Condensed Matter

We describe how to construct emergent strong higher-form symmetries in mixed quantum states that act unitarily on Hilbert space. Our construction uses (quasi-)local recovery channels from quantum error correction to some nearby simple (stabilizer or more general commuting projector) model. We prove that when the recovery is done in an appropriate (deterministic) manner, the resulting operators continue to be unitary. When applied to operators acting on topologically non-trivial sub-manifolds (loops, surfaces), the resulting unitaries inherit the logical algebra of the fixed point model. More generally, the unitarity of the emergent symmetries allows one to define emergent excitations whose statistics follow those of the fixed point limit. for correlations other than the diffusion constant.

Quantum phases at zero temperature can be defined as equivalence classes under local unitary transformations: two ground states are in the same phase if they can be transformed into each other via a local unitary circuit. In this talk, I will discuss how to generalize this circuit-based characterization of phases to systems at finite-temperature described by Gibbs states. We construct a local quantum channel circuit that approximately transforms one Gibbs state into another provided the two are connected by a path in parameter space along which a certain correlation-decay condition holds. This correlation-decay condition is expected to be satisfied in the interior of many noncritical thermal phases. As an application, I will show that any system in the same thermal phase as a zero-temperature topological code coherently preserves quantum information for a macroscopically long time, establishing self-correction as a universal property of thermal phases.

Are you thinking about transitioning to Industry? Join the Quantum Industry Networking Event to hear from speakers who have transitioned from academia to quantum industry and participate in the speed networking session following their talks. **Confirmed guests include:** Aggie Branczyk – Quantum Salon Bohdan Kulchytskyy – Nord Quantique Alexander Neirinckx and Enrico Olivucci – Irréversible Abdullah Khalid and Yongchao Tang – 1QBit Meenu Kumari and Ningping Cao - National Research Council Canada Ben MacLellan - Open Quantum Design / Ki3 Photonics Mercedes Gilroy - Coin Edge Yushao Chen - Xanadu Chang Liu - WaveRyde Stephanie Bohaichuk - Quantum Valley Ideas Lab (QVI)

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Strongly symmetric interactions, i.e. those that preserve a system's symmetry, however, can enforce non-trivial quantum entanglement patterns. We show that the highly mixed steady states of strongly symmetric unital quantum channels that preserve a non-Abelian symmetry are generically entangled. Remarkably, for non-Abelian continuous symmetries such as SU(2), the bipartite entanglement of formation scales logarithmically ∼ log N with the number of qudits N. Next, we show that such highly entangled steady states can also arise in models which exhibits quantum Hilbert space fragmentation. These states exhibit a surprising hierarchical entanglement structure, with volume-law negativity but sub-volume law entanglement of formation. Finally, we study strongly symmetric Gibbs states, or the canonical ensemble, at finite temperatures for generic local Hamiltonians with global on-site symmetries. Unlike the usual Gibbs state, we prove that the canonical ensemble remains entangled at all finite temperatures even for Abelian symmetries, and has no sudden death of entanglement.

We identify fundamental limitations in machine learning by demonstrating that non-trivial mixed-state phases of matter are computationally hard to learn. Focusing on unsupervised learning of distributions, we show that autoregressive neural networks fail to learn global properties of distributions characterized by locally indistinguishable (LI) states. We demonstrate that conditional mutual information (CMI) is a useful diagnostic for LI: we show that for classical distributions, long-range CMI of a state implies a spatially LI partner. By introducing a restricted statistical query model, we prove that nontrivial phases with long-range CMI, such as strong-to-weak spontaneous symmetry breaking phases, are hard to learn. We validate our claims by using recurrent, convolutional, and Transformer neural networks to learn the syndrome and physical distributions of toric/surface code under bit flip noise. Our findings suggest hardness of learning as a diagnostic tool for detecting mixed-state phases and transitions and error-correction thresholds, and they suggest CMI and more generally "non-local Gibbsness'' as metrics for how hard a distribution is to learn.

Preparation of quantum ground and thermal states of many-body systems is a key computational challenge for quantum simulation, with applications in physics, chemistry, and classical optimization. We will describe simple and efficient algorithms for ground and thermal state preparation, combining engineered bath resetting and modulated system-bath coupling to derive a quantum channel approximately satisfying quantum detailed balance relations. We will show that the fixed point of the channel approximates the Gibbs state with a controlled error. We will illustrate the cooling mechanism by developing a kinetic-theory description, which yields quantiative predictions for cooling rates for systems with well-defined quasiparticles. Further, we provide extensive numerics for one- and two-dimensional systems, confirming that the protocol successfully prepares ground and thermal state throughout the finite-temperature phase diagrams, including near the quantum phase transition. Our algorithm provides a path to efficient quantum simulation of quantum-correlated states with current and near-term quantum processors.

I will discuss some recent experimental collaborations probing the onset of deconfined gauge theories by controlling individual atoms: (i) U(1) quantum spin liquids arising from non-equilibrium dynamics in neutral atom arrays (https://arxiv.org/abs/2602.18555) and (ii) non-abelian S3 topological order and its universal anyon-based gate set from adaptive quantum circuits in a trapped-ion quantum processor (https://arxiv.org/abs/2601.20956).