Condensed Matter

I will introduce the notion of a braided fusion complex --- a mathematical structure designed to encapsulate the universal fusion and braiding data of abelian excitations of gapped quantum phases. This structure provides a framework for characterizing and classifying fracton phases of matter.

I will discuss a class of probes of 2D invertible phases of matter based on replica permutation operators. These probes are defined by introducing multiple replicas of a many-body system and evaluating expectation values of permutation operators acting in different spatial regions. A notable example is the Rényi modular commutator, which is conjectured to detect the chiral central charge. I will also discuss variants of these probes for symmetry-protected topological phases.

In this talk I will discuss constraints on renormalization group (RG) flows and the stability of phases in nonequilibrium systems using information-theoretic inequalities, with examples drawn from both quantum and classical settings. The central quantity underlying these constraints is the conditional mutual information (CMI), which quantifies correlations between spatially separated regions that are not mediated by their surroundings. Assuming a UV-finite and sufficiently regular CMI scaling function, I will argue that a fixed point with smaller CMI cannot be destabilized toward one with larger CMI. I will discuss implications of this result for phase diagrams of classical nonequilibrium steady states, as well as examples involving strong-to-weak symmetry breaking, topological order, and SPT order. Time permitting, I will discuss a bound relating CMI of a convex mixture to the CMI of its pure-state components. I will use this bound to argue for the perturbative stability of spontaneous-symmetry-breaking states against arbitrary p-bounded quantum channels, even when the channel explicitly breaks the symmetry. This implies the existence of steady states with long-range order whose corresponding Liouvillian has no standard 0-form symmetry --- a phenomenon one might call "spontaneous symmetry breaking without symmetry." This work is in collaboration with Yu-Hsueh Chen.

n generic open quantum systems, universal dynamical processes tend to exhibit classicality - dissipation washes out quantum effects. Here I consider open quantum dynamics in the presence of a global U(1) symmetry. In mixed states, this symmetry can be either strong or weak, and distinct dynamical phases can be characterized by the spontaneous breaking of either symmetry. The strong-to-weak spontaneous symmetry breaking (SW-SSB) transition is characterized by various information theoretic quantities which are non-linear in the system's mixed state density matrix. Within a Lindblad framework for U(1) dynamics, we show that a finite-time SW-SSB transition occurs in two and three dimension, whereas in one dimension the correlation length grows linearly with time and diverges only in the infinite-time steady state. Moreover, with carefully chosen Lindblad dynamics, the SW-SSB transition signals a finite time breakdown of quantum dynamics, giving rise to classical dynamics described by a stochastic Langevin equation (Model F of Halperin-Hohenberg). When the weak symmetry is spontaneously broken, the system enters a superfluid state with classical hydrodynamics. I will describe observation of a SW-SSB phase and phase transition in cold atomic gas simulators, as revealed by an appropriately chosen quantum-classical cross-correlator.

I discuss how the low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged, and cannot be eliminated by a constant-depth local unitary circuit. This refines conventional notions of complexity beyond the linear circuit depth which is required to prepare any topological phase, and provides a new resource-theoretic characterization of topological orders. A central technical result is a no-go theorem establishing that stabilizer states--even up to constant-depth local unitaries--cannot approximate low-energy states of non-Abelian string-net models which satisfy the entanglement bootstrap axioms. Moreover, we show that stabilizer-realizable Abelian string-net phases have mutual braiding phases quantized by the on-site qudit dimension, and that any violation of this condition necessarily implies extensive long-range magic. Extending to higher spatial dimensions, we argue that any state obeying an entanglement area law and hosting excitations with nontrivial fusion spaces must exhibit extensive long-range magic. This applies, in particular, to ground-states and low-energy states of higher-dimensional quantum double models.

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.