Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots
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arXiv
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2023
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| author | Bragar, Igor Cywiński, Łukasz |
| author_facet | Bragar, Igor Cywiński, Łukasz |
| contents | We analyze in detail a procedure of entangling of two singlet-triplet ($S$-$T_{0}$) qubits operated in a regime when energy associated with the magnetic field gradient, $ΔB_{z}$, is an order of magnitude smaller than the exchange energy, $J$, between singlet and triplet states [Shulman M. et al., Science 336, 202 (2012)]. We have studied theoretically a single $S$-$T_{0}$ qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for time dependence of components of its Bloch vector for quasistatical fluctuations of $ΔB_{z}$ and quasistatical or dynamical $1/f^β$-type fluctuations of $J$. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two $S$-$T_{0}$ qubits. Particularly, we have obtained an analytical expression for evolution of two qubits affected by $1/f^β$-type fluctuations of $J$. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment, the $S$-$T_{0}$ qubits were affected by uncorrelated $1/f^β$ charge noises. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_16583 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots Bragar, Igor Cywiński, Łukasz Mesoscale and Nanoscale Physics Quantum Physics We analyze in detail a procedure of entangling of two singlet-triplet ($S$-$T_{0}$) qubits operated in a regime when energy associated with the magnetic field gradient, $ΔB_{z}$, is an order of magnitude smaller than the exchange energy, $J$, between singlet and triplet states [Shulman M. et al., Science 336, 202 (2012)]. We have studied theoretically a single $S$-$T_{0}$ qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for time dependence of components of its Bloch vector for quasistatical fluctuations of $ΔB_{z}$ and quasistatical or dynamical $1/f^β$-type fluctuations of $J$. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two $S$-$T_{0}$ qubits. Particularly, we have obtained an analytical expression for evolution of two qubits affected by $1/f^β$-type fluctuations of $J$. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment, the $S$-$T_{0}$ qubits were affected by uncorrelated $1/f^β$ charge noises. |
| title | Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2312.16583 |