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Large Detuning Scheme for Spin-Based fullerene Quantum

Computation

Mang Feng and Jason TwamleyDepartment of Mathematical Physics

National University of Ireland MaynoothMaynooth. Co. Kildare

Ireland

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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)

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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.

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Two coupled fullerenes

where

Consider Hamiltonian in the absence of radiation

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Fig.1a

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Fig.1b

We need

DETUNING

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Fig.2

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Two qubit conditional phase gat

• Hamiltonian related to Fig.2 is

where

(4)

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We suppose

Then the intermediate levels |1/2,3/2> and |3/2,1/2> will

not be populated. By second-order perturbative expansion ..

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Effctive Hamiltonian

Then we have time evolution

where

(6)

(5)

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Conditional phase gating

In the computation subspace, we have

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Discussion

1.

2.

3. For estimating gating time, we suppose

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Fig.3

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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.

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Usefulness for the readout of QC

• No 11. 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>

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Usefulness for the readout of QC

•No 2S1=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.

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Thank You