Aaron Lauda
University of Southern California, CA·Mathematics & Statistics
Quantum computers could solve problems far out of reach for ordinary machines, but the information they hold is fragile and easily ruined by noise. One way to protect it is to store it in the overall shape of a system rather than in any single part.
- Fields
Mathematics & Statistics
Physics
Computer Science
- Topics
representation theory
low-dimensional topology
topological quantum computation
- Grants
- 1 known grant, through Jul 2029
What they work on
- Develop non-semisimple topological quantum field theories as a working framework for topological quantum computation, including density of braid group images in noncompact unitary groups and Hermitian forms on unrolled quantum group representation categories.
- Control leakage into indefinite sectors and design algorithms that approximate indefinite unitary transformations from finite gate sets, making braiding of Ising anyons practical for universal computation.
- Bring Hodge Laplacian methods from a quantum algorithm for Khovanov homology into higher representation theory by equipping categorified braid group actions and Rouquier complexes with inner products, and study the resulting spectra.
- Construct a circuit-to-Hamiltonian mapping from Turaev-Viro, Walker-Wang and Crane-Yetter topological quantum field theories, producing local Hamiltonians whose ground states encode computations and whose spectral gaps can be analyzed.
More about the research
Topology, the branch of mathematics about features of a shape that survive bending and stretching, supplies that idea. A leading proposal encodes information in anyons, exotic particles whose paths can be braided around one another, so the result of a computation depends only on the braid pattern and not on small local wobbles. This project develops topology together with representation theory, the mathematics of symmetry, into tools for building and programming such machines, along three directions.
Why it matters
Fault-tolerant quantum computing depends on knowing which physical systems can carry out universal computation and how to program them. By showing which topological systems have full computational power and supplying concrete mathematical recipes for braiding-based gates and for Hamiltonians whose ground states encode computations, this work could guide the design of hardware that is intrinsically protected from noise.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Cris Negron
University of Southern California, CA·Mathematics & Statistics·Early-career
Build rigorous mathematical realizations of topological quantum field theories whose spaces of lowest-energy states (moduli of vacua) are non-compact, using homotopical methods in representation theory.
Abhishek Mallick
Dartmouth College, NH·Mathematics & Statistics
Establish new structural results for instanton, monopole and Heegaard Floer theories, which are invariants built from physics-inspired equations, in settings where spaces carry symmetries such as rotations or reflections.
Chelsea Walton
Rice University, TX·Mathematics & Statistics
Extend classical properties of algebras over a field to algebras in monoidal categories, and identify properties that carry significant meaning only in the categorical setting.
The school
University of Southern California: 47 labs on PI Pages, $1.3B a year on research, 882 research doctorates a year.
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