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Quantum Computer Implementations University of Michigan Department of Physics Christopher Monroe US Advanced Research and Development Activity US Army Research Office US National Security Agency National Science Foundation

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ENIAC (1946)

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The first solid-state transistor (Bardeen, Brattain & Shockley, 1947)

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i386 i486 Pentium Pentium Pro Source: Intel Projected # Transistors Moore’s Law Pentium III

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“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 Feynman

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A 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

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…BAD NEWS… Measurement gives random result e.g., |011 GOOD NEWS… N qubits can store 2 N numbers simultaneously Example: 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

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…GOOD NEWS! quantum interference before measurement Deutsch (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 quantum XOR gate: superposition entanglement depends on all inputs quantu m gates fast number factoring

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Quantum Entanglement: Einstein’s “Spooky action-at-a-distance” or “superposition” “entangled superposition”

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Quantum computer hardware requirements 1.Must make states like |000…0 + |111…1 x x + 2. Must measure state with high efficiency strong coupling between qubits weak coupling to environment strong coupling to environment

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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0.3 mm

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Ion Trap Primer + E(r) ? + E(r) NO! E saddle point z Trick: apply sinusoidal electric field (rotate saddle) RF (PAUL) TRAP

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x + [ 2 cos t]x = 0 2 = eV 0 /md 2 Dynamics of a single ion in a rf trap e= ion charge m=ion mass V 0 =rf voltage amplitude d=trapsize time position x “secular” motion at frequency trap 2 / MHz “micromotion” at frequency 100 MHz Mathieu Equation: x(t) bounded for <<

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V 3D ion trap geometry ring endcap d

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2 m Michigan Ion Trap

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0.2 mm |0 |1

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“Perfect” quantum measurement of a single atom state |0 state |1 # photons collected in 200 s Probability ion fluoresces 10 8 photons/sec laser ion remains dark # photons collected in 200 s >99% detection efficiency!

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Atomic Cd + energy levels or Be +, Mg +, Sr +, Ca +, Ba +, Cd +, Hg +,…. S 1/2 P 3/2 |1 |0 ~10 8 photons/sec 215nm 15GHz

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S 1/2 P 3/2 |1 |0 2-photon “stimulated Raman” transitions Coherent transitions between |0 and |1

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S 1/2 P 3/2 |1 |0 2-photon “stimulated Raman” transitions Mapping: ( |0 + |1 ) |0 m |0 ( |0 m + |1 m )

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( 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)

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Trapped Ion Quantum Computer laser cool to rest laser j k map j th qubit to collective motion laser j k flip k th qubit if collective motion laser j k map collective motion back to j th qubit Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995) Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)

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State-of-the-art: Four-qubit quantum logic gate Sackett, et al., Nature 404, 256 (2000) |0000 |0000 + e i |1111

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Why only 4 ? fluctuating electric patch potentials on surface technical, not fundamental limitation More ions: difficult (& slow) to isolate single mode of motion Decoherence of motion: 0.5 mm

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quantum memory “refrigerator” ions suppress motional decoherence Scaling proposal 1: the “quantum CCD” few mm (Kielpinski, Monroe, Wineland, submitted to Nature)

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“accumulator”

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target quantum bits entangled laser pulse

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motion head target pushing laser Scaling proposal 2: ion trap array and head Cirac and Zoller, Nature 404, (2000).

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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Optical Lattices (trapped neutral atoms) /2 lasers induce electric dipole that interacts with laser itself! = E U = E = |E| 2 U(x) = |E(x)| 2 polarizability

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moving neutral atoms qubits together for entanglement

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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Individual photons A B | 1 = |0 A |1 B + |1 A |0 B Quantum Entanglement! send single photons 50/50 weak laser qubit: |0 = zero photons |1 = one photon

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single photon source: optical parametric downconversion BUT… not scalable! Prob(downconversion)~10 -8 ultraviolet ( ) visible (or infrared) ( ) X (2) nonlinear crystal (e.g., ADP, BBO,…)

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M1 M2 Interaction strength between atom & photon U = atomE 1 (Vol) 1/2 L = 1 mm, > sec requires Reflectivity > % atom L qubit: |0 = zero photons in cavity |1 = one photon in cavity cavity-QED: deterministically creating and storing single photons in a resonator

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Quantum Network Cirac, Zoller, Kimble, Mabuchi, Phys. Rev. Lett. 78, 3221 (1997) (t) (-t)

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H.J. Kimble (CalTech) M. Chapman (Georgia Tech) G. Rempe (Max Planck Inst., Garching)

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H. J. Kimble, CalTech

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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Superconducting charges Nakamura (NEC-Japan) Schoelkopf (Yale) Devoret (Yale)

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Single-qubit rotations on a Cooper-pair Box |N |N+1 (N=# Cooper pairs) Nakamura, et. al., Nature 398, 786 (1999)

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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Superconducting currents J.E. Mooij,… Science 285, 1036 (1999). quantized flux qubit states

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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Semiconductor Quantum Dots e.g., Duncan Steel (University of Michigan) GaAs AlGaAs Optical Field

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~10.5 ps ~18.5 ps Exciton Population Pulse Area Excitonic Rabi oscillations T. Stievater, et al. (submitted)

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GaAs AlGaAs Optical Field GaAs AlGaAs

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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Nuclear Magnetic Resonance liquid state, room temperature NMR several “qubit operations” demonstrated, BUT: no entanglement not scalable (signal decreases exponentially with # qubits) (not quantum computing?) Gershenfeld and Chuang, Science 275, 350 (1997)

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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Platzman and Dykman, Science 284 (1999) Electrons floating on liquid helium 1-dimensional “atom”

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geometry

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readout positive bias applied imaging channel plate … electrons tunnel out only if in state 2

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Fabrication of submerged electrodes (J. Goodkind, UCSD)

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

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Phosphorus atoms in Silicon Kane, Nature 393, 133 (1998) U. Maryland, Los Alamos, Australia NOTE: Bruce Kane will give Physics Dept. colloquium Wed., Nov. 7, 4PM qubit stored in phosphorus nuclear spin (P: spin-1/2) (Si: spin 0)

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Single-qubit rotations: electron/nuclear spin-spin interaction (hyperfine interaction) Two-qubit entangling gates: bring adjacent donor electrons together (exchange interaction)

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Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon scales works

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Quantum Computing Abyss ? noise reduction new technology # quantum bits error correction efficient algorithms 5 5>1000 <100>10 9 theoretical requirements for “useful” QC state-of-the-art experiments # quantum bits # logic gates

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