Scientific Series

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

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

We investigate the nature of the Giddings-Strominger wormhole in axion gravity, whose stability remains contested despite previous work in this direction. Unlike what is done in these works, we follow a Lorentzian approach which directly addresses the factorization problem. To probe the thermodynamic stability of wormholes in the gravitational path integral, we look for fixed-area saddle points. However, taking care to choose the appropriate boundary conditions, we find that there are no fixed-area axion wormholes in Lorentzian signature. We then discuss how we could go beyond this analysis, considering off-shell axion wormhole configurations with fixed-length.

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Zoom link https://pitp.zoom.us/j/98119789932?pwd=N1RCanJCdk56eWJ3RHJCRG5KU21lQT09

Abstract TBA

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Zoom link https://pitp.zoom.us/j/96982969023?pwd=MjgzaU5mZUVuV3pNVG11dHM2WUd4UT09

Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must be gauge symmetries. In particular this includes CRT symmetry (in even
dimensions usually combined with a rotation to become CPT), which in quantum field theory is always a symmetry and seems likely to be a symmetry of quantum gravity as well. I'll discuss what it means to gauge a spacetime inversion symmetry, and explain some of the more unusual consequences of doing this. In particular I'll argue that the gauging of CRT is automatically implemented by the sum over topologies in the Euclidean gravity path integral, that in a closed universe the Hilbert space of quantum gravity must be a real vector space, and that in Lorentzian signature manifolds which are not time-orientable must be included as valid configurations of the theory.

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Zoom link https://pitp.zoom.us/j/98089579253?pwd=NDBhUjBUTTEwT0R5YmhYVElZenJtZz09

Major improvements in the theoretical aspects of Cosmology have been possible in recent years due to QFT-inspired methods, such as the effective field theory of large-scale structure (EFTofLSS). In this talk, I will explore further connections between high-energy physics and cosmology. I will present a systematic approach to renormalizing the galaxy bias parameters using path integrals and a finite cutoff scale Λ. I will derive the differential equations of the Wilson-Polchinski renormalization group that describe the evolution of the finite-scale bias parameters with Λ, analogous to the β-function running in QFT. I will then discuss how the RG-flow of EFTofLSS can lead to improvements in the extraction of cosmological parameters and also serve as a tool for sanity checks.

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Zoom link https://pitp.zoom.us/j/93248279658?pwd=Z1M1UnI3eVh3NTZ3NCt4NUtGaW5idz09

Quantum error-correcting codes are a key pillar of quantum computing. They allow for the recovery of quantum information in the presence of noise. There are three main ways to depict a quantum code: by the list of codewords, by an encoding circuit, or by a stabilizer tableau. Although the latter is used most often, all three of these have pros and cons. In this talk, I will showcase ZX calculus, a graphical language that can be used to talk about quantum states, circuits, measurements, and importantly, codes. I will demonstrate its power and versatility and showcase a canonical form for states, circuits, and codes. The power of this theorem allows us to compile these quantum objects to a unique, elegant, and simple form which serves as a much better depiction than any of the three methods above.

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Zoom link https://pitp.zoom.us/j/91431057660?pwd=cW9xKzNXejdIekp3amFacFZ5OHN5dz09

We develop the theory of quantum scars for quantum fields. By generalizing the formalisms of Heller and Bogomolny from few-body quantum mechanics to quantum fields, we find that unstable periodic classical solutions of the field equations imprint themselves in a precise manner on bands of energy eigenfunctions. This indicates a breakdown of thermalization at certain energy scales, in a manner that can be characterized via semiclassics. As an explicit example, we consider time-periodic non-topological solitons in complex scalar field theories. We find that an unstable variant of Q-balls, called Q-clouds, induce quantum scars. Some technical contributions of our work include methods for characterizing moduli spaces of periodic orbits in field theories, which are essential for formulating our quantum scar formula. We further discuss potential connections with quantum many-body scars in Rydberg atom arrays. Based on work in arXiv:2212.01637 with Jordan Cotler.

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Zoom link https://pitp.zoom.us/j/91572728134?pwd=Q0Jzb0lwQW5VU0ptRnRWL2tOTTdLdz09

Frustrated quantum magnets provide a promising platform for realizing exotic phase transitions known as deconfined quantum critical points (DQCPs), where a conventional Landau-Ginzburg description fails and the resulting description involves emergent gauge fields. In the first part of my talk, I will propose a unified theory for describing a pair of continuous phase transitions numerically observed in the frustrated square lattice Heisenberg antiferromagnet, where a spin liquid phase appears to emerge in between Neel and valence bond solid (VBS) phases. The proposed DQCPs exhibit a plethora of unconventional phenomena, including anisotropic fixed points and dangerously irrelevant perturbations. In the second part of my talk, I will describe recent work analyzing an effective model of triangular lattice antiferromagnetism which supports coplanar magnetic order as well as VBS and spin liquid phases. We show that this effective model is sign-problem-free and amenable to large-scale Monte Carlo simulations, which reveal a direct transition between magnetic and VBS phases.

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Zoom link https://pitp.zoom.us/j/98562300020?pwd=OXYrL0dJTGkzNk5memlVM0tqY3hNQT09

Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas. We provide a simplifying perspective onto convolutions through tensor networks (TNs) which allow reasoning about the underlying tensor multiplications by drawing diagrams, and manipulating them to perform function transformations and sub-tensor access. We demonstrate this expressive power by deriving the diagrams of various autodiff operations and popular approximations of second-order information with full hyper-parameter support, batching, channel groups, and generalization to arbitrary convolution dimensions. Further, we provide convolution-specific transformations based on the connectivity pattern which allow to re-wire and simplify diagrams before evaluation. Finally, we probe computational performance, relying on established machinery for efficient TN contraction. Our TN implementation speeds up a recently-proposed KFAC variant up to 4.5x and enables new hardware-efficient tensor dropout for approximate backpropagation.

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Zoom link https://pitp.zoom.us/j/99090845943?pwd=NHBNVTNnbDNSOGNSVzNGS21xcllFdz09

Recently, models with different properties have been proposed for polymerized dust collapse and regular black holes. To fully understand their properties and differences, we provide a systematic procedure to construct effective polymerized spherically symmetric models encoding holonomy corrections as $1+1$d field theory from effective regular cosmological dynamics or stationary effective metrics. We apply this formalism and consider models that have the following advantages: The effective dynamics can be derived from a class of extended mimetic gravity Lagrangians in 4 dimensions. The models admit a consistent Lemaitre-Tolman-Bondi (LTB) condition, by which the dynamics is completely decoupled along the radial direction in LTB coordinates, trivializing the junction condition in dust collapse. The class of effective dynamics admits a polymerized Birkhoff-like theorem, which leads to a stationary effective metric in the polymerized vacuum. The effective dynamics can reproduce known regular black hole solutions, including Bardeen and Hayward, by a suitable choice of holonomy corrections. As a concrete example, we construct an effective model compatible with the improved dynamics of loop quantum cosmology in the decoupled LTB sector. We compare it with several effective polymerized models recently introduced in the context of loop quantum gravity and gain some new insights into the presence of shocks.

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Zoom link https://pitp.zoom.us/j/99966795418?pwd=Ty9mRXNML3NsUXdvcU1WUTdCaWpVZz09

Extreme mass-ratio binary black hole systems, known as EMRIs, are expected to radiate low-frequency gravitational waves detectable by planned space-based Laser Interferometer Space Antenna (LISA). We hope to use these systems to probe black hole spacetimes in exquisite detail and make precision measurements of supermassive black hole properties. Accurate models using general relativistic perturbation theory will allow us to unlock the potential of these unique systems. Such models must include post-geodesic corrections, which account for forces driving the smaller black hole away from a geodesic trajectory. When a spinning body orbits a black hole, its spin couples to the curvature of the background spacetime, introducing post-geodesic correction called the spin-curvature force. In this talk, I will present our calculation of EMRI waveforms that include both spin-curvature forces and the leading backreaction due to gravitational radiation. We use a near-identity transformation to eliminate dependence on the orbital phases, allowing for very fast computation of completely generic worldlines of spinning bodies; such efficiency is crucial for LISA data analysis. Finally, I will discuss what aspects still need to be included in future calculations so that we can use EMRIs for a new era of precision gravitational-wave astronomy, addressing outstanding puzzles in astrophysics, cosmology and fundamental theoretical physics.

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Zoom link https://pitp.zoom.us/j/91917788358?pwd=MWp5OUhxbkRmZDFxWWE4cHR0VlBTUT09