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Although there are good reasons to believe that quantum states are sometimes relativized to observers, there are difficulties for the view that quantum states can only be relativized to conscious macroscopic observers, and also for the view that quantum states can be relativized to any physical system. In this talk, I will argue for an alternative `emergence' approach such that we can indeed write down a description relative to any physical system, but the full formalism of quantum theory emerges only in the limit as the reference system becomes large. If this is true, it poses a challenge for attempts to understand the emergence of the classical regime from the quantum world, since our standard quantum descriptions may presuppose a classical system to which they are relativized. I will describe how this idea might give new insight into Extended Wigner's Friend paradoxes and the measurement problem, and then sketch some ideas for how we might generalize beyond quantum mechanics to characterize descriptions relative to other kinds of reference systems.

Decoded Quantum Interferometry (DQI) has been recently proposed as a new quantum algorithm for optimization. Hamiltonian Decoded Quantum Interferometry (HDQI), an extension of DQI, adapts this paradigm to Hamiltonian optimization and Gibbs state preparation. In this work, I will introduce HDQI for general Pauli Hamiltonians and discuss its application to the approximation of Gibbs states.

Non-local quantum computation studies the complexity of implementing quantum channels non-locally and has fascinating connections to cryptography, complexity theory and quantum gravity. In this talk, I will survey some of these connections, with an emphasis on circuit and communication complexity. Building on ideas, I will present new lower bounds on the magic cost of quantum gates, quantum speedups in communication, and approaches to position verification with privacy guarantees.

As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided by score functions. Real-life data, like images, is often spatially structured in low-dimensional spaces. However, ordinary diffusion models ignore this local structure and learn spatially global score functions, which are often computationally expensive. In this work, motivated by recent advances in statistical physics, we develop a generic framework for defining phases of data distributions and use it to analyze the locality requirements of denoisers in diffusion models. We define two distributions as belonging to the same data distribution phase if they can be mutually connected via spatially local operations such as local denoisers. We demonstrate that the reverse denoising process consists of an early trivial phase and a late data phase, sandwiching a rapid phase transition where local denoisers must fail. We further demonstrate that the performance of local denoisers is closely tied to spatial Markovianity, which provides an operational criterion for diagnosing such phase transitions. We validate this criterion through numerical experiments on real-world datasets. Our work suggests guidance for simpler and more efficient architectures of diffusion models: far from the phase transition point, we can use small local neural networks to compute the score function; global neural networks are only necessary around the narrow time interval of phase transitions. This result also opens up new directions for studying phases of data distributions, the broader science of generative artificial intelligence, and guiding the design of neural networks inspired by physics concepts.