PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Quantum computer hardware requirementsSlide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Quantum Computing AbyssSlide 67Quantum Computer ImplementationsUniversity of MichiganDepartment of Physicshttp://monroelab2.physics.lsa.umich.edu/Christopher MonroeUS Advanced Research andDevelopment ActivityUS Army Research OfficeUS National Security AgencyNational Science FoundationENIAC(1946)The first solid-state transistor(Bardeen, Brattain & Shockley, 1947)197519801985199019952000200520102015808680286i386i486PentiumPentium ProSource: IntelProjected103104105106107108109# TransistorsMoore’s LawMoore’s LawPentium III“When we get to the very, very small world – say circuits of seven atoms - we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics…”“There's Plenty of Room at the Bottom”(1959 APS annual meeting)Richard FeynmanA quantum computer hosts quantum bits which can store superpositions of 0 and 1 classical bit: 0 or 1 quantum bit: |0 + |1Benioff (1980)Feynman (1982)“qubit” =two-level system|0|1|0|1…BAD NEWS…Measurement gives random resulte.g.,   |011GOOD NEWS…N qubits can store 2N numbers simultaneouslyExample: N=3 qubits = a 0 |000 + a 1 |001 + a 2 |010 + a 3 |011 a 4 |100 + a 5 |101 + a 6 |110 + a 7 |111…GOOD NEWS!quantum interference before measurementDeutsch (1985)Shor (1994)Grover (1996)|0 |0  |0 |0|0 |1  |0 |1|1 |0  |1 |1|1 |1  |1 |0e.g., (|0 + |1)|0  |0|0 + |1|1 quantumXOR gate:superposition  entanglementdepends on all inputsquantum gatesfast number factoringQuantum Entanglement: Einstein’s “Spooky action-at-a-distance”oror“superposition”“entangled superposition”Quantum computer hardware requirements1. Must make states like |000…0 + |111…1xx+2. Must measure state with high efficiency• strong coupling between qubits• weak coupling to environment•strong coupling to environmentPhysical Implementations1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)3. Semiconductorsquantum dots4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon0.3 mmIon Trap Primer+E(r) ?+E(r)NO! E 0saddle pointzTrick: apply sinusoidal electric field (rotate saddle)RF (PAUL) TRAPx + [2 cost]x = 02 = eV0/md2Dynamics of a single ion in a rf trap e = ion charge m =ion mass V0=rf voltage amplitude d =trapsizetimeposition x “secular” motionat frequency trap  2/  MHz“micromotion”at frequency  100 MHzMathieu Equation: x(t) bounded for  << V3D ion trap geometryringendcapendcapd2 mMichiganIon Trap0.2 mm|0|1““Perfect” quantum measurement of a single atomPerfect” quantum measurement of a single atomstate |0state |1# photons collected in 200sProbability302010000.2ion fluoresces 108 photons/seclaserlaserion remains dark302010001# photons collected in 200s>99% detection efficiency!Atomic Cd+ energy levelsor Be+, Mg+, Sr+, Ca+, Ba+, Cd+, Hg+,….S1/2P3/2|1|0 ~108photons/sec215nm15GHzS1/2P3/2|1|02-photon“stimulated Raman”transitionsCoherent transitions between |0 and |1•••012•••012S1/2P3/2|1|02-photon“stimulated Raman”transitionsMapping: (|0 + |1) |0m  |0 (|0m + |1m)0 20 40 60 80 10001 (s)Prob(|0)Single ion transitions between |0|rest  and |1 |moving • Prepare in |0|rest • Pulse Raman beams for time • Pulse Detection beams for 200 ms• step CM, et. al., Phys. Rev. Lett. 75, 4714 (1995)Trapped Ion Quantum ComputerTrapped Ion Quantum Computerlaser cool to restlaserjkmap jth qubit to collective motionlaserjkflip kth qubit if collective motionlaserjkmap collective motion back to jth qubit Cirac and Zoller, Phys. Rev. Lett. Cirac and Zoller, Phys. Rev. Lett. 7474, 4091 (1995), 4091 (1995)State-of-the-art:Four-qubit quantum logic gateSackett, et al., Nature 404, 256 (2000)|0000  |0000 + ei|1111Why only 4 ?Why only 4 ?fluctuating electric patch potentials on surfacetechnical, not fundamental limitation• More ions: difficult (& slow) to isolate single mode of motion• Decoherence of motion:0.5 mmquantummemory“refrigerator” ions suppress motional decoherenceScaling proposal 1: the “quantum CCD”few mm(Kielpinski, Monroe, Wineland, submitted to Nature)“accumulator”target quantumbits entangledlaserpulsemotionheadtargetpushinglaserScaling proposal 2: ion trap array and headCirac and Zoller, Nature 404, 579-581 (2000).Physical Implementations1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)3. Semiconductorsquantum dots4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in siliconOptical Lattices (trapped neutral atoms)/2lasers induce electric dipolethat interacts with laser itself! = EU =  •E = |E|2U(x) = |E(x)|2polarizabilitymoving neutral atoms qubits together for entanglementPhysical Implementations1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)3. Semiconductorsquantum dots4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in siliconIndividual photonsAB|1 = |0A|1B + |1A|0BQuantumEntanglement!send singlephotons50/50weaklaserqubit: