Simulating adiabatic evolution of gapped spin systems
Simulating adiabatic evolution of gapped spin systems
复制标题
模拟有隙自旋系统的绝热演化
DOI：
10.1103/physreva.75.032321
复制
发表时间：
2006
影响因子：
2.9
通讯作者：
T. Osborne
中科院分区：
文献类型：
--
作者：
T. Osborne
结果表明，我们可以有效地模拟具有谱隙的低维量子自旋晶格的绝热演化。特别地，我们证明了只要基态和第一激发态之间的光谱间隔E是与自旋总数$n无关的任何常数，那么局域算符的基态期望值，如关联函数，就可以利用多项式的空间和时间资源来计算。我们的结果还表明，同一量子相中任意两个自旋模型的局域基态性质可以有效地相互获得。这些结果的一个结果是，如果谱间隙不随$n$而变化，则可以有效地模拟绝热量子算法。我们描述的模拟方法发生在Heisenberg图中，并且没有使用有限关联的状态-Char21-矩阵乘积状态形式。
We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap $\ensuremath{\Delta}E$ between the ground state and the first excited state is any constant independent of $n$, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from each other. A consequence of these results is that adiabatic quantum algorithms can be simulated efficiently if the spectral gap does not scale with $n$. The simulation method we describe takes place in the Heisenberg picture and does not make use of the finitely correlated state\char21{}matrix product state formalism.