Grover's quadratic speedup is provably optimal in the black-box setting. We expect general SAT to be essentially unstructured and as hard as the black-box setting (strong exponential time hypothesis). It's believable that Grover is optimal there. But this is not clear for 3-SAT!

A measurement-driven quantum algorithm for SAT: Performance guarantees via spectral gaps and measurement parallelization scirate.com/arxiv/2511.096… The Boolean satisfiability problem (#SAT) is of central importance in both theory and practice. Yet, most provable guarantees for

Variational quantum eigensolvers and classical tensor network methods provide upper bounds to ground-state energies. Lower bounds are known but often less appreciated, even though they can be quite tight. I have decided to turn the note scirate.com/arxiv/2301.061… into a small

This is a publication I am extremely happy about. It is a bit rebellious, and yet it touches upon an old and important question: How can we learn an unknown quantum state from data? This is the quantum state tomography problem, and even the name “tomography” comes from the

Context for “Erdős failed to solve this:” One, he was in his 80s when this was published. Two, the man wrote ~1,500 papers. That level of output requires willingness to declare papers sufficient and move on to other projects without dwelling on every possible additional theorem.

We are hiring a postdoctoral researcher and a PhD student to join a strong research team to work on #quantumerrorcorrection for cold atomic platforms, funded by the BMFTR. The topics range from abstract considerations to hardware-tailored approaches. We can provide a

Times are changing. From the acknowledgments of Lance Fortnow's new paper on search vs decision for S_2^P. (arxiv.org/abs/2512.02808)

Well over a decade ago, Alan Aspuru-Guzik and I had the idea for a quantum algorithm to efficiently simulate essentially any chemistry experiment by simulating dynamics mimicking it. After lots of hard work from people who aren’t me, it’s now finally out. pubs.rsc.org/en/content/art…

This is a fantastic essay that anyone genuinely serious about forwarding AI for the automation of science should reckon with.

An upbeat blog post for Christmas: Quantum Error Correction goes FOOM algassert.com/post/2503

Stim pushed the field forward... but I worry it may also hold it back. For example, Stim doesn't understand adaptive strategies like "measure again if you see a suspicious thing". If too many researchers rely on stim, adaptivity will be under-explored!

Do Bose-Hubbard type systems have a speed of sound for particle propagation? scirate.com/arxiv/2601.001… Yes. Indeed, it has long been an open question whether interacting bosonic systems also feature finite speeds of sound in information and particle propagation—a question that

A three-decade-old open problem of mine just got solved! Matt Kovacs-Deak, Daochen Wang and Rain Zimin Yang showed that if a Boolean function f is exactly computed by a low-degree rational function, the quotient of two polynomials, then f has low decision-tree complexity. 1/2

This is a paper I very much like, for its foundational and somewhat "rebellious" character: We show that notions channel capacities are strongly altered if one simply assumes that all operations one can implement are efficient. scirate.com/arxiv/2601.153… To the point,

This is a massive overreaction. We are seeing a few solved recently, but all of them low-hanging fruit. And humans have been solving steadily for years already! Many problems on the Erdos site are some of the most difficult in maths; some harder than the Riemann Hypothesis.

Some thoughts on AI and mathematics, inspired by "First Proof."