Transcript NUIM Presentation - Department of Mathematical Physics

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
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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
Consider Hamiltonian in the absence of radiation
where
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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
(5)
where
(6)
Then we have time evolution
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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 1
1.
2.
3.
4.
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>
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Usefulness for the readout of QC
•No 2 Quantum information transferred to a magnetic molecule
S1=3/2
S2=33/2
1.
Qubits |1/2>
Qubits |31/2>
Consider the subspace spanned by {1/2, -1/2 3/2} and
{31/2,-31/2,33/2}
2. Our scheme can yield information transfer from |1/2> and
|-1/2> to |31/2> and |-31/2>
Micro-SQUID is able
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Thank You
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