论文标题
$ j_1 $ - $ j_2 $ -model的变量量子eigensolver ansatz
Variational Quantum Eigensolver Ansatz for the $J_1$-$J_2$-model
论文作者
论文摘要
由于高度挫败感，二维$ J_1-J_2 $ -MODEL的基础状态非常具有挑战性。这使该模型成为有前途的候选人，量子计算机可能会有所帮助，并可能探索古典计算机无法达到的政权。 $ J_1-J_2 $ -MODEL是一种量子自旋模型，由沿矩形晶格边缘的海森堡相互作用组成，并沿着下一个最邻居旋转之间的对角线边缘。我们为变量量子本索（VQE）提出了一个ANSATZ，以近似于抗铁磁$ J_1-J_2 $ -HAMILTONIAN的基态状态，用于不同的晶格大小，不同的比率为$ j_1 $和$ j_2 $。此外，我们证明了这种Ansatz可以工作，而无需沿着对角的邻居相互作用进行大门。对于基于固态的硬件，在矩形网格上具有Qubits，这种简化至关重要，在该硬件上，它消除了对交换门的需求。此外，我们还为较大晶格尺寸所需的门数和参数的数量提供了推断，这表明这些晶格的生长在量子数中的生长将小于二次，直到晶格大小，最终无法再用经典计算机处理。
The ground state properties of the two-dimensional $J_1-J_2$-model are very challenging to analyze via classical numerical methods due to the high level of frustration. This makes the model a promising candidate where quantum computers could be helpful and possibly explore regimes that classical computers cannot reach. The $J_1-J_2$-model is a quantum spin model composed of Heisenberg interactions along the rectangular lattice edges and along diagonal edges between next-nearest neighbor spins. We propose an ansatz for the Variational Quantum Eigensolver (VQE) to approximate the ground state of an antiferromagnetic $J_1-J_2$-Hamiltonian for different lattice sizes and different ratios of $J_1$ and $J_2$. Moreover, we demonstrate that this ansatz can work without the need for gates along the diagonal next-nearest neighbor interactions. This simplification is of great importance for solid state based hardware with qubits on a rectangular grid, where it eliminates the need for SWAP gates. In addition, we provide an extrapolation for the number of gates and parameters needed for larger lattice sizes, showing that these are expected to grow less than quadratically in the qubit number up to lattice sizes which eventually can no longer be treated with classical computers.
