论文标题
使用具有次指数上限的有效张量网络收缩算法模拟量子电路
Simulating quantum circuits using efficient tensor network contraction algorithms with subexponential upper bound
论文作者
论文摘要
我们在$ d \ geq 2 $尺寸的有限张张量网络收缩的经典计算时间上得出了严格的上限。因此，我们表明，单量子和有限的两分门的量子电路可以在范围内的次指数时间中进行经典模拟。此外，我们介绍并实施了一种保证满足我们的界限的算法，并在实践中找到了计算时间较低的收缩顺序。在许多实际上相关的情况下，这击败了标准模拟方案，对于某些量子电路也是一种最新方法。具体而言，我们的算法导致对二维量子电路的幼稚收缩方案的加速速度，少于$ 8 \ times 8 $ lattice。我们为Google的nicamore型量子电路，瞬时量子多项式时间电路和非均匀的（2+1） - 尺寸尺度随机量子电路获得了类似有效的收缩方案。
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be classically simulated in subexponential time in the number of gates. Moreover, we present and implement an algorithm guaranteed to meet our bound and which finds contraction orders with vastly lower computational times in practice. In many practically relevant cases this beats standard simulation schemes and, for certain quantum circuits, also a state-of-the-art method. Specifically, our algorithm leads to speedups of several orders of magnitude over naive contraction schemes for two-dimensional quantum circuits on as little as an $8 \times 8$ lattice. We obtain similarly efficient contraction schemes for Google's Sycamore-type quantum circuits, instantaneous quantum polynomial-time circuits, and non-homogeneous (2+1)-dimensional random quantum circuits.
