Last week I defended my thesis "Quantum Qomrades: Catalysts in Resource Theories and Memories in Dynamic Programming". This journey was possible thanks to all my human comrades, especially my amazing adviser @nellynghy.bsky.social !

Our tutorial "A friendly guide to exorcising Maxwell's demon" (journals.aps.org/prxquantum/p...) is out! The big question after the tutorial is whether I’m finally done drawing demons?

This is actually the first no-go result for robust catalysis (i.e. catalytic transformations that are catalytic even with small state preparation noise) outside completely resource non-generating operations. Next step: robust catalysis in LOCC or stabiliser operations?🥴🥴

A fun project with Seok Hyung, Jeongrak ( @perp-waterfall.bsky.social ), @nellynghy.bsky.social , and Paul Boes. We dusted off some old notes because there seemed to be renewed interest in what differentiates thermal operations from Gibbs-preserving maps. arxiv.org/abs/2507.16637

Years down the road, Jeongrak and I were trying to figure out whether robust catalytic advantage exists for thermal operations. We then realized that the conceptual key was hidden in those early, unannounced results by our friends all along! arxiv.org/abs/2412.06900

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.

Grover's algorithm is reinterpreted as a product formula approximation of imaginary-time evolution in a new paper. @marekgluza.mathstodon.xyz.ap.brid.gy @perp-waterfall.bsky.social @nellynghy.bsky.social @qzoeholmes.bsky.social arxiv.org/abs/2507.15065

Finally, we show that quantum signal processing can be used to implement imaginary time evolution for unstructured search without post selection. And this enables us to design a new `fixed-point' quantum search algorithm i.e., a Grover type algorithm that never overshoots the solution

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.

Check out this arXiv paper if you're interested! arxiv.org/abs/2507.15065

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!

Our paper (w/ Marek, @ryujitakagi.bsky.social, @nellynghy.bsky.social ) on Quantum Dynamic Programming has recently been published in PRL: journals.aps.org/prl/abstract... Xin Yi from CQT wrote a great highlight article for this paper: www.cqt.sg/highlight/20...

Thm.2 is derived from Eq. (16), which I am particularly fond of. This equation shows that any linear combination of a Hermitian matrix and the identity can be applied to a quantum state exactly and deterministically (given one can synthesise the exponential of a commutator).

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.

A new paper introduces Double-Bracket QSP (DB-QSP), a novel quantum signal processing approach that eliminates the need for auxiliary qubits and post-selection by using approximate unitary synthesis. arxiv.org/abs/2504.01077

Nelly Ng "Robust Catalysis and Resource Broadcasting: The Possible and the Impossible" #QuantumResources2025 I asked if there might be implications for Deutschian closed timelike curves. When I asked my question, I wasn't so serious, but thinking more afterwards, I think there is more to explore

Another paper of the week! scirate.com/arxiv/2412.0... In resource theories, catalysis provides many amazing advantages. However, it turns out that whenever there is system preparation error, most of them stop being catalytic. Fret not! We introduced a new class that is robust under such errors.

Nature cools things easily but getting a quantum computer to do it is hard! Give us an approx ground state, we present an algorithm that approximates imaginary time evolution to: - Cool that state by an amount proportional to its energy fluctuations - Increase its fidelity with the ground state

New preprint on arXiv! scirate.com/arxiv/2412.0... Quantum imaginary-time evolution (QITE) is amazing, but its compilation is not straightforward. We found an iterative way of doing this, using the equivalence of QITE and double-bracket flows.

Double-bracket quantum algorithms for quantum imaginary-time evolution https://arxiv.org/pdf/2412.04554 Marek Gluza, Jeongrak Son, Bi Hong Tiang, Yudai Suzuki, Zoë Holmes, Nelly H. Y. Ng