush Kerry

Bush

KerryBush

Unbalanced function


0 f(0) 1 f(1)

2T

0 f(0)

1 f(1)

T

(a) (b)

O+

| x >

| y > f(x) >

| x >

| y >

T(c)

Uf


Quantum TeleportationQuantum Teleportation

• The process of transferring the state of a The process of transferring the state of a quantum particle to possibly distant one.quantum particle to possibly distant one.

• Based upon the entanglement.Based upon the entanglement.

• No cloning - the original state is destroyed in the No cloning - the original state is destroyed in the

quantum teleportation process.quantum teleportation process.


Carol

iY

CNOT particle 1 - target qubit particle 3 - control qubit

particle 1

Aliceparticle

2

The measurement on the pair (1&3) changes the state of particle 2 to one of four states: S1,

S2, S3, S4

particle1

particle2

ClassicalChannel

Bob

particle 3

I ZX

Pair of entangled qubits

particle 3

Measurementparticle 3 - measuredparticle 1 - unchanged

QuantumChannel

Send to Bob results of measurement

00 01 10 11

Receive from Alice results of measurements

00 01 10 11

Z

Particle 2 is in the same state as particle 3


A Teleportation ExperimentA Teleportation Experiment

• Francesco De Martini, University of Rome, 1997.Francesco De Martini, University of Rome, 1997.

• Based upon an idea of Sandu Popescu.Based upon an idea of Sandu Popescu.

• A UV laser beam interacts with a non-linear medium, a A UV laser beam interacts with a non-linear medium, a crystal of dihidrogen phosphate to generate two photons crystal of dihidrogen phosphate to generate two photons for an incoming one – for an incoming one – parametric downconversionparametric downconversion..

• The polarization entanglement of the two photons is The polarization entanglement of the two photons is converted into a converted into a path entanglementpath entanglement..


Reflecting mirror

Source

PolarIzer

Alice Bob

Carol

h

A

B

D

C

h

v

v

Reflecting mirror

Reflecting mirror

Reflecting mirror


Communication with Entangled Communication with Entangled ParticlesParticles

• Even when separated, two entangled particles Even when separated, two entangled particles continue to interact with one another.continue to interact with one another.

• Basic idea. Consider three particlesBasic idea. Consider three particles– Two particles (particle 1 and particle 2) Two particles (particle 1 and particle 2) in an in an

anti-correlated state (spin up and spin down). anti-correlated state (spin up and spin down). – We measure particle 1 and particle 3 and set We measure particle 1 and particle 3 and set

them in an anti-correlated state.them in an anti-correlated state.– Then particle 2 ends up in the same state Then particle 2 ends up in the same state

particle 3 was initially in. particle 3 was initially in.


Quantum Key DistributionQuantum Key Distribution

• Classical methods for key distribution are in Classical methods for key distribution are in principle insecureprinciple insecure physical difficulty to physical difficulty to detect the presence of an intruder when detect the presence of an intruder when communicating through a classical communicating through a classical communication channel. All classical methods communication channel. All classical methods of key distribution can be broken if enough of key distribution can be broken if enough computer power is available.computer power is available.

• Quantum key distribution ensures that an Quantum key distribution ensures that an eavesdropper can succeed only with a very low eavesdropper can succeed only with a very low probability.probability.

• No amount of computing power will allow No amount of computing power will allow breaking of a quantum key distribution breaking of a quantum key distribution protocol.protocol.


(a)

Vertical Horizontal 45 deg

Vertical/Horizontal (VH) Diagonal (DG)

(b)

(c)Classical communication channel

Quantum communication channel

Classical wiretap

Quantum wiretapPhoton

separationsystem

Source ofpolarizedphotons

Alice Bob

Eve

135 deg


Information Encoding for Quantum Key Information Encoding for Quantum Key Distribution Distribution

• A photon with A photon with vertical/horizontal (VH) vertical/horizontal (VH) polarizationpolarization– 1 1 a photon with vertical polarization a photon with vertical polarization– 0 0 a photon with a horizontal polarization. a photon with a horizontal polarization.

• A photon withA photon with diagonal (DG) polarization diagonal (DG) polarization – 1 1 a photon with 45 deg polarization, and a photon with 45 deg polarization, and – 0 0 a photon with a 135 deg polarization. a photon with a 135 deg polarization.


Alice sends to Bob photons with X(V/H) and Z(D45/D135 ) polarization.

bases

results

X XZ X X Z Z ZZ ZZZ XXZ X X X X

X XZ X X Z Z ZZ ZZZ XXZ X X X X

X X X ZZZ XZ X X X

Bob chooses a base and measures incoming photons.

Bob sends the basis he used for each photon over a classical channel.

Alice tells Bob which ones are correct over a classical channel.

Bob examines the ones they agree upon (if no eavesdropping).

1 0 0 0111 1 10 0

Bob decodes the photons.

Alice sends Bob the parity of a selected subset.

1 0 0 0111 1 10 0Parity of

1,4,5,9,11.. =EVEN

Bob verifies the parity of a selected subset.

1 0 0 0111 1 10 0 Parity of 1,4,5,9,11.. = OK

111 10 0 Secret Key


Physical Embodiment of a QubitPhysical Embodiment of a Qubit • PhotonPhoton information encoded as the photon polarization; information encoded as the photon polarization;

e.g., horizontal and vertical.e.g., horizontal and vertical.

• ElectronElectron information encoded as the electron spin; information encoded as the electron spin;

two independent spin values, +1/2 and -1/2.two independent spin values, +1/2 and -1/2.

• Quantum dotsQuantum dots information encoded as the information encoded as the presence/absence of electronspresence/absence of electrons– Small devices that contain a tiny droplet of free electrons.Small devices that contain a tiny droplet of free electrons.– Fabricated in semiconductor materials; typical dimensions between Fabricated in semiconductor materials; typical dimensions between

nanometers to a few microns.nanometers to a few microns.– The size and shape of these structures and therefore the number of electrons The size and shape of these structures and therefore the number of electrons

they contain, can be precisely controlled; a quantum dot can have anything they contain, can be precisely controlled; a quantum dot can have anything from a single electron to a collection of several thousandsfrom a single electron to a collection of several thousands. .


Physical Embodiment of a Qubit Physical Embodiment of a Qubit (cont’d)(cont’d)

• A two-level atom in an optical cavity.A two-level atom in an optical cavity.

• Two internal states of an ion in a trap. Two internal states of an ion in a trap.

• OthersOthers– Liquid-state NMR.Liquid-state NMR.– NMR spin lattices.NMR spin lattices.– Nitrogen vacancies in diamond.Nitrogen vacancies in diamond.– Josephson junctions.Josephson junctions.


Milestones in Quantum ComputingMilestones in Quantum Computing

• 1961 - Rolf Landauer1961 - Rolf Landauer computation is physical.computation is physical.

• 1973 - Charles Bennett1973 - Charles Bennett logical reversibility of logical reversibility of computations. computations.

• 1981 - Richard Feynman1981 - Richard Feynman physical systems including physical systems including quantum systems can be simulated quantum systems can be simulated exactlyexactly with with quantum computers. quantum computers.

• 1982 - Peter Benioff1982 - Peter Benioff develops quantum mechanical develops quantum mechanical models of Turing machines.models of Turing machines.

• 1994 - Peter Shor1994 - Peter Shor algorithm for factoring large numbers.algorithm for factoring large numbers.

• 1995 - Lov Grover1995 - Lov Grover quantum database searching quantum database searching algorithmalgorithm


Milestones in Quantum Information Milestones in Quantum Information TheoryTheory

• 1984 - Charles Bennett and Gilles Brassard1984 - Charles Bennett and Gilles Brassard quantum cryptography.quantum cryptography.

• 1985 - David Deutsch1985 - David Deutsch reinterprets the reinterprets the Church-Turing conjecture.Church-Turing conjecture.

• 1993 - Bennett, Brassard, Crepeau, Jozsa, 1993 - Bennett, Brassard, Crepeau, Jozsa, Peres, WoottersPeres, Wootters quantum teleportation. quantum teleportation.

• 1994 - Calderbank, Shor, Steane 1994 - Calderbank, Shor, Steane quantum quantum error correcting codeserror correcting codes


The point is: We must make it as simple as possible … but not simpler !


Final RemarksFinal Remarks

• Building a quantum computer faces tremendous Building a quantum computer faces tremendous technological and theoretical challenges. technological and theoretical challenges.

• We are years, possibly decades away from We are years, possibly decades away from actually building a quantum computer. All we had actually building a quantum computer. All we had on February 13 2007 was a 7 qubit liquid NMR on February 13 2007 was a 7 qubit liquid NMR quantum computer able to factor the integer 15. quantum computer able to factor the integer 15.

• Applications of quantum cryptography seem ready Applications of quantum cryptography seem ready for commercialization. In 2003 a successful for commercialization. In 2003 a successful quantum key distribution experiment over a quantum key distribution experiment over a distance of some 100 km has been announced.distance of some 100 km has been announced.


“Success is the ability to go from failure to failure with no loss of enthusiasm.”

Sir Winston Churchill


The Answer to the PuzzleThe Answer to the Puzzle

• The filter block of the 16 qubit quantum computer The filter block of the 16 qubit quantum computer that that D-Wave SystemsD-Wave Systems plan to unveil on Feb 13... plan to unveil on Feb 13... The filter block is an electronic interface between The filter block is an electronic interface between our world and the quantum entangled world. our world and the quantum entangled world.

• An array of 128 lumped element filters, one for An array of 128 lumped element filters, one for

each input line. The space is constrained because each input line. The space is constrained because the filters and wires need to fit into the dilution the filters and wires need to fit into the dilution fridge cylinder. The filters remove noise and fridge cylinder. The filters remove noise and crosstalk (opposite of an antenna) from the signals crosstalk (opposite of an antenna) from the signals that drop down to the heart of a new quantum that drop down to the heart of a new quantum computer, cooled to 0.005 above absolute zero… computer, cooled to 0.005 above absolute zero…

http://www.dwavesys.com/


D-Wave Press Release - February 14D-Wave Press Release - February 14

• Right now, Orion is a "proof of concept," a demonstration of what Right now, Orion is a "proof of concept," a demonstration of what the final product could look like. At the demonstration, Rose had the the final product could look like. At the demonstration, Rose had the system come up with answers to Sudoku problems and, in another system come up with answers to Sudoku problems and, in another demo, seek out similar molecules to the active ingredient in the demo, seek out similar molecules to the active ingredient in the drug Prilosec in a chemical database. The computer found several drug Prilosec in a chemical database. The computer found several molecules that shared similar structural elements with Prilosec, but molecules that shared similar structural elements with Prilosec, but the molecule that matched it closest was the active ingredient in the molecule that matched it closest was the active ingredient in another drug called Nexium. Plucking out Nexium demonstrated the another drug called Nexium. Plucking out Nexium demonstrated the system's accuracy, the company said. Nexium is actually a mirror system's accuracy, the company said. Nexium is actually a mirror image of the molecule in Prilosec that AstraZeneca invented to image of the molecule in Prilosec that AstraZeneca invented to extend its patents. extend its patents.

• The computer itself--which is cooled down to 4 millikelvin (or nearly The computer itself--which is cooled down to 4 millikelvin (or nearly minus 273.15 degrees Celsius) with liquid helium--was actually in minus 273.15 degrees Celsius) with liquid helium--was actually in Canada. Attendees only saw the results on a screen. Still, it was the Canada. Attendees only saw the results on a screen. Still, it was the largest demonstration of a quantum computer ever, Rose said. largest demonstration of a quantum computer ever, Rose said.


D-Wave Press Release - February 14D-Wave Press Release - February 14

• End of 2007 End of 2007 32 qubit quantum computer. 32 qubit quantum computer.

• In mid 2008 In mid 2008 512 qubit quantum computer 512 qubit quantum computer

• End of 2008 End of 2008 1024 qubit quantum computer 1024 qubit quantum computer

quantum information a glimpse at the strange and intriguing future of information dan c. marinescu...

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