Quantum state transfer and maximal entanglement between distant qubits using a minimal quasicrystal pump

TL;DR

The paper presents a minimal, topological quantum pump based on a 1D Fibonacci chain that leverages winding edge states to enable coherent state transfer over long distances by switching only the two outermost bonds. The authors show adiabatic pumping of a winding state, analyze robustness to disorder, and demonstrate the Fibonacci pump functioning as a quantum bus that mediates complete state transfer and generates maximally entangled Bell states between two distant qubits. They quantify performance with a weighted fidelity and explore one-step and two-step protocols, highlighting a large operational window and practical robustness. The approach promises low-control, scalable long-range quantum connectivity across platforms such as superconducting resonators and photonic networks, enabling flexible quantum information processing tasks.

Abstract

Coherent quantum state transfer over macroscopic distances between non-neighboring elements in quantum circuits is a crucial component to increase connectivity and simplify quantum information processing. To facilitate such transfers, an efficient and easily controllable quantum pump would be highly beneficial. In this work, we demonstrate such a quantum pump based on a one-dimensional quasicrystal Fibonacci chain~(FC). In particular, we utilize the unique properties of quasicrystals to pump the edge-localized winding states between the two distant ends of the chain by only minimal manipulation of the FC at its end points. We establish the necessary conditions for successful state transfer within a fully time-dependent picture and also demonstrate robustness of the transfer protocol against disorder. We then couple external qubits to each end of the FC and establish highly adaptable functionality as a quantum bus with both on-demand switching of the qubit states and generation of maximally entangled Bell states between the qubits. Thanks to the minimal control parameters, the setup is well-suited for implementation across diverse experimental platforms, thus establishing quasicrystals as an efficient platform for versatile quantum information processing.

Figures (15)

• Figure 1: The FQP consists of an FC with weak bonds $J_A$ (blue) and strong bonds $J_B$ (red). The transfer protocol $V(t)$ dynamically modifies the outermost bonds of the FC and induces a transfer of a winding state from the left end (light orange) to the right (dark orange). External qubits $Q_1$ and $Q_2$ are coupled to the FQP with coupling constant $g$. The FQP can transfer a state between the two qubits or generate maximally entangled states between them.
• Figure 2: (a) Eigenvalues $E$ as a function of phason angle $\phi$. Red and black curves represent winding states in one of the larger quasicrystal energy gaps (gray shaded). (b) Flipping between strong (red) and weak (blue) bonds indicated by arrows, when changing phason angle from $\phi_1$ (green) to $\phi_2$ (orange), also marked in (a). (c) Spatially resolved amplitude of the red winding state along the chain at $\phi_1$ (green) and $\phi_2$ (orange). Inset shows the eigenvalue spectrum $E_m$ as a function of the state index $m$ for phason angles $\phi_1$ (green) and $\phi_2$ (orange), with red dot and arrow marking the winding state. Here we use a $C_8$ FC with $L=F_8+1=35$ sites and $\rho=1.5$, $\phi_1=0.73 \pi$, and $\phi_2=0.78 \pi$.
• Figure 3: (a) Eigenvalue evolution $E(t)$ of the winding state (solid) and the next excited state (dashed) as a function of time $t$ for the $C_8$ FC with $L=F_8+1=35$ (red) and $L=2F_8+1=69$ (green). Inset shows zoomed-in excitation gap. Here $\rho=1.5$. (b) Same as (a) but for different hopping ratios $\rho=1.5$ (blue) and $2.0$ (orange) for the FC $L=F_8+1=35$. (c) Evolution of the winding state as a function of time $t$ and spatial position $i$ for $\rho=1.5$ for the FC $L=F_8+1=35$. (d) Same as (c) but for $\rho=2.0$. In all panels, the transfer rate is $\Omega=10^{-4}$.
• Figure 4: (a) Weighted fidelity $\bar{\mathcal{F}}$ as a function of hopping ratio $\rho$ and rate $\Omega$ for the $C_8$ FC with $L=F_8+1=35$. The frequency axis is on a logarithmic scale. (b) $\bar{\mathcal{F}}$ as a function of $\rho$ for fixed $\Omega=10^{-4}$ for FCs with $L=F_8+1=35$ (red) and $2F_8+1=69$ (green) for the one- (solid) and two-step (dashed) transfer protocols.
• Figure 5: (a) Spatially resolved amplitude of the winding state at initial time $t=0$ (green) and final time $t=t_f$ (orange) using the transfer protocol in inset with changes only to the hopping amplitudes $J_1$ and $J_{N_B}$. (b) Amplitudes $\lvert \alpha_{1,2,3}(t) \rvert^2$ of the time-evolved many-body state for initial state $\ket{101}$ as a function of time. (c) Concurrence $C$ as a function of time for the same initial state as in (b). Inset shows the probability of obtaining the two Bell states. (d-e) Repeats (a-c), but changes only one of the hopping amplitudes in the unit cell. Here we use the $C_8$ FC with $L=F_8+1=35$ and $\rho=1.4$, while $g=1.0$, $\Omega=10^{-4}$, and $E_l=E_r=0.0$.