Quantum Information Science (NIST trapped ion group) Dilbert confronts Schrödinger s cat, 4/17/12

Transcription

1 Quantum Information Science (NIST trapped ion group) Dilbert confronts Schrödinger s cat, 4/7/

2 Data storage: classical: computer bit: (0) or () quantum: qubit α 0 +β superposition Scaling: Consider 3-bit register (N = 3): Classical register: (example): (0) Quantum register: (3 qubits): Ψ= C 000 0,0,0 + C 00 0,0, + C 00 0,,0 + C 0 0,, + C 00,0,0 + C 0,0, + C 0,,0 + C,, (represents 3 numbers simultaneously) For N = 300 qubits, store numbers simultaneously (> classical information in universe!) Parallel processing: single gate operates on all N inputs simultaneously But!: quantum measurement rule: measured register gives only one number Factoring: Shor s Algorithm (994)

3 Atomic ion quantum computation: J. I. Cirac, P. Zoller, Phys. Rev. Lett. 74, 409 (995). START MOTION IN GROUND STATE. SPIN MOTION MAP Ignacio Cirac Peter Zoller MOTION DATA BUS (e.g., center-of-mass mode) INTERNAL STATE SPIN QUBIT m = 3 m = m = m = 0 m for motion Motion qubit states

4 Atomic ion quantum computation: J. I. Cirac, P. Zoller, Phys. Rev. Lett. 74, 409 (995). START MOTION IN GROUND STATE. SPIN MOTION MAP 3. SPIN MOTION GATE Ignacio Cirac Peter Zoller MOTION DATA BUS (e.g., center-of-mass mode) INTERNAL STATE SPIN QUBIT m = 3 m = m = m = 0 m for motion Motion qubit states

5 Interactions with laser beams : information transfer 0 alternative:, = hyperfine levels, + two-photon stimulated-raman transitions long coherence times ~ 30 min optical frequency 0 0 MHz (motional mode frequency)

6 SPIN-MOTION GATE: (Chris Monroe et al. PRL, 95) 0 ~ GG = σσ zz σσ zz 0 aux 0

7 Quantum computer algorithm to efficiently factorize large numbers ψ 0 3 in = N i= 0 Process all possible inputs simultaneously bit no. i N-qubits: Peter Shor (~ 994) e.g., for N = 3, Ψ in = 0,0,0 + 0,0, + 0,,0 +,0,0 + 0,, +,0, +,,0 +,, Circuit model: two-qubit gates U = U r,s (π) U p,q (π) R k (θ,φ) U i,j (π) N single qubit bit gate (manipulate superpositions)

8 Quantum computer algorithm to efficiently factorize large numbers ψ Process all possible inputs simultaneously bit no. 0 3 in = N i= 0 i N-qubits: analogous to waterwave interference (photo,hannover Univ.) two-qubit gates Peter Shor (~ 994) incident waves U = U r,s (π) U p,q (π) R k (θ,φ) U i,j (π) single qubit bit gate (rotation) N

9 Quantum computer algorithm to efficiently factorize large numbers Peter Shor (~ 994) ψ Process all possible inputs simultaneously bit no. 0 3 in N = i ψ = i i= 0 two-qubit gates U = U r,s (π) U p,q (π) R k (θ,φ) U i,j (π) out small selection measure qubits use measured i in classical algorithm to determine factors N single qubit bit gate (rotation) e.g., factorize 50 digit decimal # ~ 0 9 ops

10 Scale up qubit numbers? small electrodes: use lithographic techniques move ions in multi-zone arrays for scaling microfab at: GTRI, Sandia, NIST, Berkeley, Innsbruck, Mainz,. mm

11 Quantum simulation: mode frequency Center-of-mass mode tilt mode add magnetic field: H ( i) ( j) = J i ˆ σ ˆ σ + B ( i), j z z ˆ σ y i< j i Transverse Ising model (JQI, Innsbruck) moving standing wave statedependent optical-dipole forces transverse mode spectrum (9 ions) for ω force ω COM = i j J ˆ σ ˆ zσ z H -D array (Penning trap) Simulation in Wigner crystal (J. Bollinger et al., NIST) i< j ( ω force > ω COM ) H = J i, j i< j J i, j ~ ˆ σ ˆ σ i z j z + J 0 i j α (J i,j > 0, anti-ferromagnetic) vary α by varying detuning α = 0 - ~3

12 Atomic ion experimental groups pursuing Quantum Information Processing: Aarhus Amherst The Citadel Tsinghua (Bejing) U.C. Berkeley U.C.L.A. Duke ETH (Zürich) Freiburg Garching (MPQ) Georgia Tech Griffiths Hannover Innsbruck JQI (U. Maryland) Lincoln Labs Imperial (London) Mainz MIT NIST Northwestern NPL Osaka Oxford Paris (Université Paris) Pretoria, S. Africa PTB Saarland Sandia National Lab Siegen Simon Fraser Singapore SK Telecom, S. Korea Sussex Sydney U. Washington Weizmann Institute

13 Atomic ion experimental groups pursuing Quantum Information Processing: Aarhus Amherst The Citadel Tsinghua (Bejing) U.C. Berkeley U.C.L.A. Duke ETH (Zürich) Freiburg Garching (MPQ) Georgia Tech Griffiths Hannover Innsbruck JQI (U. Maryland) Lincoln Labs Imperial (London) Mainz MIT NIST Northwestern NPL Osaka Oxford Paris (Université Paris) Pretoria, S. Africa PTB Saarland Sandia National Lab Siegen Simon Fraser Singapore SK Telecom, S. Korea Sussex Sydney U. Washington Weizmann Institute + many other platforms: neutral atoms, Josephson junctions, quantum dots, NV centers in diamond, single photons,

14 Applications: Al + quantum-logic clock P Coulomb interaction P 3/ 3 P 0 Till Rosenband David Leibrandt λ = 67 nm Al + λ = 80 nm 5 Mg + (F=, m F = -) S / S 0 hyperfine qubit (F=3, m F = -3) α Al + β Al motion superposition α Mg + β Mg laser-cooled Mg + keeps Al + cold Mg + helps to calibrate B from all sources collisions observed by ions switching places Systematic uncertainty = 0.8 x 0-7

15 Future: More and better (more qubits, smaller gate errors) - dirty laundry: ion heating Simulation quantum logic gates emulate spin-spin coupling Example: transverse Ising model H now 0-3 per -qubit gate, need 0-4 for error correction improve hardware: e.g., optical fibers for UV collaborate with NIST surface group, D. Pappas et al. = ( i) ( j) J i ˆ σ ˆ σ + B ( i), j x x ˆ σ y i< j i useful simulations can tolerate higher errors Universal digital quantum simulation Metrology quantum-logic spectroscopy improve beyond standard quantum limit for phase measurements Factoring machine???? extend to molecules

16 NIST IONS, June 04 Jim Bergquist, John Bollinger, Joe Britton, Justin Bonet, Ryan Bowler, John Gaebler, Andrew Wilson, Dave Wineland, David Leibrandt, Peter Burns, Raghu Srinivas, Shon Cook, Robert Jordens David Hume Ting Rei Tan Shlomi Kotler, Dustin Hite, Katie McCormick,Susanna Todaro, Leif Waldner, Yiheng Lin, Daniel Slichter, James Chou, David Allcock, Didi Leibfried, Jwo-Sy Chen, Sam Brewer, Kyle McKay Not pictured: Brian Sawyer, Yong Wan, Aaron Hankin, Till Rosenband, Wayne Itano, Dave Pappas, Bob Drullinger