1. 1 Belfast Jan 2003 Large Detuning Scheme for Spin-Based fullerene Quantum Computation Mang Feng and Jason Twamley Department of Mathematical Physics National University of Ireland Maynooth Maynooth. Co. Kildare Ireland

2. 2 Belfast Jan 2003 Introduction to Spin-Based Fullerene QC Locally addressed One ----W.Harneit, PRA 65, 032322(2002) ----D.Suter and K.Lim, PRA 65, 052309(2002) Global Addressed One -----J.Twamley, PRA 67, 052318(2003)

3. 3 Belfast Jan 2003 Key Points of Our Scheme Based on locally addressed QC. We need magnetic field gradient Consider the ground state of the electronic spin of the doped atoms N or P of C60 S=3/2 We encode qubits in |m s=1/2, -1/2 > and use | m s= 3/2> as an auxiliary state. Two fullerenes interact by magnetic dipolar coupling.

4. 4 Belfast Jan 2003 Two coupled fullerenes where Consider Hamiltonian in the absence of radiation

5. 5 Belfast Jan 2003 Fig.1a

6. 6 Belfast Jan 2003 Fig.1b We need DETUNING

7. 7 Belfast Jan 2003 Fig.2

8. 8 Belfast Jan 2003 Two qubit conditional phase gat Hamiltonian related to Fig.2 is where (4)

9. 9 Belfast Jan 2003 We suppose Then the intermediate levels |1/2,3/2> and |3/2,1/2> will not be populated. By second-order perturbative expansion..

10. 10 Belfast Jan 2003 Effctive Hamiltonian Then we have time evolution where (6) (5)

11. 11 Belfast Jan 2003 Conditional phase gating In the computation subspace, we have

12. 12 Belfast Jan 2003 Discussion 1. 2. 3. For estimating gating time, we suppose

13. 13 Belfast Jan 2003 Fig.3

14. 14 Belfast Jan 2003 Conclusion Our scheme can achieve a two-qubit phase gating by one step of operation. But it is a slow gating !! Increasing T2 is necessary. Our scheme is hopeful for quantum computing with small numbers of qubits In the absence of field gradient, we have shortest implementaton time. But we need field gradient for single qubit operation.

15. 15 Belfast Jan 2003 Usefulness for the readout of QC No 1 1. Detected |1/2> or |–1/2> 2. 3. Detector (|1/2>+|-1/2>) 4.For |1/2> Detector turns to (|1/2>-|-1/2>) then to |1/2> For |-1/2> Detector remains (|1/2>+|-1/2>) then to |-1/2>

16. 16 Belfast Jan 2003 Usefulness for the readout of QC No 2 S1=3/2 Qubits |1/2> S2=33/2 Qubits |31/2> Consider the subspace spanned by {1/2, -1/2 3/2} and {31/2,-31/2,33/2} Our scheme can yield information transfer from |1/2> and |-1/2> to |31/2> and |-31/2> Quantum information transferred to a magnetic molecule Micro-SQUID is able 1. 2.

17. 17 Belfast Jan 2003 Thank You