Scientific Series

I will explore subtle aspects of rank-one 4d N=2 supersymmetric QFTs through their low-energy Coulomb-branch physics. The low-energy Lagrangian is famously encoded in "the Seiberg-Witten (SW) curve", which is a one-parameter family of elliptic curves. Here I will explain precisely how "global" aspects of the SQFT such as its spectrum of lines, which cannot be read off from the Lagrangian, are encoded into the SW curve -- more precisely, how they are encoded in its Mordell-Weil group of rational sections. In particular, I will
discuss in detail the difference between the pure SU(2) and the pure SO(3) N=2 SYM theories from this low-energy perspective. I will also comment on the global forms of rank-one 5d SCFTs compactified on a circle.

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Zoom link https://pitp.zoom.us/j/94967350368?pwd=SHZZUnZNL3ZveFc3NElCaVc5YkY3Zz09

Deep learning (DL) methods have demonstrated great potential for extracting rich non-linear information from cosmological fields, a challenge that traditional summary statistics struggle to address. Most of these DL methods are discriminative models, i.e., they directly learn the posterior constraints of cosmological parameters. In this talk, I will make the argument that learning the field-level likelihood function using generative modeling approaches such as Normalizing Flows usually leads to more effective extraction of cosmological information. This approach also enables anomaly detection to improve the robustness of the analysis. To scale the modeling to high dimensional data and improve its generalization capabilities, we further incorporate physical inductive biases, such as symmetries and multiscale structure, into the architecture of the normalizing flow models. On mock weak lensing maps, I will show that the model leads to significant improvement in constraining power compared to power spectrum and alternative DL models. I will also show that it is able to detect domain shifts between training simulations and test data, such as noise miscalibration and baryonic effect, which, if left unaddressed, could introduce systematic biases in parameter constraints. Finally, I will talk about our ongoing work on applying this model to the field-level cosmic shear analysis for HSC.

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Zoom link https://pitp.zoom.us/j/97478701784?pwd=UVg4TVp1WFArcXNETG5ITGd0S0NuZz09

It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extraordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extraordinary and special fixed points when d = 3 and N is greater or equal to 2. I'll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I'll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models.

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Zoom link https://pitp.zoom.us/j/97209122334?pwd=UHQ2OXR4bnVZREV0SlJOYXphWjh0QT09

Uncertainty relations are a familiar part of any introductory quantum mechanics course. In this talk, I will summarize how uncertainty relations have been re-interpreted and re-expressed in the language of information theory, leading to connections with the geometry of quantum state space and the limits of computational and information processing efficiency. As two particular examples, I will discuss how uncertainty relations allow one to design information-theoretically optimal measurement protocols for function estimation in networks of quantum sensors and how they enable one to bound the speed at which analog quantum computers can possibly perform optimization tasks. Based primarily on arXiv:2110.07613 and arXiv:2210.15687. 

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Zoom link https://pitp.zoom.us/j/98258695315?pwd=Q2pEcmg5MGhLWmFlR1FPako0NVFlQT09

Symmetric mass generation (SMG) is a novel interaction-driven mechanism that generates fermion mass without breaking symmetry, unlike the standard Anderson-Higgs mechanism. SMG can occur in the fermion system without quantum anomalies. In this talk, I will focus on the SMG for the systems with finite fermion density, i.e., the Fermi surface. I will discuss the Fermi surface anomaly and Fermi surface SMG. Lastly, I will talk about its application in the newly found nickelate superconductors, where the superconductivity emerges without a nearby spontaneous symmetry-breaking phase.

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Zoom link https://pitp.zoom.us/j/92511977879?pwd=MGgyZ0tsZ0hUZDMvZ2wzc3hJVmprZz09

Isometric tensor networks (isoTNS) form a subclass of tensor network states that have an additional isometric condition, which implies that they can be efficiently prepared with a linear-depth quantum circuit. In this work, we introduce a procedure to construct isoTNS encoding of certain 2D classical partition functions. By continuously tuning a parameter in the isoTNS, the many-body ground state undergoes quantum phase transitions, exhibiting distinct 2D topological order. We illustrate this by constructing an isoTNS path with bond dimension $D = 2$ interpolating between distinct symmetry-enriched topological (SET) phases. At the transition point, the isoTNS wavefunction is related to a gapless point in the classical six-vertex model. Furthermore, the critical wavefunction supports a power-law correlation along one spatial direction while remains long-range ordered in the other spatial direction. We provide an exact linear-depth parametrized local quantum circuit that realizes the path. The above features can therefore be efficiently realized on a programmable quantum device. In the second part of my talk, I will show how to discover efficiently measurable order parameters for quantum phases using model-independent training of quantum circuit classifiers. The possibility of the efficient realization of phase transition path is useful for benchmarking quantum phase recognition methods in higher than one dimension.

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Zoom link https://pitp.zoom.us/j/93183360141?pwd=RVdYeUxUbE1aZ1dUbzRSL3lBb0lHZz09

Counting partitions in diverse dimensions is a long-standing problem in enumerative combinatorics. It also plays a prominent role in the physics of instanton counting and in algebraic geometry through the computation of Donaldson-Thomas invariants. In this talk I will give an overview of these counting problems, and discuss how recent developments in the computation of instanton/Donaldson-Thomas partition functions clarify some open problems in the enumeration of higher-dimensional partitions.

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Zoom link https://pitp.zoom.us/j/92547375606?pwd=VDBiTTV6QjBtWThnSjJPc0phVEI1dz09

According to the Belinski-Khalatnikov-Lifshitz conjecture, the Bianchi IX spacetime describes the evolution of each spatial point close to a generic spacelike singularity. However, near the singularity, quantum effects are expected to be relevant. Therefore, in this work a quantum analysis of the model is performed, mainly focusing on its chaotic nature. Considering some minimal approximations, it is possible to encode all the information of the quantum degrees of freedom in certain canonical variables, expanding thus the classical phase space. In this way, we can apply the usual methods of dynamical systems for studying chaos. In particular, two techniques are considered. On the one hand, an analytical study is carried out, which provides an isomorphism between the quantum dynamics of Bianchi IX and the geodesic flow on a Riemannian manifold. On the other hand, by means of numerical simulations, the fractal dimension of the boundary between points with different outcome in the space of initial data is studied. The main conclusion is that, although the quantum system is chaotic, the quantum effects considerably reduce this behavior as compared to its classical counterpart.

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Zoom link https://pitp.zoom.us/j/91559466008?pwd=UzQvTGRkR3VQWm9MWDlaaVAyNi9EQT09

I will discuss an explicit way to construct Hopf algebras and quasi-triangular Hopf algebras (their Drinfeld doubles) within 3d TQFT, using extended operators on boundary conditions -- dubbed `spark' algebras. The representation categories of these algebras capture boundary and bulk line operators. Overall, the construction realizes Tannakian duality geometrically; in perturbative TQFT's, it is closely connected to the holographic Koszul duality of Costello and Paquette. I'll illustrate the construction for Dijkgraaf-Witten theory (a.k.a. gauge theory with finite gauge group), and then sketch an application to the B-type topological twist of 3d N=4 gauge theories, which initially motivated these investigations. (Work in progress with T. Creutzig and W. Niu.)

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Zoom link https://pitp.zoom.us/j/93746215441?pwd=YjdhaDNFeko3VDVKQW5ZV1MzL1cvUT09

Entanglement renormalization circuits are quantum circuits that can be used to prepare large-scale entangled states. For years, it has remained a mystery whether there exist scale-invariant entanglement renormalization circuits for chiral topological order. In this paper, we solve this problem by demonstrating entanglement renormalization circuits for a wide class of chiral topologically ordered states, including a state sharing the same topological properties as Laughlin's bosonic fractional quantum Hall state at filling fraction 1/4 and eight states with Ising-like non-Abelian fusion rules. The key idea is to build entanglement renormalization circuits by interleaving the conventional multi-scale entanglement renormalization ansatz (MERA) circuit (made of spatially local gates) with quasi-local evolution. Given the miraculous power of this circuit to prepare a wide range of chiral topologically ordered states, we refer to these circuits as MERA with quasi-local evolution (MERAQLE).\

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Zoom link https://pitp.zoom.us/j/98523529456?pwd=dUlNbUQyemZGNFlCUGFJNStPU0xxdz09

In the quest to understand the fundamental structure of spacetime (and subsystems) in quantum gravity, it may be worth exploring the ultimate consequences of non-perturbative canonical quantization, carefully taking into account the constraints and gauge invariance of general relativity. As the reduced phase space (or even the pre-phase space) of gravity lacks a natural linear structure, a generalization of the standard method of quantization (based on global conjugate coordinates) is required. One such generalization is Isham's method based on transitive groups of symplectomorphisms, which we test in some simple examples. In particular, considering a particle that lives on a sphere, in the presence of a magnetic monopole flux, we algebraically recover Dirac's charge quantization condition from a "Casimir matching principle", which we propose as an important tool in selecting natural representations. Finally, we develop the non-perturbative reduced phase space quantization of causal diamonds in (2+1)-dimensional gravity. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$. Applying Isham's quantization we find that the Hilbert space of the associated quantum theory carries a (projective) irreducible unitary representation of the $BMS_3$ group. From the Casimir matching principle, we show that the states are realized as wavefunctions on the configuration space with internal indices in unitary irreps of $SL(2, \mathbb{R})$. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the boundary length.

Papers on quantization of causal diamonds:
https://arxiv.org/abs/2308.11741
https://arxiv.org/abs/2310.03100

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Zoom link https://pitp.zoom.us/j/98636934234?pwd=THBCcFpYWHYzWmY0YjViY3Q1a3VYdz09

To perform reliable quantum computations in the midst of noise from the environment, it is imperative to use a quantum error-correcting code — i.e., a scheme for redundantly encoding information so that errors may be detected and corrected as they occur. One of the most promising classes of quantum error-correcting codes are those based on topological phases of matter, such as the celebrated toric code. Although there is a rich classification of topological phases of matter, the toric code has by far received the most attention as a practical quantum error-correcting code, due to its simple representation within the stabilizer formalism.

In this talk, I will discuss three works in which we extend the stabilizer formalism to topological orders beyond that of the toric code. This includes the construction of two-dimensional stabilizer codes characterized by Abelian topological orders with gapped boundaries, three-dimensional stabilizer codes that host arbitrary two-dimensional Abelian topological orders on their surface, and two-dimensional subsystem codes also characterized by arbitrary Abelian topological orders. This work thus opens the door to encoding and processing quantum information using the exotic properties exhibited by the wide range of Abelian topological phases of matter.

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Zoom link https://pitp.zoom.us/j/94640905425?pwd=aDd0Qnl1TUU0QytaNWJJLzEyZlQrQT09