Holographically Emergent Gauge Theory in Symmetric Quantum Circuits

• URL: http://arxiv.org/abs/2511.21685v1
• Date: Wed, 26 Nov 2025 18:58:11 GMT
• Title: Holographically Emergent Gauge Theory in Symmetric Quantum Circuits
• Authors: Akash Vijay, Jong Yeon Lee,
• Abstract summary: We develop a novel holographic framework for mixed-state phases in random quantum circuits, both unitary and non-unitary.<n>For unitarity circuits, the bulk gauge state is deconfined, but under a generic non-unitary circuit (e.g. channels)<n>We identify that the charge sharpening transition from the measurement side is complementary to a decodability transition in the bulk.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a novel holographic framework for mixed-state phases in random quantum circuits, both unitary and non-unitary, with a global symmetry $G$. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent gauge wavefunction in one higher dimension, and a random non-symmetric layer, which consists of random multiplicity tensors. For unitarity circuits, the bulk gauge state is deconfined, but under a generic non-unitary circuit (e.g. channels), the bulk gauge theory can undergo a decoherence-induced phase transition: for $G\,{=}\,\mathbb{Z}_N$ with local symmetric noise, the circuit can act as a quantum error-correcting code with a distinguished logical subspace inheriting the $\mathbb{Z}_N$-surface code's topological protection. We then identify that the charge sharpening transition from the measurement side is complementary to a decodability transition in the bulk: noise of the bulk can be interpreted as measurement from the environment. For $N\,{\leq}\,4$, weak measurements drive a single transition from a charge-fuzzy phase with sharpening time $t_{\#}\sim e^{L}$ to a charge-sharp phase with $t_{\#}\sim \mathcal{O}(1)$, corresponding to confinement that destroys logical information. For $N>4$, measurements generically generate an intermediate quasi-long-range ordered Coulomb phase with gapless photons and purification time $t_{\#}\sim \mathcal{O}(L)$.

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