Digital Quantum Simulation of Flat-Band and All-Bands-Flat Dynamics for Tunable Quantum Transport

TL;DR

This work addresses the challenge of simulating flat-band physics on NISQ devices by combining digital quantum simulation with tensor-network circuit compression. Using a diamond lattice model, it demonstrates how FB and ABF configurations (tuned by a flux) produce delocalization and localization, respectively, and shows that ABF can function as a quantum transport switch when embedded in a 1D structure. The study extends to two-particle dynamics, revealing that transport remains controllable by adjusting hopping amplitudes even in the presence of interactions. The results establish flat-band engineering as a viable route for scalable quantum transport control, with potential applications in qubit isolation, particle trapping, and state transfer on quantum hardware.

Abstract

Flat-band systems offer a uniquely powerful tool for quantum control in dynamics due to their characteristic feature of having a dispersionless energy band. Simulating such highly sensitive systems on current digital quantum computers is a challenging task, due to the intrinsic limitations of the noisy intermediate-scale quantum (NISQ) devices. Here we present high-fidelity digital quantum simulations of flat-band (FB) and all-bands-flat (ABF) lattices, using an advanced tensor-network-based circuit compression method. With the compressed quantum circuits, we first explore single-particle dynamics and observe two distinct behaviours: strong localization in ABF lattices and delocalization in FB lattices. By integrating FB and ABF lattices into a one-dimensional hybrid structure, we achieve controllable quantum transport, where the ABF lattice acts as a quantum switch. Extending to two-particle dynamics, we show that transport remains controllable by tuning the hopping amplitude alone, even in the presence of interactions. These results establish flat-band engineered systems as a promising pathway for scalable control of quantum transport in emerging quantum technologies, with potential applications in qubit isolation, particle trapping, and state transfer.

Figures (10)

• Figure 1: (a) Schematic representation of the diamond chain FB lattice, where red dashed line represent the complex hopping. (b) and (c) Energy band diagram for $\phi=0$ and $\phi=\pi$, respectively. The unit cell, outlined in blue dashed lines, consists of the u (up), c (center), and d (down) sites.
• Figure 2: (a) The figure shows time evolution operator $\hat{U}(t)$ applied to the initial state $\ket{\psi(0)}$ where $\hat{U}(t)$ is discretized into discrete steps (b) The unitary operators $\hat{U}(\delta t)$ are decomposed into two-qubit unitary operators.
• Figure 3: (a) Schematic of the 13-site flat-band lattice with the particle initially localized at the center and corresponding initial state is $\ket{\psi_0} = c_{6}^{\dagger}\ket{vac}$. (b) Density evolution of the particle obtained from the simulator. (c) The density evolution of the original, unoptimized quantum circuit (UQC) executed on IBM-Q. (d) The density evolution on the optimized quantum circuit (OQC) using tensor-network executed on IBM-Q, respectively. The color bar indicates the particle density $\langle n_i \rangle$ at each site. (e) Fidelity over time for UQCs (blue squares) and OQCs (red circles) executed on IBM-Q, benchmarked against the simulator. (f) Circuit depths of UQCs (blue bars) and OQCs (red bars) at different evolution times on IBM-Q. The green dashed line indicates the compression ratio (CR) in %, highlighting the significant reduction in circuit depth achieved through optimization.
• Figure 4: (a) Schematic of the 4-site FB lattice with uniform hopping ($J$), where the particle is initially localized at site '0'. Figures (b) and (c) show the density evolution on the Simulator and IBM-Q, respectively. (d) Schematic of the ABF lattice by reversing the hopping ($-J$) on one of the link. Figures (e) and (f) show the density evolution on the Simulator and IBM-Q, respectively. The colour bars indicate the particle density $\langle n_i \rangle$ at each site.
• Figure 5: (a) Schematic of the ABF lattice consisting of two unit cells and the red dashed line indicates the reversal of hopping ($-J$) in the link. Figures (b) and (c) show the density evolution on the ideal quantum simulator and IBM-Q, respectively. The color bar represents the particle density $\langle n_i \rangle$ at each site.(d) Figure shows the overlap $\mathcal{O}(t)$ define in Eq. \ref{['eq:overlap']} as a function of time. (e) Figure shows the Fast Fourier Transform (FFT) of the overlap, $\mathcal{O}(t)$.