Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers. Finding exact solutions to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers. Yet experimental implementations have so far been restricted to molecules involving only hydrogen and helium. Here we demonstrate the experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, determining the ground-state energy for molecules of increasing size, up to BeH2. We achieve this result by using a variational quantum eigenvalue solver (eigensolver) with efficiently prepared trial states that are tailored specifically to the interactions that are available in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We demonstrate the flexibility of our approach by applying it to a problem of quantum magnetism, an antiferromagnetic Heisenberg model in an external magnetic field. In all cases, we find agreement between our experiments and numerical simulations using a model of the device with noise. Our results help to elucidate the requirements for scaling the method to larger systems and for bridging the gap between key problems in high-performance computing and their implementation on quantum hardware.

中文翻译：

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用于小分子和量子磁铁的硬件高效变分量子特征求解器

量子计算机可用于解决材料科学和凝聚态物理学中的电子结构问题和问题，这些问题可以表述为相互作用的费米子问题，这些问题扩展了现有高性能计算机的极限。在数值上找到这些问题的精确解的计算成本随着系统的大小呈指数增长，而蒙特卡洛方法由于费米符号问题而不适用。经典计算方法的这些局限性使得解决甚至少原子电子结构问题对于使用中型量子计算机实现也很有趣。然而，迄今为止，实验实施仅限于仅涉及氢和氦的分子。在这里，我们展示了对多达 6 个量子位和超过 100 个泡利项的哈密顿问题的实验优化，确定了大小不断增加的分子的基态能量，直至 BeH2。我们通过使用变分量子特征值求解器 (eigensolver) 来实现这一结果，该求解器具有有效准备的试验状态，这些状态专门针对我们的量子处理器中可用的相互作用进行定制，并结合费米子哈密顿量的紧凑编码和稳健的随机优化例程。我们通过将其应用于量子磁性问题（外部磁场中的反铁磁海森堡模型）来证明我们方法的灵活性。在所有情况下，我们发现我们的实验与使用带有噪声的设备模型的数值模拟之间是一致的。