Zhian Jia

Temporal quantum states generalize the multipartite density operator formalism to the time domain, enabling a unified treatment of quantum systems with both timelike and spacelike correlations. Despite a growing body of temporal state formalisms, their precise operational relationships and conceptual distinctions remain unclear. In this work, we resolve this issue by extending the Kirkwood-Dirac (KD) quasiprobability distribution to arbitrary multi-time quantum processes and, more broadly, to general spatiotemporal settings. We define left, right, and doubled temporal KD quasiprobabilities, together with their real components, which we identify as temporal Margenau-Hill (MH) quasiprobabilities. All of these quantities are experimentally accessible through interferometric measurement schemes. By characterizing their nonclassical features, we show that the generalized KD framework provides a unified operational foundation for a wide class of temporal state approaches and can be directly implemented via temporal or spatiotemporal Bloch tomography.

A bstract: We investigate domain walls between 2 d gapped phases of Turaev-Viro type topological quantum field theories (TQFTs) by constructing domain wall tube algebras. We begin by analyzing the domain wall tube algebra associated with bimodule categories, and then extend the construction to multimodule categories over N base fusion categories. We prove that the resulting tube algebra is naturally equipped with a C ^∗ weak Hopf algebra structure. We show that topological excitations localized on domain walls are classified by representations of the corresponding domain wall tube algebra, in the sense that the functor category of bimodules admits a fusion-preserving embedding into the representation category of the domain wall tube algebra. We further establish the folding trick and Morita theory in this context. Then, most crucially, we provide a rigorous construction of the Drinfeld quantum double from weak Hopf boundary tube algebras using a skew-pairing, and establish an isomorphism between domain wall tube algebra and Drinfeld quantum double of boundary tube algebras. Motivated by the correspondence between the domain wall tube algebra and the quantum double of the boundary tube algebras, we introduce the notion of an N -tuple algebra and demonstrate how it arises in the multimodule domain wall setting. Finally, we consider defects between two domain walls, showing that such defects can be characterized by representations of a domain wall defect tube algebra. We briefly outline how these defects can be systematically treated within this representation-theoretic framework.

A ‐D lattice model inspired is proposed by a weak Hopf algebra generalization of the cluster state model. This construction serves as a candidate framework for systematically realizing the Haagerup fusion category symmetry on spin chains. It is shown that the model exhibits Haagerup fusion algebra symmetry and features a tensor product Hilbert space. The construction begins with a reconstruction of the Haagerup weak Hopf algebra from the Haagerup fusion category , ensuring that the representation category of is equivalent to . Utilizing the framework of symmetry topological field theory (SymTFT), an ultra‐thin weak Hopf quantum double model that has a smooth topological boundary condition is developed. It is shown that this model supports Haagerup fusion algebra symmetry. Finally, the ground state of the model is solved for in terms of a weak Hopf matrix product state, which serves as a natural generalization of the cluster state, embodying Haagerup fusion algebra symmetry. Since the Haagerup fusion category is an anomalous symmetry, the model presented realizes the gapped Haagerup spontaneous symmetry breaking (SSB) phase.

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Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can exactly and efficiently represent stabilizer code states—a class of highly entangled quantum states that are central to quantum error correction. Given a set of stabilizer generators, we develop an efficient algorithm to determine both the RBM architecture and the exact values of its parameters. Our findings provide new insights into the expressive power of RBMs, highlighting their capability to encode highly entangled states, and may serve as a useful tool for the classical simulation of quantum error-correcting codes.