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Quantum error correction and symmetries are two key notions in quantum information and physics. The competition between them has fundamental implications in fault-tolerant quantum computing, many-body physics and quantum gravity. We systematically study the competition between quantum error correction and continuous symmetries associated with a quantum code in a quantitative manner. We derive various forms of trade-off relations between the quantum error correction inaccuracy and three types of symmetry violation measures. We introduce two frameworks for understanding and establishing the trade-offs based on the notions of charge fluctuation and gate implementation error. From the perspective of fault-tolerant quantum computing, we demonstrate fundamental limitations on transversal logical gates. We also analyze the behaviors of two near-optimal codes: a parametrized extension of the thermodynamic code, and quantum Reed–Muller codes.

Zoom Link: TBD

This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced.

Topics will include (but are not limited to): - Quantum error correction in quantum gravity and condensed matter - Quantum information scrambling and black hole information - Physics of random tensor networks and random unitary circuits

JT gravity in AdS was shown by Saad, Shenker and Stanford to be described by a matrix ensemble of random hamiltonians. We couple JT to a bulk scalar field and extend the matrix ensemble to include a second matrix, dual to the scalar field. We therefore consider a 2-matrix model that can be thought of as a (better defined) generalization of Eigenstate Thermalization Hypotheses: it is a coupled matrix model of a random hamiltonian and a random operator. The 2-matrix model has an interesting integrability structure: correlation functions are expressed via SL(2,R) 6j-symbols that obey unlacing rules and Yang-Baxter equations. We compute the two-sided 2-point function on the double-trumpet geometry from the matrix model and find agreement with the matter loop contribution in the bulk. Based on work in progress with Jafferis, Kolchmeyer and Sonner.

Zoom Link: https://pitp.zoom.us/j/92268935307?pwd=dytCdTJlWVc3QXkweWxzcy83Sk9PZz09

This course is designed to introduce modern machine learning techniques for studying classical and quantum many-body problems encountered in condensed matter, quantum information, and related fields of physics. Lectures will focus on introducing machine learning algorithms and discussing how they can be applied to solve problem in statistical physics. Tutorials and homework assignments will concentrate on developing programming skills to study the problems presented in lecture.

Does inflation have to happen all in one go? The answer is no!

All cosmological problems can be solved by a sequence of bursts of cosmic acceleration, interrupted by short epochs of decelerated expansion.

In this rollercoaster cosmology, models that seem excluded for a single long stage become viable again, and high-scale inflation is more natural.

At the same time, we expect interesting predictions at several different length scales, such as gravitational wave signals potentially detectable by LISA.

I will describe the general framework, and focus on a realization with two stages of monodromy inflation.

Zoom Link: https://pitp.zoom.us/j/99206384855?pwd=dUpDdWVxV1lXc0g1bU9uZ2lrMzVXUT09

This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced.

Topics will include (but are not limited to): - Quantum error correction in quantum gravity and condensed matter - Quantum information scrambling and black hole information - Physics of random tensor networks and random unitary circuits

We are used to thinking of there being different types of fault-tolerant gates allowing reliable computation on states in a noisy quantum computer: Some are transversal, some involve measurement and magic states, some involve topological manipulations, etc.  In this talk, we will demonstrate that transversal gates can be seen as a topological effect, and we will propose an over-arching framework for thinking about fault tolerance in terms of fiber bundles over the Grassmanian, the manifold of subspaces of Hilbert space.  The violin will harmonize with the chalkboard to put the talk to music.

Zoom Link: https://pitp.zoom.us/j/97600230984?pwd=NDJ4VjdvUS9palA4YzFnZHBwcnJkUT09

This course is designed to introduce modern machine learning techniques for studying classical and quantum many-body problems encountered in condensed matter, quantum information, and related fields of physics. Lectures will focus on introducing machine learning algorithms and discussing how they can be applied to solve problem in statistical physics. Tutorials and homework assignments will concentrate on developing programming skills to study the problems presented in lecture.

Topics will include (but are not limited to): Canonical formulation of constrained systems, The Dirac program, First order formalism of gravity, Loop Quantum Gravity, Spinfoam models, Research at PI and other approaches to quantum gravity.