Scientific Series

A quantum error-correcting code depends on a classical decoding algorithm that uses the outcomes of stabilizer measurements to determine the error that needs to be repaired. Likewise, the design of a decoding algorithm depends on the underlying physics of the quantum error-correcting code that it needs to decode. The surface code, for instance, can make use of the minimum-weight perfect-matching decoding algorithm to pair the defects that are measured by its stabilizers due to its underlying charge parity conservation symmetry. In this talk I will argue that this perspective on decoding gives us a unifying principle to design decoding algorithms for exotic codes, as well as new decoding algorithms that are specialised to the noise that a code will experience. I will describe new decoders for exotic fracton codes we have designed using these principles. I will also discuss how the symmetries of a code change if we focus on restricted noise models, and how we have leveraged this observation to design high-threshold decoders for biased noise models. In addition to these examples, this talk will focus on recent work on decoding the color code, where we found a high-performance decoder by investigating the defect conservation laws at the boundaries of the color code. Remarkably, our results show that we obtain an advantage by decoding this planar quantum error-correcting code by matching defects on a manifold that has the topology of a Moebius strip.

Zoom Link: https://pitp.zoom.us/j/91540245974?pwd=RDkzaVJZZ2tkTldxM2pkdXU5VHlIZz09

Complex and poorly understood astrophysics impacts our ability to constrain cosmological and astrophysical models from the large scale structure. Two major sources of systematic errors are galaxy biasing (non-linear mapping between dark matter and galaxies) and baryonic feedback (impact of supernovae or AGN on LSS). In the first part of my talk, I will describe a hybrid perturbation theory model of galaxy biasing and show its validation at sub-percent accuracy. I will then describe the cosmological constraints obtained using this model on the measurements from the first three years of observations of the Dark Energy Survey (DES). In the second part of my talk, I will describe tomographic measurements and analysis of the cross-correlations between thermal Sunyaev-Zel'dovich (tSZ) effect and gravitational lensing. Using data from ACT, Planck, and DES, we obtain the highest significance (20 sigma) measurements to-date and use them to constrain models for the pressure profiles of halos across a wide range of halo mass and redshift. We find evidence for reduced pressure in low mass halos, consistent with predictions for the effects of increased feedback from AGN. Lastly, we also comment on application of this study to the sigma8 tension and hydrostatic mass bias as inferred from the cluster count analysis.

General relativity does not distinguish a preferred reference frame, and conservatively one ought to expect that its quantization does not necessitate such background structure. However, this desire stands in contrast to orthodox formulations of quantum theory which rely on a background time parameter external to the theory, and in the case of quantum field theory a spacetime foliation. Such considerations have led to the development of the Page-Wootters formalism, which seeks to describe motion relative to a reference frame internal to a quantum theory that encompasses both the system of interest and employed reference frame. I will begin by reviewing a modern formulation of the Page-Wootters formalism in terms of Hamiltonian constraints, generalized coherent states, and covariant time observables. I will then present Kuchar’s criticisms of the Page-Wootters formalism, and discuss their resolution by showing the equivalence between the formalism and relational Dirac observables. These Dirac observables will then be used to introduce a gauge-invariant, relational notion of subsystems and entanglement. Finally, a field-theoretic extension of the Page-Wootters formalism will be introduced and used to recover the Schwinger-Tomonaga equation.

Zoom Link: https://pitp.zoom.us/j/91420728439?pwd=cXlGZ21tTGZEUjFDVjRKMWxaVFlVZz09

Over the past decades, the asymptotic safety scenario has matured into a viable contender for a consistent theory of quantum gravity. However, the pressing question of unitarity is far from being settled. I will present important steps towards tackling this issue and show the first direct computation of the graviton spectral function in asymptotically safe quantum gravity with a novel Lorentzian renormalisation group approach. We find a positive graviton spectral function, showing a massless one-graviton peak and a multi-graviton continuum with an asymptotically safe scaling for large spectral values. For small spectral values, the effective field theory result is approached. I will indicate consequences for scattering amplitudes and unitarity.

Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. Motivated by the expected behavior of wormholes in quantum gravity, Brown and Susskind conjectured that the quantum complexity of the state output by a random circuit on n qubits grows linearly as more and more random gates are applied, until saturating after a number of gates exponential in n. We prove this conjecture by studying the dimension of the set of all unitaries that can be accessed with a given arrangement of two-qubit gates. Our core technical contribution is a lower bound on this dimension, using techniques from algebraic geometry and considerations based on Clifford circuits. In the second part of my talk, I'll discuss some thermodynamic and effective information-theoretic aspects of the complexity of quantum states and its growth in quantum many-body systems, establishing a resource theory to capture a notion of quantum complexity and drawing a connection between the concepts of complexity and entropy.

Joint work with: Jonas Haferkamp, Teja Naga Bhavia Kothakonda, Anthony Munson, Jens Eisert, Nicole Yunger Halpern

Zoom Link: https://pitp.zoom.us/j/94288479163?pwd=Nm8wOUdReGhreDErdUpJTzFETlBUUT09

In this talk I will review work on `decomposition,' a property of 2d theories with 1-form symmetries and, more generally, d-dim'l theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are equivalent to ('decompose into’)  disjoint unions of other QFTs, known in this context as "universes.” Examples include two-dimensional gauge theories and orbifolds with matter invariant under a subgroup of the gauge group. Decomposition explains and relates several physical properties of these theories -- for example, restrictions on allowed instantons arise as a "multiverse interference effect" between contributions from constituent universes. First worked out in 2006 as part of efforts to understand string propagation on stacks, decomposition has been the driver of a number of developments since. In the first half of this talk, I will review decomposition; in the second half, I will focus on the recent application to anomaly resolution of Wang-Wen-Witten in two-dimensional orbifolds.

Quantum metrology, which studies parameter estimation in quantum systems, has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on the estimation precision, called the Heisenberg limit, which is achievable in noiseless quantum systems, but is in general not achievable in noisy systems. This talk is a summary of some recent works by the speaker and collaborators on error-corrected quantum metrology. Specifically, we present a necessary and sufficient condition for achieving the Heisenberg limit in noisy quantum systems. When the condition is satisfied, the Heisenberg limit is recovered by a quantum error correction protocol which corrects all noises while maintaining the signal; when it is violated, we show the estimation limit still in general has a constant factor improvement over classical strategies, and is achievable using approximate quantum error correction. Both error correction protocols can be optimized using semidefinite programs. Examples in some typical noisy systems will be provided.

Zoom Link: https://pitp.zoom.us/j/95698542740?pwd=OWJtcTViKzZqNDg1bWk4cDFtaTRxZz09

We expect certain universal results in classical gravity to come unaltered from a quantum theory of gravity. In this talk, I will firstly discuss new ideas on this topic, and the latest understanding we have on this, in an accessible way. After that, I will focus on local symmetries in gravity, and obtain the most general off-shell algebra of diffeomorphisms that acts non-trivially at corners, where gauge charges are supported. Noether charges in Einstein gravity are then shown to generate a faithful representation of this algebra. After pausing and reviewing the covariant phase space formulation, explaining the questions and issues our community faced in successfully applying it to gravity, I will show how a careful treatment of embeddings allows us to establish a field space where Noether charges act canonically via Poisson bracket. This solves a longstanding puzzle in this field, opening doors to new promising investigations. I will conclude by mentioning them and commenting on how new proposals might shed light on old unanswered questions in quantum gravity.

Zoom Link: https://pitp.zoom.us/j/96552295909?pwd=cFZwcGxLdWlaWWhRS21RMExUd1RjQT09

In this talk I will give an overview of recent and ongoing work regarding rotating black holes in dynamical Chern-Simons (dCS) gravity. dCS gravity is a well motivated modified theory of gravity which has been extensively studied in gravitational and cosmological contexts. I will first discuss unique geometric structures, `the Chern-Simons caps,' which slowly rotating black holes in dCS gravity were recently found to possess. Motivated by the dCS caps, I will then discuss superradiance in the context of slowly rotating dCS black holes and show that there are corrections to the usual solution for a Kerr black hole. Lastly, I will comment on the observable implications for these corrections and point towards avenues for future work.

Zoom Link: https://pitp.zoom.us/j/95228483630?pwd=dWk1c3p5dUU3RXJrNEhIT2M3Tk1Kdz09

I will review the history of anyons, particles that are neither bosons nor fermions, starting with their theoretical proposal all the way to their definitive experimental observation over 40 years later.  I will further discuss why the more general idea of non-abelian anyons is of intense interest for quantum computation.  If time permits I will give a status report on some of the current non-abelian anyon experiments.

Zoom Link: https://pitp.zoom.us/j/98698779123?pwd=SWIyak9OZ0dud2ZGcWdoazdkVURHQT09