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arXiv:0802.0240 · Physical Review A

Hyperfine-interaction-induced decoherence and deterministic teleportation of electrons in a quantum-dot nanostructure

Siqing Yu, Elton Yechao Zhu, Ye Yeo

Published Jun 27, 2008• 2 citations
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Abstract

Recently, de Visser and Blaauboer [Phys. Rev. Lett. 96, 246801 (2006)] proposed the most efficient deterministic teleportation protocol $\mathcal{T}$ for electron spins in a semiconductor nanostructure consisting of a single and a double quantum dot. However, it is as yet unknown if $\mathcal{T}$ can be completed before decoherence sets in. In this paper we analyze the detrimental effect of nuclear spin baths, the main source of decoherence, on $\mathcal{T}$. We show that nonclassical teleportation fidelity can be achieved with $\mathcal{T}$ provided certain conditions are met. Our study indicates that realization of quantum computation with quantum dots is indeed promising.

DOI
10.1103/physreva.77.062338

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Recently, de Visser and Blaauboer [Phys. Rev. Lett. 96, 246801 (2006)] proposed the most efficient deterministic teleportation protocol T\mathcal{T}T for electron spins in a semiconductor nanostructure consisting of a single and a double quantum dot. However, it is as yet unknown if T\mathcal{T}T can be completed before decoherence sets in. In this paper we analyze the detrimental effect of nuclear spin baths, the main source of decoherence, on T\mathcal{T}T. We show that nonclassical teleportation fidelity can be achieved with T\mathcal{T}T provided certain conditions are met. Our study indicates that realization of quantum computation with quantum dots is indeed promising.
We present a proposal for deterministic quantum teleportation of electrons in a semiconductor nanostructure consisting of a single and a double quantum dot. The central issue addressed in this Letter is how to design and implement the most efficient--in terms of the required number of single and two-qubit operations--deterministic teleportation protocol for this system. Using a group-theoretical analysis, we show that deterministic teleportation requires a minimum of three single-qubit rotations and two entangling (square root SWAP) operations. These can be implemented for spin qubits in quantum dots using electron-spin resonance (for single-spin rotations) and exchange interaction (for square root SWAP operations).
We consider a system of two strongly coupled electron spins in zero magnetic field, each of which is interacting with an individual bath of nuclear spins via the hyperfine interaction. Applying the long-spin approximation that we introduced in a previous paper [Europhys. Lett. 95, 47009 (2011)] (here each bath is replaced by a single long spin), we numerically study the electron spin and entanglement dynamics. We demonstrate that the decoherence time is scaling with the bath size according to a power law. As expected, the decaying part of the dynamics decreases with increasing bath polarization. However, surprisingly it turns out that, under certain circumstances, combining quantum dots of different geometry to the double dot setup has a very similar effect on the magnitude of the spin decay. Finally, we show that even for a comparatively weak exchange coupling the electron spins can be fully entangled.
The decoherence and fidelity of spin states in a localized single-electron quantum dot in the presence of a dc magnetic field, arising either from the nuclear hyperfine interaction within the dot or due to its coupling with another localized quantum dot, are examined in detail. A general framework for determining the time evolution of the reduced density matrix. for a single dot is presented, which is exact up to the second order in interaction with any reservoir. In particular, it is applied to the problem of nuclear hyperfine coupling, and approximate estimates of coherence decay time are made when the nuclear spins are either polarized or unpolarized and the internal dynamics of nuclear spins is determined mainly by the nuclear magnetic dipole-dipole interaction. The fidelity of a pure unperturbed electronic one-qubit spin state is obtained as a function of time, which is exact even on a very short timescale of logic gate operations. The time variation of the fidelity of the same one-qubit state on the localized dot as a part of the direct product with another one-qubit state on another localized dot arising because of coupling between these quantum dots is also calculated in this paper. In this case, we include both the single-particle tunnelling between the dots as well as the direct and exchange Coulomb interactions, including on-site Coulomb repulsion. This allows for the double occupation of a single dot. It is found that the loss of fidelity of such two-qubit states due to double occupancy and additional phase errors in the presence of appreciable dot-dot coupling can become a more severe limiting factor than that due to the hyperfine interaction in individual dots.
The dominant source of decoherence for an electron spin in a quantum dot is the hyperfine interaction with the surrounding bath of nuclear spins. The decoherence process may be slowed down by subjecting the electron spin to suitable sequences of external control pulses. We investigate the performance of a variety of dynamical decoupling protocols using exact numerical simulation. Emphasis is given to realistic pulse delays and the long-time limit, beyond the domain where available analytical approaches are guaranteed to work. Our results show that both deterministic and randomized protocols are capable to significantly prolong the electron coherence time, even when using control pulse separations substantially larger than what expected from the upper cutoff frequency of the coupling spectrum between the electron and the nuclear spins. In a realistic parameter range, the total width of such a coupling spectrum appears to be the physically relevant frequency scale affecting the overall quality of the decoupling.
The dominant source of decoherence for an electron spin in a quantum dot is the hyperfine interaction with the surrounding bath of nuclear spins. The decoherence process may be slowed down by subjecting the electron spin to suitable sequences of external control pulses. We investigate the performance of a variety of dynamical decoupling protocols using exact numerical simulation. Emphasis is given to realistic pulse delays and the long-time limit, beyond the domain where available analytical approaches are guaranteed to work. Our results show that both deterministic and randomized protocols are capable to significantly prolong the electron coherence time, even when using control pulse separations substantially larger than what expected from the upper cutoff frequency of the coupling spectrum between the electron and the nuclear spins. In a realistic parameter range, the total width of such a coupling spectrum appears to be the physically relevant frequency scale affecting the overall quality of the decoupling. 1
The hyperfine coupling of the electronic spins in quantum dots to nuclear spins in the semiconductor host material poses a major challenge, as it can lead to decoherence of the electron spins. In this work, the authors revert the typical approach in which the nuclear spins are considered as an environment for the electronic spin, but rather rather view the nuclear spins as the quantum system coupled to an electronic environment with an exceptional degree of tunability. They show that nuclear spin bath could be turned from the dominant source of decoherence into a useful resource for manipulating an electron spin qubit.