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[[Image:DoubleQuantumDot.jpg|thumb|250px|right|A double [[quantum dot]].  Each electron spin S<sub>L</sub> or S<sub>R</sub> define one quantum two-level system, or ''[[qubit]]'' in the Loss-DiVincenzo proposal. A narrow gate between the two dots can modulate the coupling, allowing [[Swap (computer science)|swap]] operations.]]
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The '''Loss–DiVincenzo quantum computer''' (or spin-qubit quantum computer) is a scalable [[semiconductor]]-based [[quantum computer]]  proposed by [[Daniel Loss]] and David P. DiVincenzo in 1997.<ref>D. Loss and D. P. DiVincenzo, "Quantum computation with quantum dots", ''Phys. Rev. A'' '''57''', p120 (1998); [http://arXiv.org/abs/cond-mat/9701055 on arXiv.org in Jan. 1997]</ref>  The proposal was to use as [[qubits]] the intrinsic spin-1/2 degree of freedom of individual electrons confined to [[quantum dots]]. This was done in a way that fulfilled DiVincenzo Criteria for a scalable quantum computer,<ref>D. P. DiVincenzo, in Mesoscopic Electron Transport, Vol. 345 of NATO Advanced Study Institute, Series E: Applied Sciences, edited by L. Sohn, L. Kouwenhoven, and G. Schoen (Kluwer, Dordrecht, 1997); [http://arxiv.org/abs/cond-mat/9612126 on arXiv.org in Dec. 1996]</ref> namely:


* identification of well-defined qubits;
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* reliable state preparation;
* low decoherence;
* accurate quantum gate operations and
* strong quantum measurements.


A candidate for such a quantum computer is a [[lateral quantum dot]] system.
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==Implementation of the two-qubit gate==
 
The Loss–DiVincenzo quantum computer operates, basically, using inter-dot gate voltage for implementing [[Swap (computer science)]] operations and local magnetic fields (or any other local spin manipulation) for implementing the [[Controlled NOT gate]] (CNOT gate).  
 
The Swap operation is achieved by applying a pulsed inter-dot gate voltage, so the exchange constant in the Heisenberg Hamiltonian becomes time-dependent:
 
:<math>H_s(t) = J(t)\vec{\sigma}_L \cdot \vec{\sigma}_R .</math>
 
This description is only valid if:
 
*the level spacing in the quantum-dot <math>\Delta E </math> is much greater than <math>\; kT </math>;
*the pulse time scale <math>\tau_s </math> is greater than <math>\hbar / \Delta E </math>, so there is no time to happen transitions to higher orbital levels and
*the [[Quantum decoherence|decoherence]] time <math>\Gamma ^{-1} </math> is longer than <math>\tau_s </math>.
 
From the pulsed Hamiltonian follows the time evolution operator
 
:<math>U_s(t) = \mathbf{T} exp\{-i\int_0^t dt' H_s(t')\}.</math>
 
We can choose a specific duration of the pulse such that the integral in time over <math>J(t)</math> gives <math>J_0 \tau_s = \pi (mod2\pi),</math> and <math>U_s</math> becomes the Swap operator <math>U_s (J_0 \tau_s = \pi) \equiv U_{sw}</math>.
 
The XOR gate may be achieved by combining <math>\sqrt{swap}</math> (square root of Swap) operations with individual spin operations:
 
:<math>U_{XOR} = e^{i\frac{\pi}{2}S_L^z}e^{-i\frac{\pi}{2}S_R^z}U_{sw}^{1/2}
e^{i \pi S_L^z}U_{sw}^{1/2}.</math>
 
This operator gives a conditional phase for the state in the basis of <math>\vec{S}_L + \vec{S}_R</math>.
 
==External links==
*[http://quantumtheory.physik.unibas.ch/ Condensed Matter Theory at the University of Basel]
 
==References==
{{reflist}}
 
{{quantum_computing}}
 
{{DEFAULTSORT:Loss-DiVincenzo quantum computer}}
[[Category:Quantum information science]]

Latest revision as of 16:49, 18 August 2014

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