Quantum Information

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.

Entanglement is usually discussed in the context of two subsystems at a fixed time. A natural question is whether this notion can be meaningfully extended to subsystems at different time slices. In this talk, I will present a family of entanglement measures defined for time-separated subsystems. A key property of these quantities is that they bound time-separated correlation functions, in close analogy with bounds on spatial correlators in terms of mutual information. For relativistic quantum field theories, our definition agrees with the analytic continuation from spacelike to timelike separated regions. I will discuss measurement protocols, computations for the Ising chain and holographic theories, and the relation of these constructions to the recently introduced timelike pseudoentropy. Based on https://arxiv.org/abs/2502.12240 .

Fault-tolerant logical entangling gates are essential for scalable quantum computing but are limited by the error rates and overheads of physical two-qubit gates and stabilizer measurements. We introduce phantom codes, a class of codes that attain the minimal possible cost: all in-block logical entangling operations reduce to qubit permutations that can be absorbed at the compilation stage, yielding zero physical-gate overhead and perfect logical fidelity. Our first main result is the discovery of such codes via four mechanisms. By exhaustively enumerating all 2.71x1010inequivalent CSS codes up to n=14 we find all codes to this scale and then identify additional instances up to n=21 using SAT methods. We then use quantum Reed-Muller constructions to find higher k instances and a "binzarization-and-concatenation" scheme to achieve higher d. Second, through end-to-end noisy simulations, we demonstrate scalable advantages of phantom codes over the surface code across multiple tasks. This includes a ~207x improvement in logical fidelity for Trotterized many-body quantum simulation at current physical error rates, with comparable qubit counts and a 22% preselection rate; the advantage persists from 8 to $64$ logical qubits. These results establish phantom codes as a viable architectural route to fault-tolerant quantum computation with scalable benefits for workloads with dense local entangling structure.