Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm
Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm
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DOI：
10.1038/s41534-019-0240-1
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发表时间：
2020-01-28
影响因子：
7.6
通讯作者：
Barnes, Edwin
中科院分区：
文献类型：
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作者：
Gard, Bryan T.;Zhu, Linghua;Barnes, Edwin
变分量子本征解算器是使用噪声中尺度量子（NISQ）处理器进行化学模拟的最有前途的方法之一。这种算法的效率关键取决于在量子处理器上准备多量子比特试验态的能力，这些试验态包括或至少接近模拟问题的实际能量本征态，同时避免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，我们提出了有效的状态准备电路，尊重粒子数，总自旋，自旋投影和时间反转对称性。这些电路包含的变分参数需要完全跨越适当的对称子空间所规定的化学问题，同时避免希尔伯特空间的所有不相关的部门的最小数量。我们将展示如何构建这些电路的任意数量的轨道，电子和自旋量子数，我们提供明确的分解和门计数在每种情况下的标准门集。我们在H2和LiH分子的量子模拟中测试了我们的电路，发现它们在精度和电路深度方面都优于标准状态制备方法。
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 multiqubit 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 H2 and LiH molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth.