1 belfast jan 2003 large detuning scheme for spin-based fullerene quantum computation mang feng and...
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1 Belfast Jan 2003
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