The Wigner function formalism has played a pivotal role in examining the nonclassical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced by Clifford gates. In this Letter, we propose a novel classical simulation method for qubit Clifford circuits based on the framed Wigner function, an extended form of the Wigner function with an additional phase degree of freedom. In our framework, Clifford gates do not induce negativity by switching to a suitable frame; thereby, a wide class of nonstabilizer states can be represented positively. By leveraging this technique, we show that some marginal outcomes of Clifford circuits with nonstabilizer state inputs can be efficiently sampled at polynomial time and memory costs. We develop a graph-theoretical approach to identify classically simulatable marginal outcomes and apply it to log-depth random Clifford circuits. We also present the outcome probability estimation scheme using the framed Wigner function and discuss its precision. Our approach opens new avenues for utilizing quasiprobabilities to explore classically simulatable quantum circuits.

中文翻译：

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通过框架 Wigner 函数扩展具有非稳定器状态的 Clifford 电路的经典可模拟边界。


Wigner 函数形式主义在研究量子态的非经典方面及其经典可模拟性方面发挥了关键作用。然而，由于 Clifford 门引起的负性，它在量子比特系统中的应用面临限制。在这封信中，我们提出了一种基于框架 Wigner 函数的量子比特 Clifford 电路的新型经典仿真方法，Wigner 函数是 Wigner 函数的扩展形式，具有额外的相位自由度。在我们的框架中，Clifford 门不会通过切换到合适的框架来诱发消极情绪;因此，可以积极表示一大类非稳定剂状态。通过利用这种技术，我们表明具有非稳定器状态输入的 Clifford 电路的一些边际结果可以在多项式时间和内存成本下进行有效采样。我们开发了一种图论方法来识别经典可模拟的边际结果，并将其应用于对数深度随机 Clifford 电路。我们还提出了使用框架 Wigner 函数的结果概率估计方案并讨论了其精度。我们的方法为利用准性来探索经典可模拟量子电路开辟了新的途径。