Spin qubit quantum computer

The Loss–DiVicenzo quantum computer proposal tried to fulfill DiVincenzo's criteria for a scalable quantum computer,^[11] 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.^[12]

Implementation of the two-qubit gate

The Loss–DiVincenzo quantum computer operates, basically, using inter-dot gate voltage for implementing

• the level spacing in the quantum-dot ${\displaystyle \Delta E}$ is much greater than ${\displaystyle \;kT}$
• the pulse time scale ${\displaystyle \tau _{\rm {s}}}$ is greater than ${\displaystyle \hbar /\Delta E}$, so there is no time for transitions to higher orbital levels to happen and
• the decoherence time ${\displaystyle \Gamma ^{-1}}$ is longer than ${\displaystyle \tau _{\rm {s}}.}$

${\displaystyle k}$ is the Boltzmann constant and ${\displaystyle T}$ is the temperature in Kelvin.

From the pulsed Hamiltonian follows the

${\displaystyle U_{\rm {s}}(t)={\mathcal {T}}\exp \left\{-i\int _{0}^{t}dt'H_{\rm {s}}(t')\right\},}$

where ${\displaystyle {\mathcal {T}}}$ is the

We can choose a specific duration of the pulse such that the integral in time over ${\displaystyle J(t)}$ gives ${\displaystyle J_{0}\tau _{\rm {s}}=\pi {\pmod {2\pi }},}$ and ${\displaystyle U_{\rm {s}}}$ becomes the swap operator ${\displaystyle U_{\rm {s}}(J_{0}\tau _{\rm {s}}=\pi )\equiv U_{\rm {sw}}.}$

This pulse run for half the time (with ${\displaystyle J_{0}\tau _{\rm {s}}=\pi /2}$) results in a square root of swap gate, ${\displaystyle U_{\rm {sw}}^{1/2}.}$

The "XOR" gate may be achieved by combining ${\displaystyle U_{\rm {sw}}^{1/2}}$ operations with individual spin rotation operations:

${\displaystyle U_{\rm {XOR}}=e^{i{\frac {\pi }{2}}S_{\rm {L}}^{z}}e^{-i{\frac {\pi }{2}}S_{\rm {R}}^{z}}U_{\rm {sw}}^{1/2}e^{i\pi S_{\rm {L}}^{z}}U_{\rm {sw}}^{1/2}.}$

The ${\displaystyle U_{\rm {XOR}}}$ operator is a conditional phase shift (controlled-Z) for the state in the basis of ${\displaystyle \mathbf {S} _{\rm {L}}+\mathbf {S} _{\rm {R}}}$.

• Kane quantum computer
• Quantum dot cellular automaton

References