论文标题
有限骨状态产品中有限级生成单粒子算子基质元素的多项式计算复杂性
Polynomial computational complexity of matrix elements of finite-rank-generated single-particle operators in products of finite bosonic states
论文作者
论文摘要
众所周知，计算矩阵$ 1+a $的永久性，其中$ a $是有限级矩阵，需要在矩阵大小中进行许多操作。由限制量子计算的玻色子采样提案的促进，我将此结果扩展到了矩阵永久的概括：在大量相同的玻色子状态的乘积中的期望值，具有有界数的玻色子。该结果补充了关于玻色子采样和相关设置中计算复杂性的早期研究。基于高斯平均的提出的技术同样适用于骨气和费米子系统。这也使我们能够为同一问题的费米子版本提高较早的多项式复杂性估计。
It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I extend this result to a generalization of the matrix permanent: an expectation value in a product of a large number of identical bosonic states with a bounded number of bosons. This result complements earlier studies on the computational complexity in boson sampling and related setups. The proposed technique based on the Gaussian averaging is equally applicable to bosonic and fermionic systems. This also allows us to improve an earlier polynomial complexity estimate for the fermionic version of the same problem.
