Quantum Algorithms to Simulate Many-Body Physics of Correlated Fermions
Quantum Algorithms to Simulate Many-Body Physics of Correlated Fermions
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DOI：
10.1103/physrevapplied.9.044036
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发表时间：
2018-04-26
影响因子：
4.6
通讯作者：
Boixo, Sergio
中科院分区：
文献类型：
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作者：
Jiang, Zhang;Sung, Kevin J.;Boixo, Sergio
在经典计算机上模拟强关联的费米子系统是出了名的困难。费曼提出的另一种方法是使用量子计算机。我们讨论了使用近期量子器件模拟强关联费米子系统。我们专注于二维（2D）或线性几何与最近邻量子位-量子位耦合，典型的超导transmon量子位阵列。我们改进了现有的算法，准备一个任意的斯莱特行列式利用酉对称。我们还提出了一个量子算法来制备任意的费米子高斯态，其门数为O（N-2），电路深度为O（N）。这两种算法都是最优的，因为量子电路中的参数数量等于描述量子态的参数数量。此外，我们提出了一种算法，以实现二维量子比特阵列上的二维费米子傅里叶变换只有O（N-1.5）门和O（根N）的电路深度，这是量子信息穿越量子比特阵列所需的最小深度。我们还提出了方法来模拟每个时间步的演变的二维费米-哈伯德模型再次在一个二维量子位阵列与O（N）门和O（根N）的电路深度。最后，我们以Hubbard模型为例讨论了如何利用这些算法确定强关联量子系统的基态性质和相图。
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. We discuss simulating strongly correlated fermionic systems using near-term quantum devices. We focus specifically on twodimensional ( 2D) or linear geometry with nearest-neighbor qubit-qubit couplings, typical for superconducting transmon qubit arrays. We improve an existing algorithm to prepare an arbitrary Slater determinant by exploiting a unitary symmetry. We also present a quantum algorithm to prepare an arbitrary fermionic Gaussian state with O(N-2) gates and O(N) circuit depth. Both algorithms are optimal in the sense that the numbers of parameters in the quantum circuits are equal to those describing the quantum states. Furthermore, we propose an algorithm to implement the 2D fermionic Fourier transformation on a 2D qubit array with only O(N-1.5) gates and O(root N) circuit depth, which is the minimum depth required for quantum information to travel across the qubit array. We also present methods to simulate each time step in the evolution of the 2D Fermi-Hubbard model-again on a 2D qubit array-with O(N) gates and O(root N) circuit depth. Finally, we discuss how these algorithms can be used to determine the ground-state properties and phase diagrams of strongly correlated quantum systems using the Hubbard model as an example.