论文标题
用于解决当地费米至问题映射的量子电路
Quantum circuits for solving local fermion-to-qubit mappings
论文作者
论文摘要
晶格上的费米金系统当地的汉密尔顿人可以映射到当地的Qubit Hamiltonians上。保持运营商的当地是以辅助自由度来增加希尔伯特空间的代价。为了检索代表费米子自由度的较低维度的希尔伯特空间，必须满足一组约束。在这项工作中，我们引入了量子电路，以完全满足这些严格的约束。我们证明了维护区域如何允许每个时间步长以恒定的电路深度执行一个trotterized的时间进化。我们的构建尤其有利，可以模拟d> 1个维度中费米子系统的时间演化运算符。我们还讨论了如何将这些电路家族用作变分量子状态，重点是两种方法：一种基于一般恒定剂量 - 数字大门的方法，以及第二种方法，第二种方法基于哈密顿变异的ANSATZ，其中特征态由参数化时间进化算子表示。我们将方法应用于找到$ t $ - $ v $型号的基态和时间进化状态的问题。
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the locality of the operators comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the lower-dimensional physical Hilbert space that represents fermionic degrees of freedom, one must satisfy a set of constraints. In this work, we introduce quantum circuits that exactly satisfy these stringent constraints. We demonstrate how maintaining locality allows one to carry out a Trotterized time-evolution with constant circuit depth per time step. Our construction is particularly advantageous to simulate the time evolution operator of fermionic systems in d>1 dimensions. We also discuss how these families of circuits can be used as variational quantum states, focusing on two approaches: a first one based on general constant-fermion-number gates, and a second one based on the Hamiltonian variational ansatz where the eigenstates are represented by parametrized time-evolution operators. We apply our methods to the problem of finding the ground state and time-evolved states of the $t$-$V$ model.
