Department of Physics, Duke University, Durham, North Carolina27708, United States.
School of Mathematical Sciences, Fudan University, Shanghai200437, China.
J Chem Theory Comput. 2023 Feb 14;19(3):790-798. doi: 10.1021/acs.jctc.2c00895. Epub 2023 Jan 25.
Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To date, experimental demonstrations of algorithms such as the Variational Quantum Eigensolver (VQE) have been limited to small molecules using minimal basis sets for this reason. In this work we propose incorporating an orbital optimization scheme into quantum eigensolvers wherein a parametrized partial unitary transformation is applied to the basis functions set in order to reduce the number of qubits required for a given problem. The optimal transformation is found by minimizing the ground state energy with respect to this partial unitary matrix. Through numerical simulations of small molecules up to 16 spin orbitals, we demonstrate that this method has the ability to greatly extend the capabilities of near-term quantum computers with regard to the electronic structure problem. We find that VQE paired with orbital optimization consistently achieves lower ground state energies than traditional VQE when using the same number of qubits and even frequently achieves lower ground state energies than VQE methods using more qubits.
近期的量子计算机在可处理信息的量子比特数量以及可相干执行的电路深度方面都受到限制。迄今为止，由于这个原因，诸如变分量子本征求解器（VQE）等算法的实验演示仅限于使用最小基组的小分子。在这项工作中，我们提出在量子本征求解器中纳入轨道优化方案，其中应用参数化部分幺正变换来对基函数集进行操作，以便减少给定问题所需的量子比特数量。通过对多达 16 个自旋轨道的小分子进行数值模拟，我们证明了这种方法有能力极大地扩展近期量子计算机在电子结构问题方面的能力。我们发现，在使用相同数量的量子比特时，与传统 VQE 相比，与轨道优化相结合的 VQE 始终能够实现更低的基态能量，甚至在使用更多量子比特时，也经常能够实现更低的基态能量。
