Talks

Long-range entangled mixed states are exotic many-body systems that exhibit intrinsically quantum phenomena despite extensive classical fluctuations. In the first part of the talk, I will show how they can be efficiently prepared with measurements and unitary feedback conditioned on the measurement outcome. For example, symmetry-protected topological phases can be universally converted into mixed states with long-range entanglement, and certain gapped topological states such as Chern insulators can be converted into mixed states with critical correlations in the bulk. In the second part of the talk, I will discuss how decoherence can drive interesting mixed-state entanglement transitions. By focusing on the toric codes in various space dimensions subject to certain types of decoherence, I will present the exact results of entanglement negativity, from which the universality class of entanglement transitions can be completely characterized.

For quantum phases of Hamiltonian ground states, the energy gap plays a central role in ensuring the stability of the phase as long as the gap remains finite. In this talk we introduce Markov length, the length scale at which the quantum conditional mutual information (CMI) decays exponentially, as an equally essential quantity characterizing mixed-state phases and transitions. For a state evolving under a local Lindbladian, we argue that if its Markov length remains finite along the evolution, then it remains in the same phase, meaning there exists another quasi-local Lindbladian evolution that can reverse the former one. We apply this diagnostic to toric code subject to decoherence and show that the Markov length is finite everywhere except at its decodability transition, at which it diverges. This implies that the mixed state phase transition coincides with the decodability transition and also suggests a quasi-local decoding channel.

Ground states as well as Gibbs states of many-body quantum Hamiltonians have been studied extensively for some time. In contrast, the landscape of mixed states that do not correspond to a system in thermal equilibrium is relatively less explored. In this talk I will motivate a rather coarse characterization of mixed quantum many-body states using the idea of "separability", i.e., whether a mixed state can be expressed as an ensemble of short-range entangled pure states. I will discuss several examples of decoherence-driven phase transitions from a separability viewpoint, and argue that such a framework also provides a potentially new view on Gibbs states. Based on work with Yu-Hsueh Chen. References: 2309.11879, 2310.07286, 2403.06553.

"Optimal fault tolerant error correction thresholds for CCS codes are traditionally obtained via mappings to classical statistical mechanics models, for example the 2d random bond Ising model for the 1d repetition code subject to bit-flip noise and faulty measurements. Here, we revisit the 1d repetition code, and develop an exact “stabilizer expansion” of the full time evolving density matrix under repeated rounds of (incoherent and coherent) noise and faulty stabilizer measurements. This expansion enables computation of the coherent information, indicating whether encoded information is retained under the noisy dynamics, and generates a dual representation of the (replicated) 2d random bond Ising model. However, in the fully generic case with both coherent noise and weak measurements, the stabilizer expansion breaks down (as does the canonical 2d random bond Ising model mapping). If the measurement results are thrown away all encoded information is lost at long times, but the evolution towards the trivial steady state reveals a signature of a quantum transition between an over and under damped regime. Implications for generic noisy dynamics in other CCS codes will be mentioned, including open issues."

We develop a Machine-Learning Renormalization Group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the $c$-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

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Asymptotically safe quantum gravity might provide a unified description of the fundamental dynamics of quantum gravity and matter. The realization of asymptotic safety, i.e., of scale symmetry at high energies, constraints the possible interactions and dynamics of a system. In this talk, I will first introduce the scenario of asymptotic safety for gravity with matter, and explain how it can be explored using functional methods. I will then emphasize, how the constraints on the microscopic dynamics of matter arising from quantum scale symmetry can turn into constraints on the gravitational dynamics, both by exploring the asymptotically safe fixed-point structure, and by exploring resulting infrared physics.

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Given a semisimple group G and a smooth projective curve X over an algebraically closed field of arbitrary characteristic, let Bun_G(X) denote the moduli space of principal G-bundles over X. For a bundle P without infinitesimal symmetries, we describe the n^th order divided-power infinitesimal jet spaces of Bun_G(X) at P for each n. The description is in terms of differential forms on X^n with logarithmic singularities along the diagonals. Furthermore, we show the pullback of these differential forms to the Fulton-Macpherson compactification space is an isomorphism, thus illustrating a connection between infinitesimal jet spaces of Bun_G(X) and the Lie operad.

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Presented in collaboration with Navigating Quantum and AI Career Trajectories: A Beginner’s Mini-Course on Computational Methods and their Applications

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Deeptech or science-based innovations often spend more than a decade percolating within academic and government labs before their value is recognized (Park et al., 2022). This development lag time prior to venture formation is only partly due to technological development hurdles. Because science-based inventions are often generic in nature (Maine & Garnsey, 2006), meaning that they have broad applicability across many different markets, the problem of identifying a first application requires the confluence of deep technical understanding with expert knowledge of the practice of commercialization. This process of technology-market matching is a critical aspect of the translation of science-based research out of the lab (Pokrajak 2021, Gruber and Tal, 2017; Thomas et al, 2020, Maine et al, 2015) and is often delayed by a lack of capacity to identify, prioritize and protect market opportunities. Typically, deeptech innovations can take 10-15 years of development, and tens (or even hundreds) of millions of dollars of investment to de-risk before a first commercial application (Maine & Seegopaul, 2016). Academics seeking to commercialize such inventions face the daunting challenge of competing for investment dollars in markets that are ill suited to the uncertainty and timescales of deep tech development. The time-money uncertainty challenge faced by science-based innovators is compounded by the fact that most of the scientists and engineers with the world-leading technical skills required to develop science-based inventions, lack innovation skills training, and so cannot navigate the complexities of early and pre-commercialization development critical to venture success. Some researchers, having developed a mix of technical and business expertise, have demonstrated a long-term ability to serially spin out successful ventures (Thomas et al., 2020). Entrepreneurial capabilities, which can be learned, enable scientistentrepreneurs to play formative roles in commercialising lab-based scientific inventions through the formation of well-endowed university spin-offs. (Park et al, 2022; 2024). Commercialization postdocs, when supported by well designed training, stipends, and de-risking supports, can lead the mobilization of fundamental research along multiple commercialization pathways. Recommendations are provided for scholars, practitioners, and policymakers to more effectively commercialise deeptech inventions.

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