Correcting noisy quantum gates with shortcuts to adiabaticity

TL;DR

This work tackles the challenge of implementing high-fidelity quantum gates in finite time under decoherence by engineering a locally driven two-qubit Hamiltonian whose ground-state dynamics realize the CNOT gate. It leverages counterdiabatic driving to suppress nonadiabatic transitions, enabling robust gate operation even when $ au$ is not strictly adiabatic and under a Lindblad-type noise model. The dynamics reduce to an effective Landau-Zener problem within a two-level subspace, yielding explicit results for fidelity and transition probabilities, and the approach generalizes to $N$-qubit gates with corresponding CD terms. Overall, the method offers a practical, scalable pathway to fast, noise-robust quantum gates with broad applicability in quantum computing architectures.

Abstract

Unitary quantum gates constitute the building blocks of Quantum Computing in the circuit paradigm. In this work, we engineer a locally driven two-qubit Hamiltonian whose instantaneous ground-state dynamics generates the controlled-NOT (CNOT) quantum gate. In practice, quantum gates have to be implemented in finite-time, hence non-adiabatic and external noise effects debilitate gate fidelities. Here, we show that counterdiabatic control can restore gate performance with near perfect fidelities even in open quantum systems subject to decoherence.

Figures (5)

• Figure 1: Energy spectrum of the Hamiltonian in Eq. (\ref{['H_main']}) for a linear drive of the second qubit, $J_2(t)=J_2t/\tau$, with $t\in[-\tau/2,\tau/2]$. Left: full spectrum. Right: spectrum in the nontrivial sector $\{|10\rangle,|11\rangle\}$. The energy gap between $E_2(t)$ and $E_1(t)$ is $\Delta(t)=2\alpha_+(t)$, with a minimum value $\Delta(0)=2g$. Parameters are: $J_2=10J_1$, $g=0.5J_1$, and $J_1=1$.
• Figure 2: (a) Instantaneous fidelity, $\mathcal{F}(t)=|\langle\Psi(t)|11\rangle|^2$ with $|\Psi(0)\rangle =|E_1(-\tau/2)\rangle$, between the target state $|11\rangle$ and the evolved state $|\Psi(t)\rangle$ in the adiabatic regime $\tau=200J^{-1}_1$. (b) Final fidelity $\mathcal{F}(\tau/2)$ as a function of the driving time $\tau$. (c) Final transition probability $\mathcal{P}(\tau)$ as a function of $\tau$. The blue line represents the numerical solution while the dashed orange line the Landau-Zener formula in Eq. (\ref{['LZ_formula']}). Here we considered $J_2(t)=J_2t/\tau$. The others parameters are: $J_2=10J_1$, $g=0.5J_1$ and $J_1=1$.
• Figure 3: Probability to end up in the ground-state $|E_1(\tau/2)\rangle$ with (continuous lines) and without (dashed lines) the counterdiabatic Hamiltonian in Eq. (\ref{['Hcd_cnot']}). Results for $g=0.3,0.4,0.5$ (in units of $J_1$) and $J_2(t)=J_2t/\tau$ are shown. In the case with $H_{\text{CD}}(t)$ all three curves for different $g$ collapse on top of each other. Parameters are: $J_2=10J_1$ and $J_1=1$.
• Figure 4: Fidelity $\mathcal{F}(\tau/2)$ between the target state $|11\rangle$ and the evolved state $\rho(\tau/2)$ in the presence of a weak Gaussian white noise of strength $\alpha$. Upper panel: density plot of $\mathcal{F}(\tau/2)$ in the $(\alpha,\tau)$ plane. Lower panel: $\mathcal{F}(\tau/2)$ as a function of $\tau$ for $\alpha=0.04,0.06,0.08,0.1$ (in units of the gap $\Delta(0)=2g$). Here we considered $J_2(t)=J_2t/\tau$. Parameters are: $J_2=10J_1$, $g=0.5J_1$, and $J_1=1$.
• Figure 5: Fidelity $\mathcal{F}(\tau/2)$ between the target state $|11\rangle$ and the evolved state $\rho(\tau/2)$ in the presence of a weak Gaussian white noise of strength $\alpha$ and considering the counterdiabatic field in Eq. (\ref{['Hcd_cnot']}). Upper panel: density plot of $\mathcal{F}(\tau/2)$ in the $(\alpha,\tau)$ plane. Lower panel: $\mathcal{F}(\tau/2)$ as a function of $\tau$ for $\alpha=0.04,0.06,0.08,0.1$ (in units of the gap $\Delta(0)=2g$). Here we considered $J_2(t)=J_2t/\tau$. Parameters are: $J_2=10J_1$, $g=0.5J_1$ and $J_1=1$.