The trapped-ion qubit tool box Contemporary Physics, 5, 531-550 (011) Roee Ozeri Weizmann Institute of Science Rehovot, 76100, Israel ozeri@weizmann.ac.il
Physical Implementation of a quantum computer David Divincenzo s criteria: 1. Well defined qubits.. Initialization to a pure state 3. Universal set of quantum gates. 4. Qubit specific measurement. 5. Long coherence times (compared with gate & meas. time).
Universal Gate set - For N qubits, a general unitary transformation U acts on a N - dimension Hilbert space. - A finite set of unitary gates that spans any such U. - The Deutsch-Toffoli gate U - D. Deutsch, Proc. R. Soc. London, Ser. A, 45, 73, (1989).
Universal Gate set - For N-qubits, and unitary transformation U on a N -dimension Hilbert space. - A finite set of unitary gates that spans any such U. Single qubit gate -qubit C-not gate U - Rotations can be approximated to e by concatenating k gates, from a finite set {V i }, where k < polylog(1/e). - Barenco et. al. Phys. Rev. A, 5, 3457, (1995).
Physical Implementation of a quantum computer David Divincenzo s criteria: How well??? Well enough to allow for a large scale computation: Fault tolerance
Fault-tolerant Quantum Computation Noisy operations One level quantum error-correction codes ECC concatenation; threshold theorem k-levels of fault-tolerant encoding if Fault tolerance threshold. Heavy resource requirements when Depends on code, noise model, arch. constraints etc. Current estimates for
Tutorial overview 1. The ion-qubit: different ion-qubit choices, Ion traps.. Qubit initialization. 3. Qubit measurement. 4. Universal set of quantum gates: single qubit rotations; two-ion entanglement gates 5. Memory coherence times How well??? Benchmarked to current threshold estimates Disclaimer: non exhaustive; focuses on laser-driven gates
Different ion-qubit choises - One electron in the valence shell; Alkali like S 1/ ground state.
Electronic levels Structure n P 3/ n P n P 1/ w/o D Be + Mg + Zn + Cd + 313 nm 80 nm 06 nm 6 nm Fine structure n-1 D 5/ n-1 D n-1 D 3/ with D Ca + Sr + Ba + Yb + Hg + 397 nm 4 nm 493 nm 369 nm 194 nm n S 1/
S 1/ Zeeman qubit (Isotopes w/o nuclear spin) e.g. 4 Mg + 64 Zn + 114 Cd + 40 Ca+ 88 Sr+ 138 Ba+ 174 Yb+ 0 Hg+ Advantages - RF separation. - Tunable. - Infinite T 1. m = 1/ Disadvantages - Energy depends linearly on B. - Transition photon caries no momentum -Momentum transfer with offresonance lasers: photon scattering. - Detection. n S 1/ m = -1/ Turn on small B field.8 MHz/G
e.g. 9 Be + 5 Mg + 67 Zn + 111 Cd + 43 Ca+ 87 Sr+ 137 Ba+ 171 Yb+ 199 Hg+ F = I 1/ S 1/ Hyperfine qubit Hyperfine structure (order depends on the sign of A hf ) Turn on small B field Advantages - MW energy separation. - B-field independent qubit. - Infinite T 1. - State selective fluorescence Detection. m = 0 Disadvantages - Few GHz energy separation. -Transition photon caries no momentum - Off resonance photon scattering. - initialization to clock transition can be more tricky 1-40 GHz S 1/ F = I + 1/ m = 0
Optical qubit D 5/ with D Ca + Sr + Ba + Yb + Hg + Innsbruck/Weizmann 79 nm 674 nm 1760 nm 411 nm 8 nm Advantages - Single optical photon (momentum). - B-field independent qubit (if nuclear spin 0). - Hardly any spontaneous decay during gates. - State selective fluorescence Detection: excellent discrimination. Disadvantages - Finite (~ 1 sec) lifetime. - Coherence time is limited by laser linewidth. S 1/
Trapping - Trap ions: a minimum/maximum to f, the electric potential. - Impossible in all directions; Laplace s equation: 0
Linear RF Paul trap Trapping Positive ion RF electrode High dc potential control electrode Low dc voltage control electrode
Dynamic trapping (pondermotive forces) Oscillating electric field: Large and slow small and fast Newton s E.O.M:
Dynamic trapping Field expansion: To 0 th order: Next order: Average over one period:
Dynamic trapping + For electric quadruple: d + Pseudo-potential: Sign of e Harmonic frequency: trap ~ ev m rf rf d
Linear RF Paul trap Trapping Potential : i Solve E.O.M MX : F e d X i a q cos( ) X 0 d V cos( t X i i i i 0 rf ) (Mathieu eq : ) Stable solution: trap ~ ev m RF d the distance between the ion and the electrodes rf d i i Drive frequency ~ 0-30 MHz RF amplitude ~ 00-300 V Secular frequency Radial ~ -3 MHz Axial ~ 1 MHz
0. 3 m m Weizmann trap. 0.6 mm + 00 V pp AC 1 MHz 0. mm + + 10 V DC - Laser machined Alumina + n n z r = 1 MHz (axial) = 3 MHz (radial) 1. mm Nitzan Akerman ~ -5 mm
Scale up? One (out of many) problem: isolating one mode of motion for gates
The ion vision: Multiplexed trap array interconnected multi-trap structure subtraps completely decoupled routing of ions by controlling electrode voltages Subtrap for different purpose: Gates, readout, etc. D. J. Wineland, et al., J. Res. Nat. Inst. Stand. Technol. 103, 59 (1998); D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (00). Other proposals: DeVoe, Phys. Rev. A 58, 910 (1998). Cirac & Zoller, Nature 404, 579 ( 000).
Multi-zone ion trap NIST rf filter board view along axis: rf control segmented linear trapping region control rf Gold on alumina construction RF quadrupole realized in two layers Six trapping zones Both loading and experimental zones One narrow separation zone Closest electrode ~140 mm from ion
NIST 100 mm separation zone 6-zone alumina/gold trap (Murray Barrett, John Jost) Ion transport 00 mm Ions can be moved between traps. Electrode potentials varied with time Ions can be separated efficiently in sep. zone Small electrode s potential raised Motion (relatively) fast Shuttling (adiabatic): several 10 ms Separating: few 100 ms
NIST Surface-electrode traps 1 mm Field lines: Trapping center RF electrodes Filter capacitor Microfabricated filter resistor Control lead Control electrodes Elbows and teejunctions possible: J. Chiaverini et al. Quant. Inform. Comp. 5, 419 (005). S. Seidelin et al. Phys. Rev. Lett. 96, 53003 (006).
Micro-fabricated traps Shappert; Georgia Tech Allcock; Oxford Amini et al. New J. Phys. 1, 033031 (010). Allcock et al. App. Phys. Lett. 10, 044103 (01). Shappert et al. arxiv quant-ph\1304. 6636 (013). Amini; NIST
Trapped ions on the tabletop PMT EMCCD Flip Mount RF resonator Vacuum ~ 10-11 Torr Room temperature (or a bit above) RF created with coax/helical resonator Atoms created by oven. Ions created by photo ionization. Approx. F1 imaging optics to EMCCD/PMT (res = 0.8 um). Microwaves f/1 lens B-field cooling,detection and excitation beams
Harmonic oscillator levels Vibrational mode quantum number 1 0 1 0 - Doppler cooling. - Resolved side band cooling.
Sideband Spectroscopy 4 D 5/ Scan the laser frequency across the S D transition 5 S 1/ 674 nm Dn < 80 Hz carrier Red sidebands Blue sidebands axial radial
Resolved-sideband Cooling P S 1033 nm 674 nm D D S ~4 MHz Red sideband n = 0 n = 1 n = n = 3
Sideband cooling to the ground state T mk Uncertainty in ion position = ground state extent 6nm m ho
Anomalous heating Fluctuating charges f -1.5 noise Thermally activated Due to monolayer of C on eletrodes: gone after Ar+ ion cleaning Deslauriers et al. Phys. Rev. Lett. 97, 103007 (006) Hite et al. Phys. Rev. Lett. 109, 103001 (01)
Qubit Initialization Zeeman qubit -Optical pumping into a dark state. -CPT possible into any superposition.. P 1/ s Error sources: - Polarization purity. e ~ 10-6 10-3 S 1/
Qubit Initialization Zeeman qubit Process tomography of optical pumping Limited to 10-3 due to stressinduced birefringence in vacum chamber optical viewports
Qubit Initialization Zeeman qubit: the D level option P 3/ P 1/ -1/ +3/ g = 0.4 Hz D 5/ Limited by off-resonance coupling of to D Power broadening and in-coherent noise e 10-4 D 3/ S 1/ Keselman, Glickman, Akerman, Kotler and Ozeri, New J. of Phys. 13, 07307, (011)
- Optical pumping into a dark state. Qubit Initialization Hyperfine qubit P 1/ Estimated: C. Langer, Ph.D Thesis, University of Colorado, (006). s p F=0 F=1 S 1/
Qubit Initialization Optical qubit - state initialization: same as previous. P 3/ - state initialization: - Rapid adiabatic passage. e ~ 10 - (Wunderlich et. al. Journal of Modern Optics 54, 1541 (007)) D 5/ - p-pulse. e ~ 10 - S 1/