Vasilii Vadimov
Seally physicist
Quantum heat engine in circuit QED — 2026-03-22
Recently, we’ve got published a theoretical paper1 about a quantum heat engine in microwave superconducting circuits. And last week we put an experimental work on arXiv2!
More units and less units — 2026-02-01
I work in an experimental group and sometimes do numerics with dimensional quantities. A typical example could be an electric quantum circuit with all the capaticances, inductances, resistances/impedances given as dimensional numbers, and I need to calculate scattering matrices or spectrum of the Hamiltonian. My colleagues also do lots of data analysis and manipulate dimensional data.
Tall and skinny SVD — 2026-01-14
Recently, in my work I needed to construct a rational approximation of a matrix-valued
function. The best algorithm I know is AAA1 and that requires
singular value decomposition of \(m \times n\) matrices with \(m \gg n\).
For scalar functions, there is no problem with that since in most cases the
matrix is reasonably sized to use svd call from standard Julia’s LinearAlgebra.
To use AAA algorithm for \(r \times c\) matrix-valued function we have to
deal with matrices \(r c\) times taller which is already painful.
Continuous version of AAA algorithm2 allows to increase number
of rows adaptively, but even with that I had hard time even to store the full
matrix in the memory: typical matrix size was millions times tens.
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I. V. Gosea and S. Güttel, “Algorithms for the Rational Approximation of Matrix-Valued Functions,” SIAM Journal on Scientific Computing, vol. 43, no. 5, pp. A3033–A3054, Jan. 2021 ↩
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T. A. Driscoll, Y. Nakatsukasa, and L. N. Trefethen, “AAA Rational Approximation on a Continuum,” SIAM Journal on Scientific Computing, vol. 46, no. 2, pp. A929–A952, Mar. 2024 ↩