Scientific Series

The asymptotic theory of quantum channel estimation has been well established, but in general noiseless and controllable ancilla is required for attaining the ultimate limit in the asymptotic regime. Little is known about the metrological performance without noiseless ancilla, which is more relevant in practical circumstances. In this work, we present a novel theoretical framework to address this problem, bridging quantum metrology and the asymptotic theory of quantum channels. Leveraging this framework, we prove sufficient conditions for achieving the Heisenberg limit with repeated application of the channel to estimate, both with and without applying interleaved unitary control operations. For the latter case, we design an algorithm to identify the control operation. Finally, we analyze several intriguing examples by our approach.

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Determining the long-range phase of matter of a strongly coupled system from its microscopic description has long been one of the central topics in physics. Simple microscopic systems often become strongly coupled at long range where we usually rely on clever approximations. Bootstrap is an alternative approach that uses positivity and equations of motion to make predictions in quantum many-body systems without making approximations. In this talk, I will show my recent work on using bootstrap to compute the ground state energy, local observables and gaps of a quantum many-body system in the thermodynamic limit with rigorous error bars.

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A cosmological network of axion strings in our Universe today may leave its imprint on the polarization pattern of the cosmic microwave background radiation through the phenomenon of axion-string-induced birefringence. I will explain how this signal arises, discuss how it depends on the properties of the string network and the axion-photon coupling, describe how existing measurements of anisotropic birefringence place constraints on axion strings, and discuss how the non-Gaussian nature of this signal could be leveraged in searches with future data.

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Elucidating the nature of dark matter, dark energy, and dynamics of the early universe stand as major challenges of modern cosmology and particle physics. I will present a new program of addressing these challenges with galaxy surveys. This program builds on theoretical particle physics tools and allows for sub-percent precision analytic understanding of galaxy clustering on large scales. I will share some results of this program that include new measurements of fundamental cosmological parameters and constraints on new physics beyond the standard models of particles and cosmology.

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Gravity creates space-time boundaries that limit observables without limiting the flow of energy and information. This means that quantum systems in cosmology are often open systems: to describe them we must include the effects of interaction with an unobservable environment. In many cosmological settings, different observers see different parts of the spacetime; the ensemble of the open systems for each observer makes up the full cosmology. In this talk I will introduce a class of out-of-equilibrium quantum systems constructed to mimic some key features of cosmology and demonstrate the utility of treating the full system as an ensemble of open systems. I will use these models to illustrate the possible connections between cosmological open quantum systems and thermodynamics, as well as open-systems-inspired ways to think about locality.

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Many quantum platforms naturally host Hamiltonians with power-law or even all-to-all connectivity, which may potentially process quantum information in a way much faster than conventional gate-based models. For such non-geometrically-local Hamiltonians, it is then important to both come up with fast protocols and understand the ultimate limit for realizing various information processing tasks. In this talk, I will first overview this quantum speed limit topic, and then dive into the particular task of quantum routing, i.e. permuting unknown quantum states on the qubits. I aim to show [1] a provably optimal Hamiltonian routing protocol on the star graph that is asymptotically faster than gate-based routing; [2] a lower bound on the time to realize the shift unitary using 1d power-law interactions which, perhaps surprisingly, can be much slower than the time for the conventional Lieb-Robinson light cone to spread across the whole system. The latter result shares interesting connections to the classification of 1d quantum cellular automata and symmetry-protected topological order.

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In this presentation, I will discuss our latest efforts to classify and characterize insulators in two spatial dimensions in the presence of interactions. I will focus on two examples, both on the square lattice. The first example is of bosonic insulators with symmetry G = p4m x K, where K is an internal symmetry group taken to be U(1), SO(3) or Z_N. The second example is of fermionic insulators with G= p4 x U(1)^f. In both scenarios, we propose a set of invariants that reproduce the classification anticipated through real space constructions and topological field theory (TFT). In doing so, we relate these invariants to coefficients appearing in the response action obtained from TFT. For the fermionic case, we propose a map from the non-interacting classification to the interacting classification.

This talk is based on work done with Naren Manjunath and Maissam Barkeshli.

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Ultra-cold Fermi gases exhibit a rich array of quantum mechanical properties, including the transition from a fermionic superfluid Bardeen-Cooper-Schrieffer (BCS) state to a bosonic superfluid Bose-Einstein condensate (BEC), which can be precisely probed experimentally. However, accurately describing these properties poses significant theoretical challenges due to strong pairing correlations and non-perturbative interactions. In this talk, I will discuss our recent development—a Pfaffian-Jastrow neural-network quantum state equipped with a message-passing architecture, designed to efficiently capture pairing and backflow correlations. We benchmark our approach against existing Slater-Jastrow frameworks and state-of-the-art diffusion Monte Carlo methods. Analysis of pair distribution functions and pairing gaps reveals the emergence of strong pairing correlations around unitarity. We demonstrate that transfer learning stabilizes the training process in the presence of strong, short-ranged interactions, allowing for an effective exploration of the BCS-BEC crossover region. Our findings highlight the potential of neural-network quantum states as a promising strategy for investigating ultra-cold Fermi gases.

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Extended BMS symmetry is believed to be a fundamental symmetry of any classical gravitational scattering process, as well as of the quantum gravity S-matrix. We explore this property using the BRST formulation of BMS symmetry, which allows to construct a non trivial solution of the Wess-Zumino consistency condition at the null boundaries of spacetime. We interpret this solution as an anomaly for asymptotic BRST Ward identities for superrotations. By relating them to the leading and subleading soft graviton theorem, we recover the well known results that the leading soft theorem is exact at all loop in perturbation theory without ever referring to Feynman diagrams, while the anomaly for superrotations is at the origin of the 1-loop correction to the subleading soft factor. This construction provides a rigorous, fully quantum origin for the invariance of the S-matrix under asymptotic symmetries.

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Recent horizon-scale images of Messier 87* and Sagittarius A* have been used to demonstrate that their spacetimes are well-described by the Kerr metric. The latter is a solution to the vacuum Einstein equations of general relativity, and is used to describe spinning black holes. While of fundamental importance, it has undesirable features such as a spacetime singularity or a Cauchy horizon. To find phenomenological resolutions of such features, using observations, studies of astrophysical processes in non-Kerr spacetimes have recently gained prominence. We will begin by briefly reviewing the current status of observational constraints on such alternatives. We will then demonstrate how future observations of the "photon ring" can grant access to new observables that will refine our physical understanding of strong-gravity. We will end by sketching how, using state-of-the-art numerical simulations, the energetics of relativistic outflows (jets) is universally described by a simple electromagnetic Penrose process (the Blandford-Znajek mechanism).

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The prototypical example of a symmetric tensor category is Rep(G) for G a compact group. The other main source of symmetric tensor categories are Deligne's interpolation categories (S_t, GL_t, and O_t) which extend a family of group representation categories defined at positive integers to all complex numbers. Harman and Snowden have developed a theory of symmetric tensor categories coming from Oligomorphic permutation groups together with a well-behaved measure on G-sets. This includes Deligne's S_t which comes from the infinite symmetric group together with a measure where the usual permutation G-set has volume t. The simplest new example of their theory is the group of order-preserving bijections of the real line with the measure given by Euler characteristic. In joint work with Harman and Snowden (arXiv:2211.15392) we give a detailed description of this new symmetric tensor category, which has a number of novel properties. We call this category the Delannoy category because the dimensions of Hom spaces are given by Delannoy numbers. In this talk I'll outline our main results, including the classification of simple objects, the tensor product rules, and a combinatorial model for the category using Delannoy paths.

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