Quantum Emergence and Quantum Computing

Research | Papers | Group | Talks | Code

Our group works at the intersection of quantum information, condensed matter, machine learning, and computing. The simple rules of quantum mechanics are responsible both for the rich behavior seen in quantum materials and devices; as well as the advantages of quantum computers over classical ones. We develop and use computational tools to better understand many-body physics and move forward quantum computing.

Quantum Computing: Our interest in quantum computing is broad but we are primarily focused on building the quantum algorithms and error correction/mitigation necessary for using quantum computers as well as collaborating closely with (currently superconducting qubit) experimentalists to develop the components (e.g. robust qubits, better readout, error detection) needed for quantum computation. Our approach to quantum algorithms spans not only core algorithms (e.g. VQE, qubitization) but also the critical aspects of state preparation and tomography with pioneering work in both fields. Another key interest of ours is better delineating the quantum-classical boundary which not only constrains where quantum advantage lies but also tells us from where the true power of quantum computing comes.

Quantum Many Body Physics: In the area of quantum materials, our goal is to be able to understand and predict material properties. We are most often motivated by universal qualitative physics arising from model Hamiltonians and are particularly inspired by the emergent behavior (complicated phenomena arising from simple rules) of strongly correlated systems which are hard to predict from simple mean-field arguments. Our approach and perspective on these problems are computational and we apply the full computational toolbox of classical techniques from quantum Monte Carlo (VMC,PIMC,AFQMC,DMC), tensor networks (MPS,PEPS,MERA), and machine learning to tackle them.

Algorithms for the quantum many-body problem (machine-learning and otherwise): We are also heavily invested in and excited about the development of new computational methods often working to overcome the exponential wall in simulating quantum many-body physics and developing new algorithms to broaden the horizon of what's possible. Amongst our most impactful work has been the development of the Neural Network Backflow (NNBF) variational approach and we are rapidly improving and applying the technique. NNBF's unique integration of mean-field physics combined with its machine learning architecture allows it to focus on capturing crucial correlations rather than re-learning basic physics and it is currently the most accurate method for simulating a wide class of fermion and frustrated magnetism systems. Beyond NNBF, we've made important methodological improvements in various areas of quantum Monte Carlo (machine-learning wave-functions, sign problems, etc.) and tensor networks (Gutzwiller projected TN, stochastic approaches) as well as developed some novel inverse approaches which allow you to learn Hamiltonians from wave-functions or symmetries - a useful tool both for Hamiltonian learning on quantum computers as well as finding model systems with interesting behavior.

Machine Learning for Experiment : Beyond simulations, we also have a goal of using and developing machine learning techniques to better analyze experimental results and control experimental apparati. A good example of this work here has been using ML to identify atomic positions in scanning transmission electron microscopy data.

You can get a good sense for what we are working on by looking at our papers by topic or chronologically.

Pedagogy

tl;dr: Check out illinois-comphys

I am heavily involved in developing the computational physics curriculum at Illinois. Much of that work has been consolidated at the illinois-comphys site. I developed from scratch our Junior/Senior computational physics course, Physics 446. Here students, among other things, develop their own quantum computing simulator (and factor 55 on it!), do numerical RG on the Ising model, and build their own diffusion model from scratch (all the while learning the underlying physics of how it works). I also re-developed a significant portion of our Sophomore computational physics course, Physics 246 including developing a number of new modules on areas such as Predator-Prey simulations (differential-equations, continuous time markov-chains, and agent-based), lattice Boltzmann methods, climate dynamics, machine learning, quantum computing, and more. I also restructured the logistics of the course around Jupyter notebooks. Most recently, I've been developing new computational modules to incorporate into our core curriculum including in Classical Mechanics, E&M, and Quantum Mechanics. Students write simulations to compute the equation of motion for coupled springs, the electric field lines of an oscillating electric dipole, diagonalize a Hydrogen atom on a grid, and compute perturbation theory to 30'th order. I also developed from scratch a graduate computational physics courses, An Algorithmic Perspective on Strongly Correlated Systems although haven't gotten a chance to teach it much and so it is unpolished.

I've also taught other courses and summer schools.

You might also be interested in learning about:

Variational Monte Carlo: See my notes and video from the Boulder Summer School; the videos [part 1, part 2] from the Cornell Summer School on Emergent Phenomena; or my tutorials.

Diffusion Monte Carlo: See my notes and video from the Boulder Summer School.

Path Integral Monte Carlo: See my tutorials (with Ken Esler and Paul Yubo).

Density Matrix Renormalization Group: Work through problem set 3 and problem set 4 from my graduate course to build a simple DMRG code in Julia.

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