(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~~

Double-bracket algorithm for quantum signal processing without post-selection

Yudai Suzuki, Bi Hong Tiang, Jeongrak Son, Nelly H. Y. Ng, Zoe Holmes, and Marek Gluza, Quantum 9, 1954 (2025). Quantum Signal Processing (QSP), a framework for implementing matrix-valued polynomials,...

quantum-journal.org

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 […]

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?🥴🥴

Nelly Ng@nellynghy.bsky.social · last yr.

We learnt that thermal operations strike a really sweet spot between encompassing non-Markovian effects in the form of robust catalysis, therefore favouring it over subsets of the theory. At the same, any other superset of the theory would require a non-equilibrium environment!

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

Thermal operations from informational equilibrium

Thermal operations are quantum channels that have taken a prominent role in deriving fundamental thermodynamic limitations in quantum systems. We show that these channels are uniquely characterized by...

arxiv.org

Nelly Ng@nellynghy.bsky.social · last yr.

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.

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

Robust Catalysis and Resource Broadcasting: The Possible and the Impossible

In resource theories, catalysis refers to the possibility of enabling otherwise inaccessible quantum state transitions by providing the agent with an auxiliary system, under the condition that this au...

arxiv.org

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

Grover's algorithm is an approximation of imaginary-time evolution

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient f...

arxiv.org

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

Grover's algorithm is an approximation of imaginary-time evolution

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient f...

arxiv.org

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).

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

Given these strengths (no post selection) / caveats (circuit depths scale super exponentially with polynomial order) We see DB-QSP as most useful to deterministically implement low order polynomials in cases where the success probability of other methods is so small as to not be worth doing.

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

Double-bracket algorithm for quantum signal processing without post-selection

Quantum signal processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciat...

arxiv.org

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

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

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.

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

Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of therm...

scirate.com

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