论文标题
瞬时量子多项式时间电路中的复杂性相变
Complexity phase transitions in instantaneous quantum polynomial-time circuits
论文作者
论文摘要
我们研究了瞬时量子多项式时间（IQP）电路的子类，其密度不同。除了已知的抗调解状态外，我们还确定了模型可模拟的新型参数条件，或者输出分布遵循波特 - 托马斯分布。通过证明这些参数状态不合时宜，我们认为模型中存在两个以上的阶段。进一步研究了该模型的输出分布的可学习性，这表明基于能量的模型即使未经抗凝聚的输出分布也无法学习。我们的研究表明，量子电路模型可以具有多个细粒复杂性阶段，即使输出分布远离波特 - 托马斯分布，也可能具有量子优势的潜力。
We study a subclass of the Instantaneous Quantum Polynomial-time (IQP) circuit with a varying density of two-qubit gates. In addition to a known anticoncentration regime, we identify novel parameter conditions where the model is classically simulable or the output distribution follows the Porter-Thomas distribution. By showing that those parameter regimes do not coincide, we argue the presence of more than two phases in the model. The learnability of the output distribution of this model is further studied, which indicates that an energy-based model fails to learn the output distribution even when it is not anticoncentrated. Our study reveals that a quantum circuit model can have multiple fine-grained complexity phases, suggesting the potential for quantum advantage even when the output distribution is far from the Porter-Thomas distribution.
