Search Talks

I will discuss our recent work on simulating and compressing the out-of-equilibrium dynamics of two-dimensional quantum systems using Pauli propagation techniques. In particular, I will discuss compression strategies based on quantum machine learning that offer significant reduction in gate count, as well as a strategy to simulate lattice fermions based on a Majorana-string propagation in two dimensions. Our methodologies achieve high accuracy on timescales comparable to state-of-the-art variational techniques and experiments that demonstrate that controlled Majorana-string truncation is a practical tool for simulating two-dimensional fermionic dynamics.

We present simple toy models of mixed state phases and phase transitions beyond thermal transitions, observed from the steady state structure of strongly symmetric local Lindbladians. To diagnose these mixed state phases and phase transitions, we introduce a local marginal fidelity that serves as a proxy for the fidelity correlator, and can be computed from tomography on a finite number of sites.

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.