论文标题
用于模拟对称量子系统的有效经典算法
Efficient classical algorithms for simulating symmetric quantum systems
论文作者
论文摘要
鉴于最近提出的量子算法，这些算法结合了量子优势，我们表明，对于足够限制的对称性，经典算法可以在某些经典的输入中有效地模仿其量子对应物。具体而言，我们给出了经典的算法，以计算基础状态和随时间推动的期望值的置换式汉密尔顿人在对称的Pauli基础上指定的，并且在系统大小中多条件。我们使用张量 - 网络方法将对称性 - 均衡运算符转换为多项式大小的块对基形成基础，然后在此基础上执行精确的矩阵乘法或对角线化。这些方法适用于广泛的输入和输出状态，包括在Schur基础上以矩阵乘积状态或任意量子状态进行的量子状态，当具有低深度电路和单个量子测量值时。
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts given certain classical descriptions of the input. Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariant Hamiltonians specified in the symmetrized Pauli basis with runtimes polynomial in the system size. We use tensor-network methods to transform symmetry-equivariant operators to the block-diagonal Schur basis that is of polynomial size, and then perform exact matrix multiplication or diagonalization in this basis. These methods are adaptable to a wide range of input and output states including those prescribed in the Schur basis, as matrix product states, or as arbitrary quantum states when given the power to apply low depth circuits and single qubit measurements.
