Exploring the ground state properties of many-body quantum systems conventionally involves adiabatic processes, alongside exact diagonalization, in the context of quantum annealing or adiabatic quantum computation. Shortcuts to adiabaticity by counter-diabatic driving serve to accelerate these processes by suppressing energy excitations. Motivated by this, we develop variational quantum algorithms incorporating the auxiliary counter-diabatic interactions, comparing them with digitized adiabatic algorithms. These algorithms are then implemented on gate-based quantum circuits to explore the ground states of the Fermi-Hubbard model on honeycomb lattices, utilizing systems with up to 26 qubits. The comparison reveals that the counter-diabatic inspired ansatz is superior to traditional Hamiltonian variational ansatz. Furthermore, the number and duration of Trotter steps are analyzed to understand and mitigate errors. Given the model’s relevance to materials in condensed matter, our study paves the way for using variational quantum algorithms with counterdiabaticity to explore quantum materials in the noisy intermediate-scale quantum era.

在量子退火或绝热量子计算的背景下，探索多体量子系统的基态特性通常涉及绝热过程以及精确的对角化。通过反绝热驾驶实现绝热性的捷径通过抑制能量激发来加速这些过程。受此启发，我们开发了包含辅助反绝热相互作用的变分量子算法，并将它们与数字化绝热算法进行比较。然后，这些算法在基于门的量子电路上实现，以利用具有多达 26 个量子比特的系统在蜂窝晶格上探索费米-哈伯德模型的基态。比较表明，反绝热启发的 ansatz 优于传统的哈密顿变分 ansatz。此外，还分析了 Trotter 步骤的数量和持续时间，以了解和减少错误。鉴于该模型与凝聚态物质中的材料的相关性，我们的研究为使用具有反对分布性的变分量子算法来探索嘈杂的中尺度量子时代的量子材料铺平了道路。