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Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing using no or few additional quantum resources, in contrast to fault-tolerant schemes that come along with heavy overheads. Error mitigation has been successfully applied to reduce noise in near-term applications. 

In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively `undone' for larger system sizes. We set up a framework that rigorously captures large classes of error mitigation schemes in use today. The core of our argument combines fundamental limits of statistical inference with a construction of families of random circuits that are highly sensitive to noise.

We show that even at poly loglog depth, a super-polynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. They also impact other near-term applications, constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.

Zoom link:  https://pitp.zoom.us/j/95736148335?pwd=akZLaHE5aStNQVZOeVFETlltNzVwdz09

I will use the S-matrix Bootstrap to carve out the space of unitary, crossing symmetric, and supersymmetric graviton scattering amplitudes in nine, ten, and eleven dimensions. I will introduce a novel extension of positivity for massless particles beyond the forward limit called “positivity in the sky” that significantly improves the convergence of the bootstrap algorithm.

I will show the bounds on the first leading correction to maximal supergravity, study the physics of the extremal amplitudes and compare them with the available nonperturbative String and M-theory results.

Zoom link:  https://pitp.zoom.us/j/99182927406?pwd=bWxIazFvUzhVQkpBdWluZURIM21wUT09

In this mini course, I shall introduce the basic concepts in 2D topological orders by studying simple models of topological orders and then introduce topological quantum computing based on Fibonacci anyons. Here is the (not perfectly ordered) syllabus.                      

•        Overview of topological phases of matter
•        Z2 toric code model: the simplest model of 2D topological orders
•        Quick generalization to the quantum double model
•        Anyons, topological entanglement entropy, S and T matrices
•        Fusion and braiding of anyons: quantum dimensions, pentagon and hexagon identities
•        Fibonacci anyons
•        Topological quantum computing.