Quantum Experiments

Quantum ExperimentsQuantum Experiments

Dan C. Marinescu and Dan C. Marinescu and Gabriela M. MarinescuGabriela M. Marinescu

Computer Science Department Computer Science Department

University of Central FloridaUniversity of Central Florida

Orlando, Florida 32816Orlando, Florida 32816, , USAUSA

The material presented is from the bookThe material presented is from the book

Lectures on Quantum ComputingLectures on Quantum Computing by Dan C. Marinescu and Gabriela M. Marinescuby Dan C. Marinescu and Gabriela M. Marinescu

Prentice Hall, 2004Prentice Hall, 2004

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

Presented byPresented by

Chensheng QiuChensheng Qiu

Supervised bySupervised by

Dplm. Ing. GhermanDplm. Ing. Gherman

Examiner: Prof. WunderlichExaminer: Prof. Wunderlich

sourcessources

Professor’s Gruszka Professor’s Gruszka BookBook

Classical Classical versusversus Quantum Experiments Quantum Experiments

ClassicalClassical Experiments Experiments Experiment with Experiment with bulletsbullets Experiment with Experiment with waveswaves

Quantum Quantum ExperimentsExperiments Two slitsTwo slits Experiment with Experiment with electronselectrons Stern-Gerlach ExperimentStern-Gerlach Experiment

Experiment with bulletsExperiment with bullets

Figure 1: Experiment with bullets

(b)

detector

wallwall

H1

H2

(a)

Gun



(b)

detector

wallwall

H1

H2

(a)

Gun

P1(x)

H1 is openH1 is open

H2 is closedH2 is closed



(b)

detector

wallwall

H1

H2

(a)

GunP2(x)





(b)

detector

wallwall

H1

H2

(a)

Gun

(c)

(x))P(x)(P(x)P 2121

12 P2(x)

P1(x)



Experiment with WavesExperiment with Waves

Figure 2: Experiments with waves

detector

wall(a)

wall

H1

H2

wave source





(b)

I1(x)

detector

wall(a)

wall

H1

H2

wave source





I2(x)

(b)

detector

wall(a)

wall

H1

H2

wave source





detector

wall(a)

wall

H1

H2

wave source

I1(x)

I2(x)

(b) (c)

2

2112 (x)(x)(x)I hh



This is a result of This is a result of interferenceinterference

Two Slit ExperimentTwo Slit Experiment

Figure 3: Two slit experiment

P2(x)

P1(x)

(b)

detector

wallwall

H1

H2

(a)

source of electrons

(c)

(x))P(x)(P(x)P 2121

12

Results intuitively expected

Are electrons Are electrons particles or particles or waves?waves?

Two Slit ExperimentTwo Slit Experiment

Figure 3: Two slit experiment

P2(x)

P1(x)

(b)

detector

wallwall

H1

H2

(a)

source of electrons

(c)

?(x)P12

Results observed

Two Slit Experiment With ObservationTwo Slit Experiment With Observation

Figure 4: Two slit experiment with observation

P2(x)

P1(x)

(b)

detector

wall

source of electrons

wall

H1

H2

(a)

light source

(c)

(x))P(x)(P(x)P 2121

12

Interference disappeared!

“⇨ Decoherence”

Now we add Now we add light sourcelight source

Stern-Gerlach ExperimentStern-Gerlach Experiment

Figure 5: Stern-Gerlach experiment with spin-1/2 particles

Will be discussed in more detail later

S

N

Conclusions From the ExperimentsConclusions From the Experiments

LimitationsLimitations of classical mechanics of classical mechanics ParticlesParticles demonstrate demonstrate wavelike behaviorwavelike behavior Effect of observationsEffect of observations cannot be ignored cannot be ignored EvolutionEvolution and and measurementmeasurement must be must be

distinguisheddistinguished

Can we use these phenomena Can we use these phenomena practically?practically?

Quantum computing and Quantum computing and informationinformation

Technological limitsTechnological limits For the past two decades we have enjoyed For the past two decades we have enjoyed Gordon Gordon

Moore’s lawMoore’s law. .

But all good things may come to an end…But all good things may come to an end…

We are limited in our ability to increase We are limited in our ability to increase the the densitydensity and and the the speedspeed of a computing engine. of a computing engine.

ReliabilityReliability will also be affected will also be affected to increase the speed we need increasingly smaller circuits (light to increase the speed we need increasingly smaller circuits (light

needs needs 1 ns to travel 30 cm in vacuum1 ns to travel 30 cm in vacuum)) smaller circuits smaller circuits systems consisting systems consisting only of a few particlesonly of a few particles

subject to Heisenberg uncertainty subject to Heisenberg uncertainty

Energy/operationEnergy/operation

IfIf there is a there is a minimum amount of energy dissipatedminimum amount of energy dissipated to to perform an elementary operation, perform an elementary operation, thenthen to increase the to increase the speed we have to increase the number of operations speed we have to increase the number of operations performed each second.performed each second.

To increase this number, we require a To increase this number, we require a linear increaselinear increase in in the amount of the amount of energy dissipatedenergy dissipated by the device. by the device.

The computer technology The computer technology in year 2000in year 2000 requires some requires some 3 x 3 x 1010-18-18 Joules per elementary operation. Joules per elementary operation.

Even if this limit is Even if this limit is reducedreduced say say 100-fold100-fold we shall see a we shall see a 10 10 (ten) times increase(ten) times increase in the amount of power needed by in the amount of power needed by devices devices operating at a speed 10operating at a speed 1033 times times larger than the larger than the speed of today's devices.speed of today's devices.

Power dissipation, circuit density, and Power dissipation, circuit density, and speedspeed

In 1992 Ralph Merkle from Xerox PARC In 1992 Ralph Merkle from Xerox PARC calculated that a calculated that a 1 GHz computer operating at 1 GHz computer operating at room temperatureroom temperature, , with 10with 101818 gates packed in a gates packed in a volume of about 1 cmvolume of about 1 cm33 would dissipate would dissipate 3 MW of of power. power. A A small city with 1,000 homessmall city with 1,000 homes each using 3 KW would each using 3 KW would

require the same amount of power; require the same amount of power; A 500 MW nuclear reactor could only power some 166 A 500 MW nuclear reactor could only power some 166

such circuits.such circuits.

Reducing heat is important…Reducing heat is important…

The The heatheat produced by a super dense computing engine is produced by a super dense computing engine is proportional to the proportional to the number of elementary computing number of elementary computing circuitscircuits..

Thus, it is proportional to the Thus, it is proportional to the volume of the enginevolume of the engine. .

The heat dissipated The heat dissipated grows as the cube of the radius of the grows as the cube of the radius of the device. device.

To prevent the destruction of the engine we have to To prevent the destruction of the engine we have to remove the heat through a surface surrounding the device. remove the heat through a surface surrounding the device.

Henceforth, our ability to remove heat increases as the Henceforth, our ability to remove heat increases as the square of the radiussquare of the radius while the amount of heat while the amount of heat increases increases with the cube of the size of the computing engine.with the cube of the size of the computing engine.

Energy consumption of a logic circuit

Speed of individual logic gates

S

E

(a) (b)

Heat removal for a circuit with densely packedlogic gates poses tremendous challenges.

Energy consumption is proportional to speed of Energy consumption is proportional to speed of computing computing

A happy marriage…A happy marriage…

The two greatest discoveries of the 20-th The two greatest discoveries of the 20-th centurycentury quantum mechanicsquantum mechanics stored program computersstored program computers

produced produced quantum computingquantum computing and and quantum quantum information theoryinformation theory

Quantum; Quantum mechanicsQuantum; Quantum mechanics QuantumQuantum is a Latin word meaning some quantity. is a Latin word meaning some quantity.

In physics it is used with the same meaning as the word In physics it is used with the same meaning as the word discretediscrete in mathematics, in mathematics, i.e., some quantity or variable that can i.e., some quantity or variable that can take only sharply defined valuestake only sharply defined values as as

opposed to a continuously varying quantity. opposed to a continuously varying quantity.

The concepts The concepts continuumcontinuum and and continuouscontinuous are known from are known from geometry and calculus. geometry and calculus.

For example, on a segment of a line there are infinitely many For example, on a segment of a line there are infinitely many points, the segment consists of a continuum of points. points, the segment consists of a continuum of points.

This means that we can cut the segment in half, and then cut This means that we can cut the segment in half, and then cut each half in half, and continue the process indefinitely.each half in half, and continue the process indefinitely.

Quantum mechanics is a Quantum mechanics is a mathematical model mathematical model of the physical of the physical worldworld

Heisenberg Heisenberg uncertainty principleuncertainty principle

Heisenberg uncertainty principle says Heisenberg uncertainty principle says we cannot we cannot determine both the position and the momentum of a determine both the position and the momentum of a quantum particle with arbitrary precision. quantum particle with arbitrary precision.

In his Nobel prize lecture on December 11, 1954 Max In his Nobel prize lecture on December 11, 1954 Max Born says about this fundamental principle of Born says about this fundamental principle of Quantum Mechanics : Quantum Mechanics : ``... It shows that not only the ``... It shows that not only the determinismdeterminism of classical of classical

physics must be abandoned, but also the physics must be abandoned, but also the naive concept of naive concept of realityreality which looked upon atomic particles as if they were which looked upon atomic particles as if they were very small grains of sand. At every instant a grain of sand very small grains of sand. At every instant a grain of sand has a definite position and velocity. has a definite position and velocity. This is not the case This is not the case with an electronwith an electron. If the position is determined with . If the position is determined with increasing accuracy, the possibility of ascertaining its increasing accuracy, the possibility of ascertaining its velocity velocity becomes lessbecomes less and vice versa and vice versa.''.''

A A revolutionary approachrevolutionary approach to computing to computing and communicationand communication

We need to consider a We need to consider a revolutionaryrevolutionary rather than rather than an evolutionary approach to computing. an evolutionary approach to computing.

Quantum theory Quantum theory does not play only a supporting does not play only a supporting rolerole by prescribing the limitations of physical by prescribing the limitations of physical systems used for computing and communication. systems used for computing and communication.

Quantum properties such as Quantum properties such as uncertainty, uncertainty, interference, and interference, and entanglement entanglement

form the foundation of a new brand of theoryform the foundation of a new brand of theory, the , the quantum information theory.quantum information theory.

In quantum information theory the In quantum information theory the computational computational and communication processes rest upon and communication processes rest upon fundamental physicsfundamental physics. .

Milestones in Milestones in quantum physicsquantum physics 19001900 - - Max PlankMax Plank presents the presents the black body radiation black body radiation

theorytheory; the quantum theory is born. ; the quantum theory is born.

19051905 - - Albert EinsteinAlbert Einstein develops the develops the theory of the theory of the photoelectric effect.photoelectric effect.

19111911 - - Ernest RutherfordErnest Rutherford develops the develops the planetary planetary model of the atom.model of the atom.

19131913 - - Niels BohrNiels Bohr develops the develops the quantum model of the quantum model of the hydrogen atom.hydrogen atom.

Milestones in Milestones in quantum physicsquantum physics 19231923 - - Louis de BroglieLouis de Broglie relates the relates the momentum of a momentum of a

particle with the wavelengthparticle with the wavelength

19251925 - - Werner HeisenbergWerner Heisenberg formulates the formulates the matrix matrix quantum mechanics.quantum mechanics.

19261926 - - Erwin SchrodingerErwin Schrodinger proposes the proposes the equation for equation for the dynamics of the wave function.the dynamics of the wave function.

Milestones in quantum physics (cont’d)Milestones in quantum physics (cont’d)

1926 1926 - - Erwin Schrodinger and Paul DiracErwin Schrodinger and Paul Dirac show the show the equivalence equivalence of of Heisenberg's matrix formulation and Dirac's algebraic one with Heisenberg's matrix formulation and Dirac's algebraic one with Schrodinger's wave functionSchrodinger's wave function..

19261926 - - Paul DiracPaul Dirac and, independently, and, independently, Max Born, Werner Heisenberg, and Max Born, Werner Heisenberg, and Pasqual JordanPasqual Jordan obtain a obtain a complete formulation of quantum dynamics.complete formulation of quantum dynamics.

19261926 - - John von NewmannJohn von Newmann introduces introduces Hilbert spacesHilbert spaces to quantum to quantum mechanics.mechanics.

19271927 - - Werner HeisenbergWerner Heisenberg formulates the formulates the uncertainty principle.uncertainty principle.

Milestones in Milestones in computing and informationcomputing and information theorytheory

19361936 - - Alan TuringAlan Turing dreams up the dreams up the Universal Universal Turing MachineTuring Machine, UTM. , UTM.

19361936 - - Alonzo ChurchAlonzo Church publishes a paper asserting publishes a paper asserting that `èvery function which can be regarded as that `èvery function which can be regarded as computable can be computed by an universal computable can be computed by an universal computing machine''. computing machine''. Church ThesisChurch Thesis..

19451945 - - ENIACENIAC, the world's first , the world's first general purpose general purpose computercomputer, the brainchild of , the brainchild of J. Presper Eckert and J. Presper Eckert and John MacaulyJohn Macauly becomes operational. becomes operational.

Milestones in Milestones in computing and informationcomputing and information theorytheory

19461946 - A report co-authored by - A report co-authored by John von NeumannJohn von Neumann outlines the von Neumann architecture.outlines the von Neumann architecture.

19481948 - - Claude ShannonClaude Shannon publishes `À Mathematical publishes `À Mathematical Theory of Communication’’.Theory of Communication’’.

19531953 - The - The first commercial computer, UNIVAC I.first commercial computer, UNIVAC I.

Milestones in Milestones in quantum computingquantum computing 19611961 - - Rolf LandauerRolf Landauer decrees that decrees that computation is computation is

physical physical and studiesand studies heat generation. heat generation.

19731973 - - Charles BennetCharles Bennet studies the studies the logical logical reversibilityreversibility of computations. of computations.

19811981 - - Richard FeynmanRichard Feynman suggests that suggests that physical physical systemssystems including quantum systems can be including quantum systems can be simulated exactly with quantum computers. simulated exactly with quantum computers.

19821982 - - Peter BeniofPeter Beniof develops develops quantum mechanical quantum mechanical models of Turing machines.models of Turing machines.

Milestones in Milestones in quantum computingquantum computing

19841984 - - Charles Bennet and Gilles BrassardCharles Bennet and Gilles Brassard introduce introduce quantum cryptographyquantum cryptography..

19851985 - - David DeutschDavid Deutsch reinterprets the reinterprets the Church-TuringChurch-Turing conjecture. conjecture.

19931993 - - Bennet, Brassard, Crepeau, Josza, Bennet, Brassard, Crepeau, Josza, Peres, WootersPeres, Wooters discover discover quantum quantum teleportationteleportation..

19941994 - - Peter ShorPeter Shor develops a clever develops a clever algorithm for algorithm for factoringfactoring large numbers. large numbers.

Deterministic versus probabilistic photon Deterministic versus probabilistic photon behaviorbehavior

(b)(a)

D1

D2

D3

D5

D7

Detector D1

Detector D2

Beam splitter

Incident beam of light

Reflected beam

Transmitted beam

The puzzling The puzzling nature of lightnature of light

If we start If we start decreasing the decreasing the intensity of the incident lightintensity of the incident light we observe the we observe the granular granular nature of light. nature of light. Imagine that we send a Imagine that we send a single single

photon. photon. Then Then eithereither detector D1 or detector D1 or

detector D2 will record the arrival detector D2 will record the arrival of a photon. of a photon.

If we If we repeatrepeat the experiment the experiment involving a involving a single photonsingle photon over over and over again we observe and over again we observe that each one of the two that each one of the two detectors records a number of detectors records a number of events. events.

Could there be Could there be hidden hidden informationinformation, which controls the , which controls the behavior of a photon? behavior of a photon? Does a photon carry a gene and Does a photon carry a gene and

one with a one with a ``transmit'' gene``transmit'' gene continues and reaches detector continues and reaches detector D2 and another with a D2 and another with a ``reflect'' ``reflect'' genegene ends up at D1 ends up at D1??

(b)(a)

D1

D2

D3

D5

D7

Detector D1

Detector D2

Beam splitter


Reflected beam

Transmitted beam

Each detector Each detector detects single detects single photons. photons. Why?Why?

What is a What is a hidden hidden information information that controls that controls thisthis

In an attempt to In an attempt to solve this puzzle solve this puzzle we design this we design this setupsetup

The puzzling nature The puzzling nature of light (cont’d)of light (cont’d)

Consider now a Consider now a cascade of cascade of beam splitters.beam splitters.

As before, we send a As before, we send a single single photonphoton and and repeat the repeat the experiment many timesexperiment many times and and count the numbercount the number of events of events registered by each detector. registered by each detector.

According to our theory we According to our theory we expect the expect the first beam splitter first beam splitter to decideto decide the fate of an the fate of an incoming photon; incoming photon; the photon is either reflected by the photon is either reflected by

the first beam splitter or the first beam splitter or transmitted by all of them. transmitted by all of them.

Thus, Thus, only the first and last only the first and last detectors in the chaindetectors in the chain are are expectedexpected to register an equal to register an equal number of events. number of events.

Amazingly enough, the Amazingly enough, the experiment shows that experiment shows that all all the detectors have a the detectors have a chance to register an chance to register an event.event.

(b)(a)

D1

D2

D3

D5

D7

Detector D1

Detector D2

Beam splitter


Reflected beam

Transmitted beam

Why all Why all these these detectors detectors detect detect light?light?

State descriptionState description

O

1V

(a)

= q

O

1V

(b)

0 0

1 1q1

q0

q1 = q

q045o

30o

A mathematical A mathematical model to describe model to describe

the state of a the state of a quantum systemquantum system

10 10

1|||| 21

20

are complex numbersare complex numbers|,| 10

Superposition and uncertaintySuperposition and uncertainty

In this model a stateIn this model a state

is a is a superpositionsuperposition of two basis states, “0” and “1” of two basis states, “0” and “1” This This state is unknownstate is unknown before we make a measurementbefore we make a measurement.. After we perform a measurement the system is no longer After we perform a measurement the system is no longer

in an uncertain state in an uncertain state but it is in one of the two but it is in one of the two basis statesbasis states. . is the is the probability of observingprobability of observing the outcome “1” the outcome “1” is the is the probability of observing the outcome “0”probability of observing the outcome “0”

10 10

1|||| 21

20

20 ||

21 ||

MultipleMultiple measurements measurements

black

white

hard

soft

(a) (b)

black

white

black

white

hard

soft

(c)

Why black Why black appears appears again in last again in last mirror?mirror?

Measurements in Measurements in multiple basesmultiple bases

| >

| >

| >

| >

|

0

1

10

0

1

Some of Some of basesbases

This vector This vector can be can be measured in measured in different different basesbases

Measurements Measurements of superposition of superposition

statesstates

The The polarization of a photon polarization of a photon is is described bydescribed by a unit vector a unit vector on a two-dimensional on a two-dimensional space with basis | 0 > and | space with basis | 0 > and | 1>.1>.

Measuring the polarization Measuring the polarization is equivalent to is equivalent to projecting projecting the random vectorthe random vector onto one onto one of the two basis vectors. of the two basis vectors.

Source S sends Source S sends randomly randomly polarized lightpolarized light to the to the screen; the measured screen; the measured intensity is I. intensity is I.

The filter A with vertical The filter A with vertical polarization is inserted polarization is inserted between the source and the between the source and the screen an the intensity of screen an the intensity of the light measured at E is the light measured at E is about I/2. about I/2.

(a)

(b)

S

E

(c)

E

S

A

intensity = I intensity = I/2

(d)

E

S

A B

intensity = 0

(e)

E

S

A B

intensity = I/8

C

0|

1

|

AA EE

Measurements Measurements of superposition of superposition

statesstates

Filter B with Filter B with horizontal horizontal polarizationpolarization is inserted is inserted between A and E. between A and E. The The intensityintensity of the light of the light

measured at E measured at E is now 0is now 0. . Filter C with a 45 deg. Filter C with a 45 deg.

polarization is inserted polarization is inserted between A and B. between A and B. The intensity of the light The intensity of the light

measured at E is about 1 / 8. measured at E is about 1 / 8. (a)

(b)

S

E

(c)

E

S

A

intensity = I intensity = I/2

(d)

E

S

A B

intensity = 0

(e)

E

S

A B

intensity = I/8

C

0|

1

|

The The superposition probabilitysuperposition probability rule rule

IfIf an event may occur an event may occur in two or more in two or more indistinguishable waysindistinguishable ways thenthen the the probability probability amplitude of the eventamplitude of the event is is the sum of the the sum of the probability amplitudesprobability amplitudes of each case of each case considered separately considered separately (sometimes known as (sometimes known as Feynman ruleFeynman rule).).

(a)

O

1V

| 0 >

| 1 >

(b)

V

| 0 >

| 1 >

(c)

1+q

+q

+q

-q

(| t >) (| t >)

(| r >) (| r >)

direction2direction1

Reflecting mirror U

Reflecting mirror L

Detector D1

Detector D2

Source S1

Beam splitter BS2Beam splitter BS1

Source S2

direction1

direction2

The experiment illustrating The experiment illustrating the superposition the superposition

probability ruleprobability rule

In certain conditions, we In certain conditions, we observe experimentally that a observe experimentally that a photon photon emitted by S1 is emitted by S1 is always detected by D1 and always detected by D1 and never by D2never by D2 and and one emitted one emitted by S2 is always detected by by S2 is always detected by D2 and never by D1.D2 and never by D1.

A photon emitted by one of A photon emitted by one of the sources S1 or S2 may the sources S1 or S2 may take one of take one of four four different different pathspaths shown on the next shown on the next slide, depending whether it is slide, depending whether it is transmitted, or reflected by transmitted, or reflected by each of the two beam each of the two beam splitters.splitters.

(a)

O

1V

| 0 >

| 1 >

(b)

V

| 0 >

| 1 >

(c)

1+q

+q

+q

-q

(| t >) (| t >)

(| r >) (| r >)

direction2direction1

Reflecting mirror U

Reflecting mirror L

Detector D1

Detector D2

Source S1

Beam splitter BS2Beam splitter BS1

Source S2

direction1

direction2

|0> = |t>|0> = |t>

|1> = |r>|1> = |r>+q+q

-q-q

transmitransmitt

reflectreflect

D1S1

(a) - The TT case: the probabilityamplitude is (+q)(+q).

T +q T +q

(b) The RR case: the probabilityamplitude is (+q)(+q).

D2

S1

(c) - The TR case: theprobability amplitude is (+q)(-q).

T +q

R -q

(d) The RT case: the probabilityamplitude is (+q)(+q).

D2

S1

T +q

R +q

D1S1

R +q R +q

direction1 direction2

BS1 BS2

BS1 BS1

BS1

BS2

BS2

BS2

L

L

U

U

A photon emitted by A photon emitted by one of the sources one of the sources S1 or S2 may S1 or S2 may take take one of one of four four different different pathspaths TT. TR, RR and TT. TR, RR and RT, depending RT, depending whether it is whether it is transmittedtransmitted, or , or reflectedreflected by each of by each of the two beam the two beam splitterssplitters

photon photon emitted emitted by S1 is by S1 is always always detected by D1 detected by D1 and never by D2and never by D2

RR=reflect+reflectRR=reflect+reflect

Why?Why?

A A photon coincidencephoton coincidence experiment experiment

Reflecting mirror U

Reflecting mirror L

Detector D1

Detector D2

Source

Beam splitter

A A glimpse into the worldglimpse into the world of quantum of quantum computing and quantum information computing and quantum information

theorytheory

Quantum key Quantum key distributiondistribution Exact simulation Exact simulation of systemsof systems with a very with a very

large state spacelarge state space Quantum Quantum parallelismparallelism

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