A two-qubit conditional quantum gate with single spins

1. A two-qubit conditional quantum gate with single spins Univ. of Stuttgart F.Jelezko, J. Wrachtrup I. Popa, T. Gaebel, M. Domhan, C.Wittmann

2. 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

3. 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

4. 1. Magnetic Resonance Force Microscopy • Rugar et al. Nature430, 329 (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, R1089 (2004) Single spin read-out 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)

5. Optical transition (2 eV) ESR (10-5 eV) Optical readout Single defect detection: Optical microscopy m n 300 nm 0 0 3 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)

6. Microwave resonator (D. Suter Univ. Dortmund) Typical value for ESR p-pulse - 10 ns Superconducting magnet Optical microscope MW and RF loop MO, N. A. 0.85 500 m Set-up Variable temperature microscope Operating temperature – 1,6 – 300 K Detection yield – 1 percent Magnetic field – up to 5 T

7. 3E 1A DE=1.945eV 3A 3 GHz Nitrogen Vacancy (NV) center in diamond Diamond: -bandgap 6 eV -Tdebay: 2000K Long T2 of defects at RT Optical detection of single defects Gruber A, Wrachtrup J et al, SCIENCE 276 2012 (1997)

8. 10 µm Single N-V centers implantation App. 2 N iones/ N-V defect

9. t Photon stream 2 1 Single center signature: photon antibunching Single photon source: Weinfurter et al. PRL 85 (2000) Grangier et al. PRL 89 (2003)

10. 40MHz Fluorescence/a.u. ms=0 ms=±1 ms=±1 ms=0 Relaxation time: T1:1-2 s (2 K) 2 ms (300 K) Observation of single electron spin quantum jump at T=2K 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) 3E 1A E~3GHz

11. Spin system: T1~ 2ms T2: ? probe ms=±1 Laser Laser I ms=0 MW Switch off the Laser light during manipulating the spin Strong probe time Inhibition of coherent spin state evolution by measurement („ a watched pot never boils“) T=300K MW pulse Weak probe

12.  /2 /2  t1  = 0.3 ms How large is T2?Hahn Echo

13. Hahn echo decay F. Jelezko et al PRL 92 (2004) 076401 Decoherence due to P1 centers ? (P1 - single substitutional nitrogen, 100 ppm in HPHT Ib diamond) „first data“: T2 0.3-0.5 s

14. /2  /2 1 t2 Hahn echo decay of single N-V center in IIa type diamond • pulse – 8 ns T2/Tgate = 105

15. Optical single nuclear spin read-out (13C diamond) 3 2 1 13C spins as qubits: Wrachtrup Opt. Spectr. 91 429 (2001) – optical spectroscopy Hyperfine splitting A1,2,3 = 130 MHz Fine Structure: Splittting: 3 GHz Experimental realization using ESR: Jelezko et al. Phys. Rev. Lett. 93, 130501 (2004)    Ab initio calculations: M.Luszczek et al. Physica B 348, 292 (2004)

16. 2 C 1 B A 3 D 4 Gates: qubits 1st qubit: electron spin of N-V 2nd qubit: nuclear spin of 13C C:130 MHz D:10 MHz A:2800 MHz B:2940 MHz ESR NMR (ENDOR)

17. 2 C 1 A 3 4 Rabi nutation of single electron and single 13C spin – single qubit operations ESR (transition A) C ENDOR (transition C) Averages over 105 Cycles

18. Input Output CROT-gatea 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 π 1 3 4

19. 2 1 3 ρ ρ 4 state state state state Tomography of state after CROT π Ideal result: Initial state:

20. CROT= Tomography of state after CROT Theory Experiment Parameters for calculation: ESR: 15 ns; T2e=1.2 s; NMR:400 ns; T2n=3.6 s; Jelezko et al. quant-ph/0402087

21. 3 2 1 Scaling up 13C spin cluster is scalable up to 3-12 qubits Fully scalable architecture – coupled NV defects Coupling: magnetic dipole (short range) Optical dipole (long range) N+ beam 5 nm Diamond NV defect

22. N+ ions, 2MeV Positioning accuracy limitations N+ ions surface of sample 1,1µm ~500nm FWHM target depth 1 nm accuracy for 1 keV ions possible

23. Summary single spin QC • Single electron and nuclear spin state read-out and coherent manipulation • 1 and 2 Qbit operation ( 3. Qbit 14N not used in experiment) • scaling requires coupling of defects (nm positioning)

24. Acknowledgment 3. Institute of Physics University of Stuttgart J. Wrachtrup I. Popa T. Gaebel, M. Domhan C.Wittmann A. Gruber* * currently at University of Chemnitz In collaboration with: 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