论文标题
改进了通用量子电路的强大模拟
Improved Strong Simulation of Universal Quantum Circuits
论文作者
论文摘要
我们发现十二个Qubit张开的$ T $ GATE MAGIC State的稳定器排名的缩放降低。对于$ t $魔术状态，这将其降低其渐近造成的约束至$ 2^{\ sim 0.463 t} $，用于$ t $魔术状态，改善了以前发现的$ 2^{\ sim 0.468 t} $的最佳限制。我们在数值上证明了这种降低。这可以建设性地产生Clifford+$ t $ Gateset的最有效的强仿真算法，以相对或乘法误差。然后，我们根据其高斯总数等级检查Pauli测量的成本，这是对稳定器等级的略有概括，并且对其渐近缩放缩放是一个下限。我们证明，这种下限似乎在低$ t $ counts处很紧，这表明在十二秒状态下发现的稳定器等级可以进一步降低至$ 2^{\ sim 0.449 t} $，我们证明并数字地表明，单pauli测量是这种情况。我们的建筑直接显示了$ 12 $ Qubits的减少是如何基于$ 6 $，$ 3 $，$ 2 $和$ 1 $ QUBITS的减少。这解释了为什么在张量因子上发现了这些量子数量原语的张量因子，这是文献中以前缺乏的解释。此外，在此过程中，我们观察到T Gate Magic State的稳定器等级与分解分解之间的有趣关系，这些分解是与单个Qubit状态量化的计算子基础，这些状态可产生最小的独特稳定器状态内部产品 - 可以在奇数dimentional oddimenty winder winder paireer paireers中产生最小数量的独特的高斯量的关系。
We find a scaling reduction in the stabilizer rank of the twelve-qubit tensored $T$ gate magic state. This lowers its asymptotic bound to $2^{\sim 0.463 t}$ for multi-Pauli measurements on $t$ magic states, improving over the best previously found bound of $2^{\sim 0.468 t}$. We numerically demonstrate this reduction. This constructively produces the most efficient strong simulation algorithm of the Clifford+$T$ gateset to relative or multiplicative error. We then examine the cost of Pauli measurement in terms of its Gauss sum rank, which is a slight generalization of the stabilizer rank and is a lower bound on its asymptotic scaling. We demonstrate that this lower bound appears to be tight at low $t$-counts, which suggests that the stabilizer rank found at the twelve-qubit state can be lowered further to $2^{\sim 0.449 t}$ and we prove and numerically show that this is the case for single-Pauli measurements. Our construction directly shows how the reduction at $12$ qubits is iteratively based on the reduction obtained at $6$, $3$, $2$, and $1$ qubits. This explains why novel reductions are found at tensor factors for these number of qubit primitives, an explanation lacking previously in the literature. Furthermore, in the process we observe an interesting relationship between the T gate magic state's stabilizer rank and decompositions that are Clifford-isomorphic to a computational sub-basis tensored with single-qubit states that produce minimal unique stabilizer state inner products -- the same relationship that allowed for finding minimal numbers of unique Gauss sums in the odd-dimensional qudit Wigner formulation of Pauli measurements.
