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arXiv 2202.09202quant-ph
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基于部分和图形稳定子分解的量子线路的经典模拟

Classical simulation of quantum circuits with partial and graphical stabiliser decompositions

Aleks Kissinger, John van de Wetering, Renaud Vilmart

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10 pages, 4 figures
发表信息：
Proceedings TQC 2022. pp. 5:1--5:13
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摘要：

量子线路的经典模拟的最新发展利用了巧妙地将魔态块分解成有效模拟的稳定态的总和。我们在这里展示了如何，通过考虑某些非稳定器纠缠态有更有利的分解，我们可以加快这些模拟。这是通过使用ZX演算，这使我们能够很容易地找到这些纠缠态的实例在简化的图表表示的量子线路进行模拟。我们还发现了一种新的技术，部分稳定剂分解，使我们能够交易魔术状态的稳定条款。使用这种技术，我们只需要$2^{αt}$稳定器项，其中$α\approx 0.396$，来模拟具有T计数$t$的电路。这与Qassim等人发现的$α$相匹配，但是，尽管他们只在渐近极限中得到这种缩放，但我们的电路适用于任何大小的电路。我们的方法建立在最近提出的方案，结合稳定器分解和优化策略的软件QuiZX中实现的模拟。通过我们的技术，我们可以在消费者笔记本电脑上在几分钟内可靠地模拟50量子位1400 T计数隐藏移位电路。

英文摘要：

Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser entangled states which have more favourable decompositions, we can speed up these simulations. This is made possible by using the ZX-calculus, which allows us to easily find instances of these entangled states in the simplified diagram representing the quantum circuit to be simulated. We additionally find a new technique of partial stabiliser decompositions that allow us to trade magic states for stabiliser terms. With this technique we require only $2^{αt}$ stabiliser terms, where $α\approx 0.396$, to simulate a circuit with T-count $t$. This matches the $α$ found by Qassim et al., but whereas they only get this scaling in the asymptotic limit, ours applies for a circuit of any size. Our method builds upon a recently proposed scheme for simulation combining stabiliser decompositions and optimisation strategies implemented in the software QuiZX. With our techniques we manage to reliably simulate 50-qubit 1400 T-count hidden shift circuits in a couple of minutes on a consumer laptop.

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