Suppressing excitations using quantum-Brachistochrone and nearest-neighbour interactions

TL;DR

The paper addresses the difficulty of achieving high-fidelity finite-time state preparation across a quantum critical point when adiabatic driving is impractically slow due to a vanishing gap. It proposes a local two-parameter control, adding a time-dependent longitudinal term $f(t)$ to the TFIM, and optimizes this control via a quantum brachistochrone–inspired variational principle that minimizes the variance of the CD Hamiltonian in the adiabatic basis. The two-parameter protocols—including a fully optimized path $f_o(t)$ and a semi-optimized form $f_s(t)$—significantly surpass truncated CD in fidelity across drive rates, with an analytical Landau–Zener framework showing preserved $n_{ex}\sim \sqrt{v}$ scaling but with reduced prefactors; the approach remains robust under classical noise, exhibiting anti-Kibble–Zurek scaling $n_{ex}\propto 1/v$ in certain noisy regimes. The method is applicable to a broad class of free-fermion models and offers a practical route to fast, noise-resilient finite-time quantum state preparation.

Abstract

We examine excitation suppression in the transverse-field Ising model (TFIM), where finite-time drive across a quantum critical point is assisted by the presence of a time-dependent coupling parameter. While conventional counterdiabatic protocols are designed to eliminate excitations, they often require complex many-body terms that are difficult to realize experimentally. In contrast, our approach employs a local, time-dependent modulation of an existing coupling term in the Hamiltonian. Within the framework of quantum optimal control, we find that under a linear ramp of the transverse field, the optimal evolution of the second parameter follows a non-monotonic trajectory. For the TFIM, this protocol yields higher fidelity and improved robustness against noise compared to several orders of approximate counterdiabatic driving. Furthermore, we provide an analytical demonstration of anti-Kibble-Zurek scaling in the presence of noise acting on either the transverse field or the longitudinal coupling. These results highlight the potential of this approach for developing simple, noise-resilient protocols for finite-time quantum state preparation.

Figures (10)

• Figure 1: Excitation probability $1-\mathcal{F}$ versus quench rate $v$ for the naive and the truncated counterdiabatic driving (with cutoffs $M=8,16,20,24$) protocol. Increasing $M$ drives the evolution closer to the adiabatic limit, while the fidelity saturates at large $v$. Parameters: $N=50$, $g_i=10$, $g_f=0$.
• Figure 2: Transverse field $g(t)$ and control pulse $1+f(t)$ for the semi-optimized and fully optimized protocols.
• Figure 3: Excitation probability vs. drive rate under a linear ramp of the transverse field from $g=10$ (paramagnetic) to $g=0$ (ferromagnetic), via different protocols. Both semi-optimized and fully optimized protocols acquire significantly lower excitations as compared to the naive and truncated CD protocols over a large range of drive rate.
• Figure 4: Transverse field $g(t)$ and control pulse $1+f(t)$ for the semi-optimized and fully optimized protocols under a full quench from $g_i=10$ to $g_f=-10$.
• Figure 5: Excitation probability vs. drive rate under a linear ramp of the transverse field from $g=10$ to $g=-10$ (paramagnetic to paramagnetic), assisted by different protocols. Once again, semi-optimized and fully optimized protocols acquire significantly lower excitations as compared to the naive and truncated CD protocols over a large range of drive rate.