The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. We test our circuits in quantum simulations of the \({H}_{2}\) and \(LiH\) molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth.

变分量子本征求解器是使用嘈杂的中级量子（NISQ）处理器进行化学模拟的最有前途的方法之一。该算法的效率主要取决于在量子处理器上准备多量子位试验状态的能力，该状态包括或至少近似逼近所模拟问题的实际能量本征状态，同时避免了与它们几乎没有重叠的状态。对称性在确定最佳试验状态中起着核心作用。在这里，我们介绍了一种高效的状态准备电路，该电路考虑了粒子数，总自旋，自旋投影和时间反转对称性。这些电路包含最小数目的变分参数，以完全跨越化学问题所决定的适当对称子空间，同时避免了希尔伯特空间的所有不相关扇区。我们展示了如何为任意数量的轨道，电子和自旋量子数构造这些电路，并且在每种情况下，我们根据标准门集提供了明确的分解和门数。我们在量子模拟中测试电路\（{H} _ {2} \）和\（LiH \）分子，发现它们在准确性和电路深度方面都优于标准状态准备方法。