Efficient approximation of the dynamics of one-dimensional quantum spin systems.
Efficient approximation of the dynamics of one-dimensional quantum spin systems.
复制标题
一维量子自旋系统动力学的有效近似。
DOI：
10.1103/physrevlett.97.157202
复制
发表时间：
2006
影响因子：
8.6
通讯作者：
T. Osborne
中科院分区：
文献类型：
--
作者：
T. Osborne
在这封信中，我们证明了对于具有哈密顿量H的n个量子自旋的一维晶格，传播子e（itH）的任意好的近似可以用n中的多项式计算资源和|不|.我们的证明利用了密度矩阵重整化群等数值重整化群算法所利用的相关态或矩阵乘积态形式。这一结果有两个直接后果。首先，维达尔的含时密度矩阵重整化群将只需要多项式资源来模拟一维量子自旋系统的对数|不|.第二个结果是，具有对数的连续时间一维量子电路|不|可以在经典计算机上有效地模拟，尽管事实上，在离散化之后，这种电路具有多项式深度。
In this Letter we show that an arbitrarily good approximation to the propagator e(itH) for a 1D lattice of n quantum spins with Hamiltonian H may be obtained with polynomial computational resources in n and the error epsilon and exponential resources in |t|. Our proof makes use of the finitely correlated state or matrix product state formalism exploited by numerical renormalization group algorithms like the density matrix renormalization group. There are two immediate consequences of this result. The first is that Vidal's time-dependent density matrix renormalization group will require only polynomial resources to simulate 1D quantum spin systems for logarithmic |t|. The second consequence is that continuous-time 1D quantum circuits with logarithmic |t| can be simulated efficiently on a classical computer, despite the fact that, after discretization, such circuits are of polynomial depth.