The spin qubit quantum computer is a quantum computer based on controlling the spin of charge carriers (electrons and electron holes) in semiconductor devices. The first spin qubit quantum computer was proposed by Daniel Loss and David P. DiVincenzo in 1997. The proposal was to use the intrinsic spin-1/2 degree of freedom of individual electrons confined in quantum dots as qubits. This should not be confused with other proposals that use the nuclear spin as qubit, like the Kane quantum computer or the nuclear magnetic resonance quantum computer. Spin qubit quantum computers based on silicon atoms can be produced at industry starndard silicon semiconductor wafer fabs used for logic chip production.
Loss–DiVicenzo proposal
The Loss–DiVicenzo quantum computer proposal tried to fulfill DiVincenzo's criteria for a scalable quantum computer, namely:
identification of well-defined qubits; 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. Earlier work on applications of quantum dots for quantum computing was done by Barenco et al.
Implementation of the two-qubit gate The Loss–DiVincenzo quantum computer operates, basically, using inter-dot gate voltage for implementing swap 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:
H s ( t ) = J ( t ) S L ⋅ S R . {\displaystyle H_{\rm {s}}(t)=J(t)\mathbf {S} _{\rm {L}}\cdot \mathbf {S} _{\rm {R}}.}
This description is only valid if:
the level spacing in the quantum-dot Δ E {\displaystyle \Delta E} is much greater than k T {\displaystyle \;kT}
the pulse time scale τ s {\displaystyle \tau _{\rm {s}}} is greater than ℏ / Δ E {\displaystyle \hbar /\Delta E} , so there is no time for transitions to higher orbital levels to happen and the decoherence time Γ − 1 {\displaystyle \Gamma ^{-1}} is longer than τ s . {\displaystyle \tau _{\rm {s}}.}
k {\displaystyle k} is the Boltzmann constant and T {\displaystyle T} is the temperature in kelvins. From the pulsed Hamiltonian follows the time evolution operator
U s ( t ) = T exp { − i ∫ 0 t d t ′ H s ( t ′ ) } , {\displaystyle U_{\rm {s}}(t)={\mathcal {T}}\exp \left\{-i\int _{0}^{t}dt'H_{\rm {s}}(t')\right\},}
where T {\displaystyle {\mathcal {T}}} is the time-ordering symbol. We can choose a specific duration of the pulse such that the integral in time over J ( t ) {\displaystyle J(t)} gives J 0 τ s = π ( mod 2 π ) , {\displaystyle J_{0}\tau _{\rm {s}}=\pi {\pmod {2\pi }},} and U s {\displaystyle U_{\rm {s}}} becomes the swap operator U s ( J 0 τ s = π ) ≡ U s w . {\displaystyle U_{\rm {s}}(J_{0}\tau _{\rm {s}}=\pi )\equiv U_{\rm {sw}}.}
This pulse run for half the time (with J 0 τ s = π / 2 {\displaystyle J_{0}\tau _{\rm {s}}=\pi /2} ) results in a square root of swap gate, U s w 1 / 2 . {\displaystyle U_{\rm {sw}}^{1/2}.}
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