Michael Ragone

My name is Michael Ragone, and I’m a Morrey visiting assistant professor in mathematics at UC Berkeley. I work at the intersection of quantum many-body physics and quantum computation/information theory, with a high emphasis on applied representation theory. My mentor is Lin Lin, who is now a Judge Shirley Hufstedler Professor at Caltech.

I particularly like to think about problems with a high degree of symmetry. Generically, we can’t “solve” physical models, but symmetry provides a bootstrap which often allows us to probe the physics with sharp analyses and shed light on more general principles.

Ongoing work: Open Quantum Systems

Since moving to Berkeley I have been thinking a lot about open quantum systems. The physical picture is that we have a quantum system interacting with a quantum bath, and we then want to describe the dynamics of our system without describing the bath. My motivations (besides a deep yearning to say “quantum thermodynamics” on a regular basis) come from a few places, which I’ll try to say a bit about here.

Gibbs State Preparation

Many of us have hope that quantum computers will one day be useful for simulating complicated quantum systems that classical computers cannot (I’m looking at you, high T superconductivity and exotic material design). There is a lot of work that needs to be done, on essentially every front. Here’s the one that I’m thinking about. Before simulating dynamics, we want to pick relevant initial states–I often don’t care how some random state evolves over time, I really just care about common configurations for a physical system. Algorithms which prepare these initial states are accordingly called state preparation algorithms, and there’s a whole bunch of them depending on which class of states you’d like to prepare. Arguably one of the most important are thermal equilibrium states (aka Gibbs states), for the simple reason that a lot of matter tends to hang out in these states. Recently (see for instance these beautiful papers: 1, 2) the community has developed quantum algorithms which allow us to prepare Gibbs states by “simulating” open system dynamics. The basic idea is that nature already creates these states by, well, just letting time go on, so it’s pretty reasonable to try to mimic that.

So–how efficient are these algorithms? This is where it gets fun. The simulation part of these algorithms is pretty efficient, at least by a theorist’s standards. The real bottleneck for most of what we’d like to run comes from the simulated physics itself.

• To illustrate, say that somebody comes up to you and says “I have a wonderful new computer program that creates beautiful crystals!” You, being naturally curious, ask how it works. Then they tell you “oh it’s the best, it does OPTIMAL simulation of REAL TIME magma cooling and reheating under the Earth’s crust”. That sounds pretty cool…until you realize that these processes might take a few days (like some of these crazy pegmatites, which can grow up to 10 meters per day) or a few thousand years.

So this brings up the first question: how long should the system take to converge? One mathematical instantiation of this idea is the notion of a mixing time. Long time Markov chain fans will find this whole discussion rather familiar. Indeed, much of what we are doing is exploring quantum versions of Markov chains–specifically, Glauber dynamics of spin systems–and trying to map the landscape of how quickly they converge. In the papers arXiv:2607.21798 and arXiv:2610.01987, we took a family of quantum systems known to exhibit some interesting phase transitions and did a thorough analysis of their mixing times (actually, relaxation times) across many temperatures.

• A central thing to look out for is the dichotomy of fast-mixing vs metastable: just as the Grand Canyon will more or less look the same tomorrow as it did 100 years ago, metastable systems stay roughly stable for a long time. So if you’re trying to build an algorithm to prepare a canyon, simulating the real-time evolution of a river probably isn’t the fastest way to do that.

But that’s not a death sentence for these algorithms. Once we know what causes these bottlenecks, we can start to ask how to design processes which avoid them. Just as we can engineer lab-grown diamonds in a few weeks instead of millennia, we can start to think about how to build processes which don’t get trapped in metastable states. That said, we are still primarily in the phase of trying to understand metastability for quantum phenomena–we really don’t have that many rigorous techniques to easily characterize when it occurs (yet). There’s a wealth of insights from the classical and the quantum statistical mechanics communities though, so I am optimistic we will be able to develop our understanding a lot in the near future.

Metastability and Reduced Dynamics: Quantum Markov State Models

If we take off our algorithm-design beanies and put on our quantum simulation bucket hats, metastability switches from a villain to a protagonist. Let’s think about the Grand Canyon again. If I’m trying to understand what happens on long timescales, I really just care about the water and wind eroding away over centuries. I don’t care too much about whether July was hot, or what fish swam in it–what matters is the overall pattern of wear-and-tear from the lovely Colorado river. So if I want to model what this system is doing over time I can throw away a lot of unnecessary details and find myself left with a core set of reduced dynamics on metastable modes. This is the heart of our recent work arXiv:2609.40214, where we define a quantum version of reduced dynamics. The hard part is showing that this can be done in a physical way–after all, if you are trying to understand how the Grand Canyon develops, you probably shouldn’t allow your model to allow rocks to teleport. For quantum systems, a first check for physicality is ensuring that the dynamics is a well-defined quantum channel, which thanks to some powerful tools from the operator theory community we were able to do. This is a really new direction for us, and I’m excited to see where we can try to use these new techniques.

Metastability and Quantum Memories

It’s worth mentioning that if we again change hats and put on our quantum error correction welding masks, metastability takes on a new identity of protector. When quantum states are metastable with respect to physical noise in a quantum device, they are capable of storing quantum information for longer periods of time. This is an extremely desirable quality: quantum computers face formidable scaleability challenges, and designing logical quantum states which are robust to noise but allow for computation could be extremely useful.

Dissertation work: SO(n) spin chains

I completed my dissertation work (arXiv:2403.09951) work under Bruno Nachtergaele at UC Davis, and still dabble on closely related problems. We are studying a fascinating class of ground state structure problems for quantum spin systems with natural Lie group symmetries. “Quantum spin systems” encapsulates a mathematically rigorous framework arising from condensed matter and quantum information theory which models particles with finite degrees of freedom on lattices (think cold atoms in an array, or vacancies in a crystal, that sort of thing). When these systems have Lie group symmetry, like a rotational SO(n) symmetry, tricky problems like determining spectral gaps or uniqueness properties of ground states become much more tractable. A classic symmetry I like to think about is rotational symmetry: “rotated ferromagnets are still ferromagnets”. My main work is on a class of SO(n)-invariant ground states which closely resemble the AKLT chain, the prototype model for symmetry protected topological (SPT) phases. My thesis is chock-full of details and specific examples to help make the story clear–I hope it helps!

LANL and PNNL Work: Variational Quantum Algorithms

Throughout my time at Los Alamos National Laboratory and Pacific Northwest National Laboratory, I worked on a handful of teams which aimed to use tools from representation theory and Lie geometry to study the potential performance of variational quantum algorithms and quantum machine learning. Much of the analysis revolved around studying “dynamical Lie algebras”, a central object in quantum control theory (and other branches of physics) which allows us to rigorously describe the somewhat vague notion of “expressibility” of a parameterized quantum circuit. Parameterized quantum circuits are essentially quantum circuits with little dials on them, and these little dials allow us to explore spaces of quantum gates, which are just collections of unitary maps. The expressibility of a circuit describes how much of the space of unitaries it can explore: circuits with high expressibility can see many unitaries, while circuits with low expressibility can only see a few.

What the field has realized is that for the existing common models of quantum machine learning, there is a fundamental tradeoff: highly expressible circuits can become prohibitively hard to train, due to the barren plateau phenomenon. But circuits with low expressibility are typically classically simulable, meaning we don’t really need a quantum computer to perform these computations. One may hope that a happy middle ground exists, but detailed classifications of dynamical Lie algebras seem to suggest no such middle ground exists.

This doesn’t necessarily mean that quantum machine learning is doomed, but it does mean that to make real progress we need at least one of two things (and my personal suspicion is that we will need both):

1. We need more thoughtful models for quantum machine learning: different architectures, different loss functions, different optimization routines…something to evade the no-go theorems of the last 5-10 years. As to what to try, that’s a great question.
2. We need good heuristics for quantum machine learning. Classical machine learning owes much of its success to years of thorough experimentation and development of good heuristics. The development of rigorous mathematical theory lags by years and is ultimately guided by what works, in some analogy to the relationship of physics and mathematical physics. But despite incredible progress for building larger quantum computers with lower error rates, we’re still a long ways out from having a machine we can play with the way we can play on our laptops.