论文标题
通过更少的高斯消除对量子电路的模拟改进
Improved Simulation of Quantum Circuits by Fewer Gaussian Eliminations
论文作者
论文摘要
我们表明，使用$ t $ t $ t $ GATE魔术状态对量子电路进行强大模拟的成本表现出其上限的非平地降低，$ t = 1 $，$ t = 2 $，$ t = 3 $，$ t = 6 $，带有奇数。这与Qubits的先前数字界限一致。我们将模拟成本定义为需要高斯消除$ t \ times t $矩阵的术语数量，因此捕获通过计算稳定器内部产品或评估二次高斯总和进行的模拟方法的成本。先前对Qubits的数值搜索无法收敛于$ t = 7 $。我们有效地将搜索这些非平地降低的空间增加了$> 10^{10^4} $，并将界限扩展到Qutrits的$ t = 14 $。这是通过使用Wigner-Weyl-Moyal形式主义来实现代数而不是依赖数字来实现的。我们发现，从$ {3^{\ sim 0.469T}} $的$ 12 $ -QUTRIT魔术状态的新降低，该状态从$ 6 $ -QUTRIT MAGIC STATE获得的限制改进，$ {\ sim 0.482T}} $。
We show that the cost of strong simulation of quantum circuits using $t$ $T$ gate magic states exhibits non-trivial reductions on its upper bound for $t=1$, $t=2$, $t=3$, and $t=6$ with odd-prime-qudits. This agrees with previous numerical bounds found for qubits. We define simulation cost by the number of terms that require Gaussian elimination of a $t \times t$ matrix and so capture the cost of simulation methods that proceed by computing stabilizer inner products or evaluating quadratic Gauss sums. Prior numerical searchs for qubits were unable to converge beyond $t=7$. We effectively increase the space searched for these non-trivial reductions by $>10^{10^4}$ and extend the bounds to $t=14$ for qutrits. This is accomplished by using the Wigner-Weyl-Moyal formalism to algebraically find bounds instead of relying on numerics. We find a new reduction in the upper bound from the $12$-qutrit magic state of ${3^{\sim 0.469t}}$, which improves on the bound obtained from the $6$-qutrit magic state of ${3^{\sim 0.482t}}$.
