Scientific Series

The concept of symmetries is crucial in our comprehension of modern theoretical physics. The Corner Proposal introduces a novel framework where symmetries are reinstated as foundational principles in our understanding of gravity. This aims to describe gravity using a language that is more adapted to quantization. In this presentation, I will start by providing an overview of the essential results leading to the main ideas the proposal. This will then allow me to state the proposal in the general case to then specialize to 1+1 dimensional gravity.

Finally, I will present elements of our recent research applying the proposal to the case of 1+1 dimensional gravity. I will demonstrate the framework's promising potential by calculating the entanglement entropy between two spatial regions—a significant challenge in quantum gravity. The result is the 1+1 dimensional equivalent of the well-established Bekenstein-Hawking area law governing the entropy of gravitational systems with the expected behavior of the quantum corrections.

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This colloquium is presented in collaboration with the Foundations of Quantum Computational Advantage conference. 

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Abstract TBA

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Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons theory and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons theory in 6 dimensions. In this talk I will introduce the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. The talk is based on the recent work https://arxiv.org/abs/2311.17551.

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Ground states as well as Gibbs states of many-body quantum Hamiltonians have been studied extensively since the inception of quantum mechanics. In contrast, the landscape of many-body quantum states that are not in thermal equilibrium is relatively less explored. In this talk I will discuss some of the recent progress in understanding decohered or dissipative quantum many-body states. One of the key ideas I will employ is that of "separability", i.e., whether a mixed state can be expressed as an ensemble of short-range entangled pure states. I will discuss several quantum phase transitions in topological phases of matter subjected to Markovian environmental noise from a separability viewpoint, and argue that such a framework also subsumes our understanding of pure quantum states as well as Gibbs states. Time permitting, I will also provide a brief overview of quantum spin-systems subjected to non-Markovian noise originating from an electronic bath, and discuss a new critical phase of matter where quantum coherence coexists with dissipation.

References: 2307.13889, 2309.11879, 2310.07286

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Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to implement QEC is one of the most pressing challenges that will facilitate a transition from NISQ to the fault tolerance era. In this talk, I will discuss two intriguing ideas that can significantly reduce these overheads. The first idea, erasure qubits, relies on an efficient conversion of the dominant noise into erasure errors at known locations, greatly enhancing the performance of QEC protocols. The second idea, single-shot QEC, guarantees that even in the presence of measurement errors one can perform reliable QEC without repeating measurements, incurring only constant time overhead.

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"Null Polygons" in N=4 SYM theory describe the multi-point correlators of 1/2-BPS local operators with large R-charge, when they approach the vertices of a light-like polygon. The leading UV divergences of null polygons is conjectured to satisfy a hierarchy of coupled Toda field theory equations [E.O., Vieira ’22]. I will present some progress towards the prediction of Null Polygons beyond leading logarithms via the hexagons technique, appropriately truncated in the light-cone regime. The method, still conjectural, relies on a series of weak-coupling derivations performed in the Fishnet limit of the theory, where the hexagon representation is derived in the basis of eigenfunctions of a conformal Heisenberg magnet in the principal series. I will present a number of worked-out examples for multi-point multi-loop Fishnet Feynman integrals and Null Polygons.

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The dynamics of closed quantum systems undergoing unitary processes has been well studied, leading to notions of measures for the expressive power of parameterized quantum circuits, relative to the unique, maximally expressive, average behaviour of ensembles of unitaries. Such unitary expressivity measures have further been linked to concentration phenomena known as barren plateaus. However, existing quantum hardware are not isolated from their noisy environment, and such non-unitary dynamics must therefore be described by more general trace-preserving operations. To account for hardware noise, we propose several, non-unique measures of expressivity for quantum channels and study their properties, highlighting how average non-unitary channels differ from average unitary channels. In the limit of large composite system and environments, average noisy quantum channels are shown to be maximally globally depolarizing. Furthermore, we rigorously prove that highly-expressive parameterized quantum channels will suffer from barren plateaus, thus generalizing explanations of noise-induced phenomena. We complement our analytical findings with numerical experiments that showcase that, in certain situations, noise can increase the expressivity of parametrized quantum circuits.

Strongly coupled confining theories are well-motivated in many BSM frameworks. The early universe cosmological history of these theories provides possibilities for observable signals. These theories undergo confinement deconfinement phase transition in the early universe, which can result in gravitational wave signals, observable in upcoming experiments. Using AdS/CFT, these theories have been studied in the Randall-Sundrum framework, and various quantitative aspects of the phase transition have been calculated. In the models that have been considered, the rate of transition from the deconfined phase to the confined phase is very small and leads to a period of supercooling. This enhances the gravitational wave signal, but presents a tension between a low confinement scale and fitting to the standard picture of BBN. In this talk, I will briefly review the calculations leading to these conclusions, and argue that some of the issues are specific to the simplified models that have been studied. I will present two modifications that are expected on general grounds, motivated by including strong IR effects systematically. Such effects change the results significantly. In particular, new qualitative features appear which have been missed in previous investigations. I will briefly comment on the phenomenological implications and open questions. The talk will be based on 2309.10090 and 2401.09633.

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Fueling and feedback couple supermassive black holes (SMBHs) to their host galaxies across many orders of magnitude in spatial and temporal scales, making this problem notoriously challenging to simulate. We use a multi-zone computational method based on the general relativistic magneto-hydrodynamic (GRMHD) code KHARMA that allows us to span 7 orders of magnitude in spatial scale, to simulate accretion onto a non-spinning SMBH from an external medium with Bondi radius ~ 2e5 G*M/c^2, where M is the SMBH mass. For the classic idealized Bondi problem, spherical gas accretion without magnetic fields, our simulation results agree very well with the general relativistic analytic solution. Meanwhile, when the accreting gas is magnetized, the SMBH magnetosphere becomes saturated with a strong magnetic field. The density profile varies as ~ r^(-1) rather than r^(-3/2) and the accretion rate is consequently suppressed by over 2 orders of magnitude below the Bondi rate. We find continuous energy feedback from the accretion flow to the external medium at a level of 1% of the accreted rest mass energy (~ 0.01 Mdot * c^2). Energy transport across these widely disparate scales occurs via turbulent convection triggered by magnetic field reconnection near the SMBH. Thus, strong magnetic fields that accumulate on horizon scales transform the flow dynamics far from the SMBH and naturally explain observed extremely low accretion rates compared to the Bondi rate, as well as at least part of the energy feedback.

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In this talk I will present an update on my work with Ben Gammage and Aaron Mazel-Gee on the 2-categories of boundary conditions in the A and B-twists. In particular I will explain how 2-categorical 3d mirror symmetry decategorifies to the Koszul duality of hypertoric categories O discovered by Braden-Licata-Proudfoot-Webster.

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Information-theoretic insights have proven fruitful in many areas of quantum physics. But can the fundamental dynamics of quantum systems be derived from purely information-theoretic principles, without resorting to Hilbert space structures such as unitary evolution and self-adjoint observables? Here we provide a model where the dynamics originates from a condition of informational non-equilibrium, the deviation of the system’s state from a reference state associated to a field of identically prepared systems. Combining this idea with three basic information-theoretic principles, we derive a notion of energy that captures the main features of energy in quantum theory: it is observable, bounded from below, invariant under time-evolution, in one-to-one correspondence with the generator of the dynamics, and quantitatively related to the speed of state changes. Our results provide an information-theoretic reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions, establishing a bridge between dynamical and information-theoretic notions.

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