For variational algorithms on the near term quantum computing hardware, it is highly desirable to use very accurate ansatze with low implementation cost. Recent studies have shown that the antisymmetrized geminal power (AGP) wavefunction can be an excellent starting point for ansatze describing systems with strong pairing correlations, as those occurring in superconductors. In this work, we show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Using AGP as the initial reference, we propose and implement a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian. The results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.

对于近期量子计算硬件上的变分算法，非常希望使用具有低实现成本的非常精确的分析。最近的研究表明，反对称的双功率（AGP）波函数可以成为描述具有强配对相关性的系统（如超导体中发生的系统）的出色起点。在这项工作中，我们展示了如何在量子计算机上有效地实现AGP，并且其电路深度，CNOT的数量以及系统尺寸中的测量数量都是线性的。使用AGP作为初始参考，我们在AGP上提出并实现了一个correlat相关器，并在配对哈密顿量的基态上对其进行了基准测试。结果表明，在该模型哈密顿量的所有相关状态下，高精度的基态能量。