We develop techniques to systematically construct local unitaries which map scale‐invariant, product state wavefunctionals to the ground states of weakly interacting, continuum quantum field theories. More broadly, we devise a “quantum circuit perturbation theory” to construct local unitaries which map between any pair of wavefunctionals which are each Gaussian with arbitrary perturbative corrections. Further, we generalize cMERA to interacting continuum field theories, which requires reworking the existing formalism which is tailored to non‐interacting examples. Our methods enable the systematic perturbative calculation of cMERA circuits for weakly interacting theories, and as a demonstration we compute the 1‐loop cMERA circuit for scalar ϕ⁴ theory and analyze its properties. In this case, we show that Wilsonian renormalization of the spatial momentum modes is equivalent to a local position space cMERA circuit. This example provides new insights into the connection between position space and momentum space renormalization group methods in quantum field theory. The form of cMERA circuits derived from perturbation theory suggests useful ansatzes for numerical variational calculations.

中文翻译：

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弱相互作用连续体场理论的重整化群电路

我们开发技术来系统地构建局部unit，将尺度不变的乘积状态波函数映射到弱相互作用的连续量子场论的基态。更广泛地讲，我们设计了一种“量子电路扰动理论”来构造局部unit，该局部unit在任意一对波函数之间映射，每个波函数都是高斯函数，具有任意扰动校正。此外，我们将cMERA推广到相互作用的连续场理论，这需要重新设计针对非相互作用示例的现有形式主义。我们的方法为弱相互作用的理论实现了对cMERA电路的系统微扰计算，并且作为演示，我们针对标量ϕ ⁴计算了1环cMERA电路。理论并分析其特性。在这种情况下，我们证明了空间动量模式的Wilsonian重归一化等效于局部位置空间cMERA电路。该示例为量子场论中的位置空间和动量空间重整化组方法之间的联系提供了新的见解。源自扰动理论的cMERA电路形式为数值变分计算提供了有用的分析方法。