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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