Robustness of Enhanced Shortcuts to Adiabaticity in Lattice Transport

TL;DR

This work investigates the robustness of Enhanced Shortcuts to Adiabaticity (eSTA) for fast atomic transport in optical lattices. By starting from an ideal STA solution for a harmonic approximation and perturbing toward a realistic lattice Hamiltonian, the authors construct eSTA corrections that substantially improve fidelity and stability compared with standard STA, even in the presence of systematic lattice errors and classical noise. They introduce practical robustness metrics, including a control function deviation measure C_Q and a systematic error bound B, to quantify and compare performance without full numerical optimization. Overall, the results show that eSTA provides a computationally efficient and analytically transparent framework to design robust quantum controls in lattice-based quantum technologies and beyond.

Abstract

Shortcuts to adiabaticity (STA) are a collection of quantum control techniques that achieve high fidelity outside of the adiabatic regime. Recently an extension to shortcuts to adiabaticity was proposed by the authors [Phys. Rev. Research 2, 023360 (2020)]. This new method, enhanced shortcuts to adiabaticity (eSTA), provides an extension to the original STA control functions and allows effective control of systems not amenable to STA methods. It is conjectured that eSTA schemes also enjoy an improved stability over their STA counterparts. We provide numerical evidence of this claim by applying eSTA to fast atomic transport using an optical lattice, and evaluating appropriate stability measures. We show that the eSTA schemes not only produce higher fidelities, but also remain more stable against errors than the original STA schemes.

Figures (8)

• Figure 1: (color online) (a) is a schematic representation of fidelity versus $\mu$. The fidelity of ${\cal{H}}_\mu$ using $\vec{\lambda}_0$ is the dot-dashed blue line. The blue square is ${\cal{H}}_{\mu_s}$ using $\vec{\lambda}_0$. The red dot is the improved fidelity of ${\cal{H}}_{\mu_s}$ using $\vec{\lambda}_s$. The dashed-orange line represents the assumed parabolic profile of the fidelity as ${\cal{H}}_{0} \rightarrow {\cal{H}}_{\mu_s}$, with the improved eSTA control $\vec{\lambda}_{\mu}$ calculated for each $\mu$. The slopes of each line at $\mu_s$ are depicted as solid-black lines. (b) is a diagram of eSTA in control space $(\vec{\lambda},F)$. The starting STA scheme fidelity (blue square), gradient (black arrow) and fidelity at $\vec{\lambda}_s$ (red dot) are shown. The resulting eSTA approximate parabola (dashed-red line), and true fidelity landscape (solid-blue line) are also displayed.
• Figure 2: Plot of STA and eSTA control functions. (a) Plot of the auxiliary functions, $q_{c,1}(t)$ (dot-dashed blue), $q_{c,2}(t)$ (dashed green) and $q_{c,3}(t)$ (solid red). In each of these plots $t_f/\tau=0.8$ and $d=\lambda/2\sigma$ (one lattice site). (b) Corresponding plots of the STA transport functions, $q_{0,1}(t)$ (dot-dashed blue), $q_{0,2}(t)$ (dashed green) and $q_{0,3}(t)$ (solid red). (c) Example of the vector components of the eSTA correction $\vec{\epsilon}$, with $q_{0,1}$ (dashed blue) and $Q_{1}$ (solid orange) shown for $t_f/\tau=0.8$ and $d=\lambda/2\sigma$. (d) Examples of the eSTA control functions. The vertical dashed lines in plots (a) and (b) indicate the smoothing boxes of length $t_f/8$ about the discontinuities in $q_{c,2}$, $q_{0,2}$, $q_{c,3}$ and $q_{0,3}$.
• Figure 3: Fidelity $F$ versus final time $t_f$, for $\delta=0$. The fidelities for the STA trajectories are given by the broken lines; $q_{0,1}(t)$ (dot-dashed blue), $q_{0,2}(t)$ (dashed green) and $q_{0,3}(t)$ (dotted red). The corresponding eSTA optimized fidelities are solid lines; $Q_{1}(t)$ (blue), $Q_{2}(t)$ (green) and $Q_{3}(t)$ (red). Inset of (a): Fidelity $F$ versus final time $t_f$ using $Q_3$ with different smoothing options. The solid-red line uses a fully discontinuous $q_{c,3}$, and the dashed-black line on top of it uses $q_{c,3}$ with only the center discontinuity smoothed over a $t_T=t_f/16$ interval. The dotted-red line uses $q_{c,3}$ smoothed in an interval of length $t_T=t_f/16$ around the three discontinuities and the dashed-red line uses $q_{c,3}$ smoothed in an interval of length $t_T=t_f/8$ around the three discontinuities.
• Figure 4: Control function deviation ${\cal{C}}_Q$ versus $t_f$ for correlated systematic error. Trajectories $Q_{1}(t)$ (solid blue), $Q_{2}(t)$ (solid green) and $Q_{3}(t)$ (solid red). Upper bound of ${\cal{C}}_Q$: trajectories $Q_{1}(t)$ (dot-dashed blue), $Q_{2}(t)$ (dashed green) and $Q_{3}(t)$ (dotted red).
• Figure 5: Fidelity at $t_f/\tau=1.1$ versus $\delta$. The fidelities for the STA trajectories are shown, for $q_{0,1}(t)$ (dot-dashed blue), $q_{0,2}(t)$ (dashed green) and $q_{0,3}(t)$ (dotted red). The corresponding eSTA optimized fidelities are $Q_{1}(t)$ (solid blue), $Q_{2}(t)$ (solid green) and $Q_{3}(t)$ (solid red). The horizontal solid-black arrows show $\left| \delta \right|$, such that $F(\delta) > F_R=0.9$ for $Q_2$ (solid green). The vertical solid-black arrow at $\delta=0$ is $F(\delta=0)-F_R$. These quantities are used in the definition of the systematic error bound ${\cal{B}}$, in Eq. \ref{['eq:B']}.