A twoqubit conditional quantum gate with single spins
A two-qubit conditional quantum gate with single spins F. Jelezko, J. Wrachtrup I. Popa, T. Gaebel, M. Domhan, C. Wittmann Univ. of Stuttgart
Outline • Introduction • Single spin states: Read-out, manipulation, coherence time • CROT gate with single electron and nuclear spin in a solid • Scaling up: Positioning of single N-V defects in diamond
History Science 275 (1997) 350 -365 A pure state (single spin EPR, NMR): but see e. g. J. Wrachtrup, A. Gruber, L. Fleury, C. von Borczyskowski „Magnetic Resonance on single nuclei“ CPL 267 (1997) 179
Single spin read-out 1. Magnetic Resonance Force Microscopy Rugar et al. Nature 430, 329 (2004); 2. Electrical detection Durkan, C. & Welland, M. E. Appl. Phys. Lett. 80, 458 -460 (2002) - STM M. Xiao, I. Martin, E. Yablonovitch, H. W. Jiang Nature 430, 435 - 439 (2004) - FET J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, L. P. Kouwenhoven Nature 430, 431 - 435 (2004) 3. Optically detected ESR on single spin See e. g. Jelezko et al. APL 81 (2002) 2160, Jelezko & Wrachtrup Journal of Physics: Condensed Matter 16, R 1089 (2004)
Optical readout Optical transition (2 e. V) ESR (10 -5 e. V) The number of scattered photons depends on spin state Brossel and Bitter (1952) Phys. Rev. 86 308 (mercury vapours) Wrachtrup et al. Nature 363, 244– 245 (1993) (single molecules) 300 nm Single defect detection: Optical microscopy 300 nm
Set-up Variable temperature microscope Operating temperature – 1, 6 – 300 K Detection yield – 1 percent Optical microscope Superconducting magnet Microwave resonator (D. Suter Univ. Dortmund) Typical value for ESR -pulse - 10 ns MW and RF loop 500 m MO, N. A. 0. 85 Magnetic field – up to 5 T
Nitrogen Vacancy (NV) center in diamond Diamond: -bandgap 6 e. V -Tdebay: 2000 K Long T 2 of defects at RT 3 A 1 A 3 GHz E=1. 945 e. V 3 E Optical detection of single defects Gruber A, Wrachtrup J et al, SCIENCE 276 2012 (1997)
Single N-V centers implantation App. 2 N iones/ N-V defect 10 µm
Single center signature: photon antibunching Photon stream t 2 1 Single photon source: Weinfurter et al. PRL 85 (2000) Grangier et al. PRL 89 (2003)
Observation of single electron spin quantum jump at T=2 K Fluorescence/a. u. Low temperature optical spectroscopy, bulk: D. Redman J. Opt. Soc. Am. B 9, No. 5, (1992). Single defects: Jelezko F et al. APL 81 , 2160 (2002) 3 E 40 MHz 1 A ms=± 1 ms=0 ms=± 1 Relaxation time: T 1: 1 -2 s (2 K) 2 ms (300 K) E~3 GHz
Inhibition of coherent spin state evolution by measurement („ a watched pot never boils“) MW pulse T=300 K probe Spin system: T 1~ 2 ms T 2: ? Weak probe ms=± 1 ms=0 Switch off the Laser light during manipulating the spin Strong probe I Laser MW time
How large is T 2? Hahn Echo /2 /2 t 1 = 0. 3 ms
Hahn echo decay F. Jelezko et al PRL 92 (2004) 076401 „first data“: T 2 0. 3 -0. 5 s Decoherence due to P 1 centers ? (P 1 - single substitutional nitrogen, 100 ppm in HPHT Ib diamond)
Hahn echo decay of single N-V center in IIa type diamond /2 1 2 pulse – 8 ns T 2/Tgate = 105
Optical single nuclear spin read-out (13 C diamond) 3 2 1 13 C spins as qubits: Wrachtrup Fine Structure: Splittting: 3 GHz Hyperfine splitting A 1, 2, 3 = 130 MHz Ab initio calculations: M. Luszczek et al. Physica B 348, 292 (2004) Opt. Spectr. 91 429 (2001) – optical spectroscopy Experimental realization using ESR: Jelezko et al. Phys. Rev. Lett. 93, 130501 (2004)
Gates: qubits 1 st qubit: electron spin of N-V 2 nd qubit: nuclear spin of 13 C 2 C 1 B A 3 C: 130 MHz A: 2800 MHz D: 10 MHz B: 2940 MHz ESR NMR (ENDOR) D 4
Rabi nutation of single electron and single 13 C spin – single qubit operations 2 C 1 A ESR (transition A) 3 C 4 ENDOR (transition C) Averages over 105 Cycles
CROT-gate a two qubit gate flips the nuclear spin dependent on the orientation of the electron spin with π/2(z) equivalent to the CNOT-gate Experimental: selective NMR π-pulse 2 1 π 3 4 Input Output
Tomography of state after CROT 2 1 π 3 4 Initial state: ρ sta te Ideal result: ρ state te state
Tomography of state after CROT Theory Experiment 0. 1 CROT= 0. 16 0. 04 0 0. 16 0. 9 0. 12 0 Parameters for calculation: 0. 04 0. 12 0 0 ESR: 15 ns; T 2 e=1. 2 s; NMR: 400 ns; T 2 n=3. 6 s; 0 0 Jelezko et al. quant-ph/0402087 0 0
Scaling up 13 C spin cluster is scalable up to 3 -12 qubits Fully scalable architecture – coupled NV defects 3 2 1 Coupling: magnetic dipole (short range) Optical dipole (long range) 5 nm NV defect N+ beam Diamond
Positioning accuracy limitations N+ ions, 2 Me. V surface of sample 1, 1µm ~500 nm FWHM target depth 1 nm accuracy for 1 ke. V ions possible
Summary single spin QC Ø Single electron and nuclear spin state read-out and coherent manipulation Ø 1 and 2 Qbit operation ( 3. Qbit 14 N not used in experiment) Ø scaling requires coupling of defects (nm positioning)
Acknowledgment 3. Institute of Physics University of Stuttgart J. Wrachtrup I. Popa T. Gaebel, In collaboration with: M. Domhan S. Kilin, A. Nizovtsev (Minsk) J. Twamley (University of Ireland) J. Buttler (NRL Washington) JD. Suter (Dortmund) J. Meyer (Bochum) J. Rabeau, S. Prawer (Melbourne) DFG, EU (QIPDDF ROSES) Landesstiftung BW C. Wittmann A. Gruber* * currently at University of Chemnitz
- Slides: 24