Whether or not you're a fan of thermal operations, there's something fundamentally special about them: by pinning down what it means to equilibrate, thermal operations uniquely emerge! With this, we also uncover nice hierarchy of unital channels, in contrast with the classical Birkhoff theorem.

The culmination of a series of papers on DBQAs :)

Zoe Holmes@qzoeholmes.bsky.social · last yr.

Here's a new perspective on why Grover’s algorithm algorithm works: Unstructured search can be written as ground state problem. Then Grover's is just a product formula approximation of imaginary-time evolution or, equivalently, a Riemannian gradient flow on SU(d) to find this ground state.

Our Grover preprint just popped up! (with Yudai Suzuki, @qzoeholmes.bsky.social, @marekgluza.mathstodon.xyz.ap.brid.gy, @nellynghy.bsky.social, @perp-waterfall.bsky.social) Turns out… Grover's algorithm is secretly moonlighting as a first-order approximation to the imaginary time evolution!

Today we posted a paper showing how a double-bracket quantum algorithm can implement quantum signal processing (DB-QSP), i.e., apply polynomial functions of operators to states. Crucially our approach doesn't need any post-selection - but this comes at the expense of increased circuit depths.

We put out a systematic study on the extent of robust catalysis! This work was a wonderful experience for me, I hope you'll like it too. Check it out at scirate.com/arxiv/2412.0... !

Jeongrak Son@perp-waterfall.bsky.social · 2y ago

Joint work with amazing collaborators: Ray Ganardi, @sminagawa.bsky.social, Francesco Buscemi, Seok Hyung Lie, and @nellynghy.bsky.social