Manuel Rudolph

Hey - we've extended Pauli and Majorana propagation to simulating thermal states

The trick is to imaginary-time evolve identity and then normalize by the trace of the Pauli (or Majorana) sum at the end

The catch is that both our analytics and numerics suggest it only works at high temperatures

🧵👇

Much love to my collaborators @aangrisani.bsky.social, Andrew Wright, Iwo Sanderski, @pvricard.bsky.social, and @qzoeholmes.bsky.social ❤️

This was a fun sprint at a slightly inconvenient time 🤝

GitHub - MSRudolph/PauliPropagation.jl: A Julia library for Pauli propagation simulation of quantum circuits and quantum systems. A Julia library for Pauli propagation simulation of quantum circuits and quantum systems. - MSRudolph/PauliPropagation.jl

Imaginary Pauli gates have been added to our library PauliPropagation.jl (github.com/MSRudolph/Pa...), and they will soon be added to MajoranaPropagation.jl (github.com/SparqleSim/M...) as well—Shoutout to Matteo D'Anna for his work there.

PP.jl underwent big changes, so keep posted for more.

Look at the pretty plots we got simulating (very) high temperature, strongly interacting fermions in the Fermi-Hubbard model with 74 Majorana modes. We start observing spin-spin correlations on triangular lattices, but we currently cannot reach the regime in which we would expect frustration.

We show how the number of Pauli operators grows as a function of beta and for different truncation thresholds in a J1-J2 Hamiltonian chain. With some code innovations, we can quickly generate billions of Paulis (and then run out of memory). High temperature states remain tracktable.

We provide error bounds on coefficient truncation and Pauli weight/ Majorana length truncation as a function of the inverse temperature beta.

I'm a simple man. Here is my simple summary.

Small beta: Good
Large beta: Bad

Ask @aangrisani.bsky.social and @pvricard.bsky.social for details.

The infinite-temerature / maximally mixed state is representable by a single operator, the identity. We define the action of imaginary time evolution, and show that we can efficiently simulate high temperature states.

Did you know you can simulate quantum states with Pauli and Majorana propagation?

In short: High-temperature states are provably and practically sparse, and we can use imaginary time evolution to get there starting from the infinite-temperature state.

scirate.com/arxiv/2602.0...

Oh, thanks for sharing!

Yanting is keeping you updated on our efforts to continually improve propagation algorithms and our code-base PauliPropagation.jl. This time with memory savings and increased robustness to truncations for simulating quantum systems with certain symmetries ⬆️ ➡️ ⬇️ ⬅️

Expect more in the future! 🚀

Phew, my score is memes: 2, emojis: 0

I heard some people delete 100+ author papers from their Google scholar to be more in line with their own work.

Does provable absence of barren plateaus imply classical simulability? - Nature Communications There has been growing evidence that strategies to circumvent the barren plateau problem in variational quantum computing might also kill potential quantum advantages. In this Perspective, the authors...

I am so, so happy to see this article published as a perspective in Nature Communications:

www.nature.com/articles/s41...

More than the paper itself, I thoroughly enjoyed chatting with all my co-authors on the implications of the absence of BPs ~ classical simulability connection

Welcoming summer the best way we know how: with pasta, physics, and a phenomenal team 🍝⚛️

A warm #Google #Quantum #AI welcome to Manuel Rudolph, who’s joining us this summer! 🎉 We’re thrilled to have his sharp mind and curious spirit with us

Thx Nikita+team for organizing

Huge thanks to @joeytindall.bsky.social. I had a great time working with him during my 4-month stay at the Flatiron Institute in New York. This guy is amazing!

A big thank you also to @mstoud.bsky.social for having me.

@flatironinstitute.org @simonsfoundation.org

Particularly interesting to us was witnessing how slowly loop correlations build up in heavy-hex processors. Loop correlations are what make loopy networks potentially significantly harder to use than loop-free MPS and tree-tensor networks.

We also introduce a bunch of metrics to certify that the samples are of high-quality. This way, we verified that we solved the biggest circuit in IBM's recent quantum chemistry experiment to numerical precision.

We combine some existing ideas with ITensorNetworks.jl and @joeytindall.bsky.social's flexible boundary MPS code to adapt to any planar geometry.

With our open-source (but not completely polished) software, you can start simulating and sampling 2D circuits today: github.com/JoeyT1994/Te...

In case you thought you can't efficiently simulate and sample quantum circuits with 2D tensor networks... Nope, you can.

Link: scirate.com/arxiv/2507.1...

We simulate IBM's recent quantum chemistry experiments and Williow + heavy-hex Heisenberg dynamics, and showcase modern, verifiable techniques.

Big congrats to @carrasqu.bsky.social's group at @ethz.ch, including Yuxuan Zhang and Roeland Wiersema, and particularly Matteo D'Anna for his amazing first-author work early in his PhD.

Oh no, haha. My bad and thanks!

I don't see any reason why not every circuit executed on hardware should be compressed. The approach can also be used to re-compile into a different gate set or topology.

Classical simulation is not just here to compete with quantum devices.

Last week, we published a paper that really excites me:
"Circuit compression for 2D quantum dynamics"

Using Pauli propagation, we (Matteo) were able to compress Trotter circuits for systems up to 30x30 with depth reductions of x2 to x13.

Link: arxiv.org/abs/2507.01883

I'm surprised Grover's is on here. Maybe not for database search but as a form of amplitude amplification?

Retweeting this for the folks (myself included) that weren't online over the long weekend

PauliPropagation.jl is open source library that you can use to approximately simulate quantum circuits

We explain the nitty gritty of how these algorithms work in practise in our latest companion paper

🧵👇

Sorry 🤐

This paper was meant to go live yesterday (still love you arXiv), but who doesn't scroll social media on a holiday 💁

Thanks to my amazing group and co-authors Tyson Jones, Yanting Teng (@yteng.bsky.social), Armando Angrisani (@aangrisani.bsky.social), and Zoë Holmes (@qzoeholmes.bsky.social)!

Pauli propagation is naturally interfaced with both quantum computers and other classical simulation methods - the perfect team player!

I love improving classical algorithms for simulating quantum computations, and I truly believe performant classical methods are good for everyone.

In VERY short:

- PP is a recent path integral method that is orthogonal to e.g. tensor networks.
- PP evolves objects that are sparse Pauli basis, commonly observables in the Heisenberg picture.
- PP is amazing for quick estimates in low-ish Magic quantum systems.
- PP is hard to converge exactly.

This "compact" 30-page main text manuscript summarizes much of what we have learned about Pauli propagation (PP) and where its strengths lie.

From the general framework description, over theoretical guarantees, to the nitty-gritty implementation details that you are happy to not have to deal with.