Jonathan P. Dowlingbaton.phys.lsu.edu/~jdowling/talks/Tulane07.pdf · • Fiber and Free Space Q....
Transcript of Jonathan P. Dowlingbaton.phys.lsu.edu/~jdowling/talks/Tulane07.pdf · • Fiber and Free Space Q....
QUANTUM TECHNOLOGIES:THE SECOND QUANTUM REVOLUTION*
Jonathan P. DowlingQuantum Science & Technologies Group Hearne Institute for Theoretical Physics
Louisiana State University
Tulane University, 25 April 2007
quantum.phys.lsu.edu
* JP Dowling & GJ Milburn, Phil. Trans. Roy. Soc. Lond. A 361 (2003) 1–20 (quant-ph/0206091)
Nano-Technology Quantum Technology
"There's Plenty of Room at the Bottom.”— Richard Feynman
{1010010100101101}
"There's Plenty MORE Room In HilbertSpace!" — JPD
A 16 bit register stores 16bits at a time.
A 16 QUBIT register “stores”216 bits at a time!
|1010010100101101>
Quantum Sciences—The First Revolution
1900s Planck Blackbody Law1920s Quantum Mechanics Completed
1920s Relativistic Quantum Mechanics1920s Dirac Quantizes E&M Field
1930s Bloch’s Theory of Solid State1940s Quantum Electrodynamics
1950s Nuclear Magnetic Resonance1950s Masers and Atomic Clocks
1950s Theory of Superconductivity 1960s Invention of the Laser
1980s Laser Cooling of Atoms and Ions1990s Bose-Einstein Condensates
Quantum Technology—The Second Revolution:Harnessing Entanglement and Coherent Quantum Systems
1970s Optical Tests of Bell’s Inequalities1980s Quantum Cryptography (QKD) Invented
1980s Quantum Computing Invented 1994 QKD Demonstrated over 10km Fiber
1994 Factoring Algorithm Discovered1994 Ekert’s Talk on Factoring Algorithm at ICAP
1994-95 NIST & DoD Workshops on QC1995 DoD Funding for QC Comes Online
1996 Quantum Error Correction—QC Scalable!1997 XOR in Ion Traps and Cavity QED
1998 Kane Scheme for QC in Semiconductors1999 Nakamura Observes Rabi Oscillations in SQUIDs
2000 Four-Fold Entanglement in Ion Trap2001 Scalable Linear Optical Quantum Computing
2002 Clark Constructs Four-Qubit Kane Prototype Mockup2003 Nakamura Entangles a SQUID Pair
Schrödinger’s Cat Revisited
Paradox? What Paradox!?
(1.) The State of the Cat is “Entangled” with That of the Atom.
(2.) The Cat is in a Simultaneous Superposition of Dead & Alive.
(3.) Observers are Required to “Collapse” the Cat to Dead or Alive
Quantum Entanglement
“Quantum entanglement is the characteristic trait ofquantum mechanics, the one that enforces its entiredeparture from classical lines of thought.”
— Erwin Schrödinger
Einstein, Podolsky, Rosen (EPR) Paradox
AlbertEinstein
Boris Podolsky
“If, without in any way disturbing a system, we canpredict with certainty ... the value of a physicalquantity, then there exists an element of physicalreality corresponding to this physical quantity."
Nathan Rosen
Hidden Variable Theory
+A B A B
Can the Spooky, Action-at-a-distance Predictions(Entanglement) of Quantum Mechanics…
+A B A B
…Be Replaced by Some Sort of Local, Statistical,Classical (Hidden Variable) Theory?
NO!—Bell’s Inequality
The physical predictions of quantum theory disagree withthose of any local (classical) hidden-variable theory!
John Bell
Quantum Technology: The Second Quantum RevolutionJPD & GJ Milburn, Phil. Trans. Roy. Soc. Lond. A 361 (2003) 1–20 (quant-ph/0206091)
QuantumMechanical
Systems
PendulumsCantileversPhonons
CoherentQuantumElectronics
SuperconductorsExcitonsSpintronics
Quantum Optics
Ion TrapsCavity QEDLinear Optics
QuantumAtomics
Bose-EinsteinAtomic CoherenceIon TrapsQuantum
InformationProcessing
Relationship Between Quantum and Nano-Technologies
QuTech NanoTechQuantumComputer
QuTech Drives NanoTech
NanoTech Drives QuTech
Quantum Computing & Information
• Quantum Search and Integrals
• Factoring Algorithm
• Quantum Error Correction
• Fault Tolerant Q. Computing
• Q. Computing Complexity
Quantum Algorithms
• Quantum Cryptoanalysis
• Quantum Key Distribution
• Relativistic Quantum Information Theory
• Quantum Channel Capacity
• Quantum Message Authentication
Quantum Information
• Cavity QED Logic Gates
• Fiber and Free Space Q. Key Distribution
• Nuclear Spins on a Chip
• Coulomb Blockade Device
• Superconducting Quantum Interference
Quantum Information Hardware
Ion Trap Q. Register
Solid State QuantumLogic Gate
Error Correction
Quantum Atomics and Atom Optics
• Atom Interferometric Gyros
• Atomic Gravity Gradiometers
• Nanofabrication by Atom Interference
• Atom Holography
• Atom Lens, Mirror, Beamsplitter
Atom Optics
• Laser Cooling Techniques (Nobel 97)
• Magneto-Optical Trapping
• All Optical Trapping
• Evaporative Cooling
• Improved Atomic Clocks
Atom Cooling and Trapping
• Bose-Einstein Condensates
• Atom Lasers
• Atom Holography
• Improved Atom Interferometry
• Entanglement-Improved Signal to Noise
Coherent States of Atomic Matter
Atom Laser
Ion Trap Atomic Clock
Coherent Quantum Electronics
• Artificial Atoms
• Excitons—Artificial Atoms II
• Cavity QED in Solid Solid State
• Control of “Phonon-The-Destroyer”
• Excitonic BEC Just Around the Corner?
Quantum Dots
• Electron Phase Devices
• Superconducting Phase Interference
• Charge Based Interference
• Quantum Size Effects
• Entangled SQUIDS -- Super Mag. Sensors?
Coherent Mesoscopic SQUIDS
• Electron Spin Transport in Solid State
• Nuclear-Electronic Interactions
• NMR Computing Qubits
• Single Nucleus as Sensor
Spintronics
Exciton
Superconducting Q. Circuit
Q. Dot
Quantum Nano-Electro-Mechanical Devices (Q-NEMS)
• Phonon Resonators
• Phonon Interferometer
• Phononic Band-Gap Materials
• Control of “Phonon-The-Destroyer”
• Phonon Laser and Squeezed States
Coherent Phonon Manipulation
• Cantilever
• Pendula
• Single Spin Magnetic Force Microscopy
Quantum Nano-Mechanical Devices
• Bucky Ball Interferometers
• Mesoscopic Cat States
• Entangled States of Mech. Resonators
Macroscopic Interference
Phonon Squeezing
Q. Mech. Resonator
Where Do You Want to Go Tomorrow? ™
TWO-SLITS & QUANTUM NONLOCALITY
CLASSICALTwo particles(resources) required tolearn about two slits.
QUANTUMOnly one particle (wave)required to “learn” abouttwo slits.
“... a phenomenon which is impossible, absolutely impossible, to explain in any classicalway, and which has in it the heart of quantum mechanics. In reality, it contains the onlymystery. We cannot make the mystery go away by ‘explaining’ how it works. We will justtell you how it works. In telling you how it works we will have told you about the basicpeculiarities of all quantum mechanics.” -Feynman
Traveling SALESMEN &QUANTUM Parallelism
A
B
E
D
F
C
A
B
E
D
F
C
CLASSICALExponential number ofclassical “bees”(particles/resources)needed to examine N!paths.
QUANTUMOnly one quantum bee(particle/wave) required to“learn” about N! paths.
c-bee
q-bee
THE ROLE OF ENTANGLEMENT
A
B
E
D
F
C
Program nonlocal quantum correlations (entanglement) into theinput register. Lift out shortest path by constructiveinterference using only N instead of N! q-bees. Exponentialspeed up in resource usage!
The readout problem: one q-bee makesone “click” on the detecting screen. Informationabout the N! paths is lost.
Quantum Parallelism & Entanglement
Classical 16-Bit Register:[1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1] 2X2X2…X2= 210
Can hold only one of 210 possible numbers at a time.
Quantum 16-Bit Register in Superposition:[0,0,0,0,0,0,0,0,0,0,000000]+…+ [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
Can hold all 210 possible numbers simultaneously!
BITS VERSUS QUBITS & UNIVERSALITY•Qubits can be in a quantum superposition of {0} and {1}.• The general state can be represented by a vector on the unit sphere.
A universal quantum computer can be constructed using rotations on Hilbertspace (sphere) and a Controlled-NOT gate (XOR).
|0> =
|1> =
QUANTUM FACTORING:Shor’s AlgorithmSecurity of the public key cryptographydepends on the assumed inabilityof a classical computer to factor C (publickey) into P and Q (private key) rapidly.Classical sieving is exponentially slow.
C=10N
10Nsteps
C/2 C/3 C/5 C/7 C/13 C/17 •••A quantum state can test anexponentially large number offactors without usingexponentially large amount ofresources.
! = " an | exp(2#iC/n)$
Constructive interferenceoccurs for computational “paths”corresponding to divisors of Cwith no remainder.
Peter Shor
Separated at Birth?
Gene Shalit
NEEDLE IN A HAY STACK
Needle
Best classical algorithm: Start at one end and prick your finger withone straw at a time until you yell “OUCH!” at the needle. Sometimesyou’ll be lucky and the needle will be near the beginning, sometimesnot and it will be near the end. On average, N/2 tries will be neededto find it. Best you can do.
GROVER’S ALGORITHM
Note from classical antenna theory: Power from an unphased arrayof N antennas scales like N, but when phased scales like N^2.
Lov Grover at Work….
Episode 12: The Getaway
At SD-6, Sloane offers Sydney a new mission: toretrieve Triad's prototype quantum gyroscope missileguidance system. She and Dixon are to interceptCarl Shatz, the courier who is transporting thegyroscope from Berlin to a lab in East France.Vaughn's countermission for Sydney is to steal thegyroscope and create a defective one for SD-6.
Quantum Sensors: Fantasy?
Quantum Sensors: Realty!
The potential payoffs are many. Entanglement and other quantum weirdness mayboost the accuracy of radar, Global Positioning System (GPS) receivers, and othernavigation devices.
It may improve manufacturers' ability to lay down tiny structures on microchips,expedite explorations for oil, improve the vision of telescopes, and increase theaccuracy of atomic clocks.
Gadgets from the QuantumSpookhouseNavigation devices and other technologies may gainfrom queer quantum effectsPeter Weiss
Quantum technology might even enable us to see objects without actuallylooking at them — and without being seen ourselves.
Photon Laser Gyro Atom Laser Gyro
Atom Gyro Prototype
Quantum Atomic Gravity Gradiometer
Pattern Shift Proportional to Changing Gravity Gradient
Atom
Objectives
Approach Status• Use quantum Optics techniques to create,manipulate and measure the collectivestate of an assembly of superconductingqubits.• cavity QED approach• Adapt techniques used in ion trapexperiments to evaluate the uncertaintyon the energy estimation (spectrometry).
Established the first relation between theuncertainty on the electric charge Qg (ormagnetic flux Fx) estimation and the numberN of qubits:
NQ xg /1!"!##
Develop theoretical techniques toenable Heisenberg-limited magneticand electric field measurementswith superconducting circuits.
Entangled SQUID MagnetometerA Guillaume & JPD, Physical Review A 73 (4): Art. No. 040304 APR 2006.
Quantum Clock Synchronization
Quantum MetrologyH.Lee, P.Kok, JPD,J Mod Opt 49,(2002) 2325
a† N a N
AN Boto, DS Abrams,CP Williams, JPD, PRL85 (2000) 2733