Large Detuning Scheme for Spin-Based fullerene Quantum Computation Mang Feng and Jason Twamley

1. 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. 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. 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 |ms=1/2, -1/2> and use | ms= 3/2> as an auxiliary state. • Two fullerenes interact by magnetic dipolar coupling.

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

5. Fig.1a

6. Fig.1b We need DETUNING

7. Fig.2

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

9. 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. Effctive Hamiltonian (5) where (6) Then we have time evolution

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

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

13. Fig.3

14. 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. Usefulness for the readout of QC • No 1 • Detected |1/2> or |–1/2> • Detector(|1/2>+|-1/2>) • 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. Usefulness for the readout of QC No 2 Quantum information transferred to a magnetic molecule 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> 1. 2. Micro-SQUID is able

17. Thank You