Teplukhin Alexander, Kendrick Brian K, Babikov Dmitri
Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Chem Chem Phys. 2020 Nov 25;22(45):26136-26144. doi: 10.1039/d0cp04272b.
Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only. For many physics and chemistry problems, the diagonalization of complex matrices is required. For example, the calculation of quantum scattering resonances can be formulated as a complex eigenvalue problem where the real part of the eigenvalue is the resonance energy and the imaginary part is proportional to the resonance width. In the present work, we generalize the QAE to treat complex matrices: first complex Hermitian matrices and then complex symmetric matrices. These generalizations are then used to compute a quantum scattering resonance state in a 1D model potential for O + O collisions. These calculations are performed using both a software (classical) annealer and hardware annealer (the D-Wave 2000Q). The results of the complex QAE are also benchmarked against a standard linear algebra library (LAPACK). This work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device.
量子计算是一种用于解决化学问题的全新且快速发展的范式。在之前的工作中，我们开发了量子退火特征值求解器（QAE），并将其应用于在D-Wave量子退火器上计算分子的振动光谱。然而，原始的QAE方法仅适用于实对称矩阵。对于许多物理和化学问题，需要对复矩阵进行对角化。例如，量子散射共振的计算可以表述为一个复特征值问题，其中特征值的实部是共振能量，虚部与共振宽度成正比。在本工作中，我们将QAE进行推广以处理复矩阵：首先是复埃尔米特矩阵，然后是复对称矩阵。这些推广随后被用于计算一维O + O碰撞模型势中的量子散射共振态。这些计算使用软件（经典）退火器和硬件退火器（D-Wave 2000Q）进行。复QAE的结果也与标准线性代数库（LAPACK）进行了基准测试。这项工作展示了在量子退火器上对任何类型的复特征值问题的首个数值解，并且是在任何量子设备上对量子散射共振的首次处理。
