Two-dimensional physics-constrained hardware-efficient ansatz on quantum computers
Xiaoxiao Xiao, Wei‐Hai Fang, Zhendong Li · Chinese Science Bulletin (Chinese Version) · 2025
One of the most significant challenges in quantum chemistry simulations is the accurate and efficient treatment of strongly correlated systems using classical computers. Quantum computational chemistry is an emerging field that has grown alongside the development of quantum computers, aiming to tackle challenges beyond the reach of traditional computational chemistry methods. Given the current limitations of quantum hardware, hybrid quantum-classical algorithms have become the dominant approach in quantum computational chemistry, with the Variational Quantum Eigensolver (VQE) serving as a representative example. In the realm of variational quantum algorithms, the design of the ansatz plays a pivotal role, as it directly determines both the accuracy of the results and the optimization efficiency of the algorithm, making it a central component in achieving success in quantum computational chemistry. However, existing ansätze often fails to strike a balance between precision and hardware efficiency, posing a major bottleneck for practical applications. In our previous work, we proposed a novel strategy for designing hardware-efficient ansätze with built-in physical constraints (PCHEA). This approach demonstrated outstanding performance in simulating one-dimensional Heisenberg models and several typical molecular systems. By embedding physical insights into the design, PCHEA not only improved computational accuracy but also significantly enhanced hardware compatibility, making it a promising candidate for near-term quantum devices. Nevertheless, challenges remain. When applying the one-dimensional PCHEA to two-dimensional systems, the circuit costs increase significantly. To address this challenge, in this work, we simplify the implementation of the physics-constrained hardware-efficient ansatz, using fSim gates arranged in hardware-efficient linear and brickwall layouts to construct one-dimensional fSim linear and fSim brickwall ansätze. This modification substantially reduces both the number of two-qubit gates and the circuit depth. These ansätze ensure universality, systematic improvement, and size consistency within a particle-number-conserving Hilbert space, with significant improvements observed in the simulation of the one-dimensional Heisenberg model. Furthermore, building on the advancements in quantum hardware connectivity, we extend the one-dimensional PCHEA to a two-dimensional version by arranging it in a grid pattern. The two-dimensional PCHEA not only retains the physical constraints of the one-dimensional PCHEA but also exploits hardware connectivity to further reduce circuit costs. Simulations on two-dimensional Heisenberg models show that the two-dimensional PCHEA achieves chemical accuracy with considerably lower circuit depth, fewer parameters, and fewer two-qubit gates compared to the one-dimensional PCHEA. This work reinforces the effectiveness of designing hardware-efficient ansätze with embedded physical constraints, presenting a promising approach to advancing the practical application of quantum computers for simulating two-dimensional systems. Such progress brings us closer to achieving more efficient and scalable quantum simulations while addressing key challenges in quantum computational chemistry.