(2) quantum-journal.org/papers/q-202..., with coauthor Yudai Suzuki, @marekgluza.mathstodon.xyz.ap.brid.gy @perp-waterfall.bsky.social @nellynghy.bsky.social @qzoeholmes.bsky.social (meme creator). A new recipe for implementing polynomial transformation of a Hermitian matrix without post selection~~
Two double-bracket works just jumped out🧑🍳🧑🍳— (1) PRL journals.aps.org/prl/abstract... With coauthors @marekgluza.mathstodon.xyz.ap.brid.gy @perp-waterfall.bsky.social @nellynghy.bsky.social @qzoeholmes.bsky.social, Yudai Suzuki, René Zander, Raphael Seidel
Double-bracket quantum imaginary-time evolution - a #quantum algorithm for implementing ground-states of local Hamiltonians is now published at PRL.
https://journals.aps.org/prl/abstract/10.1103/rw81-k8vk
and the equivalent freely accessible preprint is here
https://arxiv.org/abs/2412.04554 […]
Thank you! It was great visiting you last year!
Same!! And the journey was great thanks to you and all my new friends! Hope to see you more often at conferences.
Thanks so much!! It was amazing collaborating with you!
Check all my papers on arXiv: arxiv.org/a/son_j_2.html
The ones I covered in my thesis are: arxiv.org/abs/2209.15213, arxiv.org/abs/2303.13020, arxiv.org/abs/2403.09187, arxiv.org/abs/2412.04554, arxiv.org/abs/2412.06900
My next step hasn't been decided yet, and I will be staying at NTU until (at most) Feb-Apr 2026 to wrap up several projects. You may soon hear about Gaussian phase-covariant operations or hybrid resource theories from me:)
My interest in catalysts grew to include other auxiliaries, particularly memories. We introduced several quantum algorithms that approximately solve certain non-linear differential equations and showed that using quantum memories without reading them can drastically improve these algorithms.
We then observed an important caveat (catalysis is fragile to noise) and characterised rather general classes of theories where robust catalysis is possible/impossible.
Since I first encountered catalysis in QI, I've been fascinated by how powerful it can be despite it returning to its exact original state. My PhD study started there: we identified a source of its power (memory effects!) and found that this alone can bridge different thermodynamic paradigms.
Jeongrak receives a cake and a hat for celebration
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 !
Yayyyy the title survived!!
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.
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!
3) We have since introduced many algorithms that are quantum recursions (check out a series of papers on double-bracket quantum algorithms). In particular, we think that double-bracket quantum imaginary-time evolution (arxiv.org/abs/2412.04554) is a strong candidate for QDP application.
2) We also compare the circuit size (depth x width) with or without QDP. Sometimes, QDP reduces the circuit size. However, even when it does not, QDP allows us to have circuit depth-width tradeoff, which I believe is quite cool.
1) We now focus on pure quantum recursions (i.e. the recursive non-linear evolution of a pure state), for which we have a better performance guarantee: the circuit depth can be exponentially reduced by using exponentially many initial copies of the state.
For those who have only read the arXiv v1, here are some summaries of the changes:
It took us over a year to publish this, since we went through numerous revisions including significant strengthening of the results. The screenshot below is an excerpt from our reply to referees.
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...
Yess exactly! We are basically working in an effective qubit space spanned by \Psi and H \Psi, and the second unitary e^{i \theta \Psi} gives the relative phase difference.
