Adiabatic many-body state preparation and information transfer in quantum dot arrays

Quantum simulation of many-body systems are one of the most interesting tasks of quantum technology. Among them is the preparation of a many-body system in its ground state when the vanishing energy gap makes the cooling mechanisms ineffective. Adiabatic theorem, as an alternative to cooling, can be exploited for driving the many-body system to its ground state. In this paper, we study two most common disorders in quantum dot arrays, namely exchange coupling fluctuations and hyperfine interaction, in adiabatic preparation of ground state in such systems. We show that the adiabatic ground-state preparation is highly robust against those disorder effects making it a good analog simulator. Moreover, we also study the adiabatic quantum information transfer, using singlet-triplet states, across a spin chain. In contrast to ground-state preparation the transfer mechanism is highly affected by disorder and in particular, the hyperfine interaction is very destructive for the performance. This suggests that for communication tasks across such arrays adiabatic evolution is not as effective and quantum quenches could be preferable.

Figure 1

(a) A fully dimerized chain, with $J_k=0$ for all even $k$, initialized in a series of singlets evolves adiabatically to the antiferromagnetic ground state of a uniform chain in which all the couplings are identical, i.e., $J_k=J$. (b) A triplet (or singlet) state initially decoupled from the rest of the system is adiabatically transferred to the other side by switching on the coupling $J_2$ and switching off the coupling $J_{N-2}$ simultaneously.

Figure 2

(a) The ideal case of fidelity $F_g\left(t\right)$ versus time $Jt$ for $N=10$ (using $T=2.9/J$) and $N=20$ (using $T=10.4/J$). (b) The energy gap $\Delta E$ (in the units of $J\hslash$) as a function of $1/N$. (c) The ramping time $J{T}_{\min }$ versus $N^2$.

Figure 3

(a) The ideal case of fidelity $F_c^{+}\left(t\right)$ versus time $Jt$ for $N=10$ (using $T=11.36/J$) and $N=20$ (using $T=23.5/J$). (b) The ideal case of fidelity $F_c^{-}\left(t\right)$ versus time $Jt$ for $N=10$ (using $T=11.36/J$) and $N=20$ (using $T=23.5/J$). (c) The minimum ramping time for singlet-triplet state transfer $J{T}_{\min }$ versus $N^2$. (d) The ideal case of fidelity $F_c\left(t\right)$ for an equally weighted superposition of singlet and triplet versus $Jt$ for $N=10$ (using $T=11.36/J$).

Figure 4

The average ground-state fidelity $\langle F_g\rangle$ at $JT=2.9$ versus $\eta$ (varience of white noise) for different static noise $\delta$ and with different hyperfine interaction: (a) $B_{\mathrm{nuc}}=0$; (b) $B_{\mathrm{nuc}}=0.02$; (c) $B_{\mathrm{nuc}}=0.06$; (d) $B_{\mathrm{nuc}}=0.1$.

Figure 5

The average fidelity for triplet transfer $\langle F_c^{+}\rangle$ and singlet transfer $\langle F_c^{-}\rangle$ at $JT=11.36$ versus $\eta$ (variance of white noise) for different static noise $\delta$ and with different hyperfine interaction: (a) and (c ) $B_{\mathrm{nuc}}=0$; (b) and (d) $B_{\mathrm{nuc}}=0.1$.

Figure 6

The average fidelity for transferring an equally weighted superposition of singlet and triplet at $JT=11.36$ versus $\eta$ (variance of white noise) for different static noise $\delta$ and with different hyperfine interaction: (a) $B_{\mathrm{nuc}}=0$; (b) $B_{\mathrm{nuc}}=0.1$. Since there are oscillations in the attainable fidelity the time that fidelity peaks is slightly after the ramping time $T$, namely $t=12.45/J$.