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Counter-diabatic driving for fast spin control in a two-electron double quantum dot.

Ban Y, Chen X - Sci Rep (2014)

Bottom Line: The techniques of shortcuts to adiabaticity have been proposed to accelerate the "slow" adiabatic processes in various quantum systems with the applications in quantum information processing.In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given.Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.

View Article: PubMed Central - PubMed

Affiliation: Department of Electronic Information Materials, Shanghai University, 200444 Shanghai, People's Republic of China.

ABSTRACT
The techniques of shortcuts to adiabaticity have been proposed to accelerate the "slow" adiabatic processes in various quantum systems with the applications in quantum information processing. In this paper, we study the counter-diabatic driving for fast adiabatic spin manipulation in a two-electron double quantum dot by designing time-dependent electric fields in the presence of spin-orbit coupling. To simplify implementation and find an alternative shortcut, we further transform the Hamiltonian in term of Lie algebra, which allows one to use a single Cartesian component of electric fields. In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given. Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.

No MeSH data available.


Electric fields of  (solid blue line) and  (dashed red line), designed from the Hamiltonian , see Eq. (4).
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f3: Electric fields of (solid blue line) and (dashed red line), designed from the Hamiltonian , see Eq. (4).

Mentions: In reality, the electron spin is subject to the device-dependent noise, which could be the amplitude noise of the electric fields20. It can be quite important, especially when the electric fields are relatively weak. From the above analysis, we find that four controllable parameters, and , x and y components of the electric fields for each electron in a double QD should be applied. If y component of the electric fields can be reduced, we can remove the amplitude noise from y component of the electric field. In addition to decreasing the total decoherent effects resulting from the device-dependent noise, the cancellation of y component of the electric field might be also useful to simplify the setup. To this end, we apply the concept of multiple Schrödinger pictures to find an alternative way to implement the shortcuts. Making unitary transformation of Hamiltonian H3233 by a rotation around z axis with the angle π/2 − ϕ, we obtain without σx term, where tan ϕ = Y/X and . Again, the maximal amplitude of Q will increase when decreasing time tf, due to the fact that X becomes dominant (the maximal amplitude of Y is unchanged). The Hamiltonian is equal to the original one H at t = 0 and tf, which guarantees that the initial (final) states of H and coincide. However, the dynamics is not same during the intermediate process, although the populations are always equal. Accordingly, we may acquire two new controllable x component of the electric fields, and , calculated from Eq. (4), see Fig. 3.


Counter-diabatic driving for fast spin control in a two-electron double quantum dot.

Ban Y, Chen X - Sci Rep (2014)

Electric fields of  (solid blue line) and  (dashed red line), designed from the Hamiltonian , see Eq. (4).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4150114&req=5

f3: Electric fields of (solid blue line) and (dashed red line), designed from the Hamiltonian , see Eq. (4).
Mentions: In reality, the electron spin is subject to the device-dependent noise, which could be the amplitude noise of the electric fields20. It can be quite important, especially when the electric fields are relatively weak. From the above analysis, we find that four controllable parameters, and , x and y components of the electric fields for each electron in a double QD should be applied. If y component of the electric fields can be reduced, we can remove the amplitude noise from y component of the electric field. In addition to decreasing the total decoherent effects resulting from the device-dependent noise, the cancellation of y component of the electric field might be also useful to simplify the setup. To this end, we apply the concept of multiple Schrödinger pictures to find an alternative way to implement the shortcuts. Making unitary transformation of Hamiltonian H3233 by a rotation around z axis with the angle π/2 − ϕ, we obtain without σx term, where tan ϕ = Y/X and . Again, the maximal amplitude of Q will increase when decreasing time tf, due to the fact that X becomes dominant (the maximal amplitude of Y is unchanged). The Hamiltonian is equal to the original one H at t = 0 and tf, which guarantees that the initial (final) states of H and coincide. However, the dynamics is not same during the intermediate process, although the populations are always equal. Accordingly, we may acquire two new controllable x component of the electric fields, and , calculated from Eq. (4), see Fig. 3.

Bottom Line: The techniques of shortcuts to adiabaticity have been proposed to accelerate the "slow" adiabatic processes in various quantum systems with the applications in quantum information processing.In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given.Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.

View Article: PubMed Central - PubMed

Affiliation: Department of Electronic Information Materials, Shanghai University, 200444 Shanghai, People's Republic of China.

ABSTRACT
The techniques of shortcuts to adiabaticity have been proposed to accelerate the "slow" adiabatic processes in various quantum systems with the applications in quantum information processing. In this paper, we study the counter-diabatic driving for fast adiabatic spin manipulation in a two-electron double quantum dot by designing time-dependent electric fields in the presence of spin-orbit coupling. To simplify implementation and find an alternative shortcut, we further transform the Hamiltonian in term of Lie algebra, which allows one to use a single Cartesian component of electric fields. In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given. Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.

No MeSH data available.