Building Bridges: Professor Lin Lin

Since 2014, Lin Lin has served as a computational mathematician in the Mathematics Department here at UC Berkeley, though he might also be a quantum chemist in disguise. By combining insights from both fields, he is interested in designing new algorithms that harness the power of quantum computers to tackle challenging problems in quantum chemistry and scientific computing more broadly. 

Showing early on the tenacity we come to expect in successful scientists, Lin sought out difficult problems when he went from small-town eastern China to Peking University for his bachelor’s. The Beijing megalopolis turned out to be a bit much, though, so when he looked for grad school he aimed for Princeton, a truly small-town eastern city. Lin studied with both a great mathematician, Weinan E, and a stellar physical chemist, Roberto Car. Doctoral student Lin Lin grew into a new, and still rare, type of scholar: a computational mathematician who tackles challenging problems in quantum chemistry and materials science. 

STEM communicators start explaining quantum many-body problems by calling them high dimensional, which may not be of much help since it sounds like ‘difficult’ using more syllables. Adding that algorithms can help solve these problems just makes us suspicious, since algorithms have been cast as the malign(ed) tools of the tech overlords. Let’s try a friendlier analogy.

Recall from your U.S. history that many of America’s founding fathers were Deists, meaning that they believed God had built the universe and started it running, like a clockmaker, and then left it alone to operate. No further maintenance required. Many physicists still think this way about matter and energy. The components of any particular chunk of material have an initial state, and they bop around according to regular rules. If you knew that initial state accurately, and all the rules, you could describe the whole history of that chunk confidently enough that you wouldn’t need to keep poking at it or measuring it to check on how it is doing. It just keeps on ticking.  

A quantum many-body problem involves understanding how a large number of interacting quantum particles (like electrons, nuclei, etc) behave collectively. This is central to physics, chemistry, materials science, and quantum information. But quantum particles don’t just act independently–they can interfere, entangle, and correlate in complex ways. To describe a dab of just 50 particles would require more than a quadrillion (1015) equations. There isn’t enough time for a classical computer to brute force it. And that’s just the tip of one tooth of one gear in the clock. 

That’s why algorithms matter. Scientists need systematic shortcuts for computing aspects of the quantum system. There are classical algorithms that do more than approximate the problem (as in ‘give me a ballpark figure’) by restructuring the approaches to make them solvable, but even cooler are new ‘quantum’ algorithms that promise to solve these problems natively. Quantum computers don’t simulate quantum mechanics — they are quantum mechanics. Quantum algorithmic innovations go beyond improvements in speed or scale by providing new ways of thinking about how to represent, approach, and resolve these many-body problems. 

This is where Lin Lin takes the lead. He designed from scratch the first mathematics course on this topic for the Fall 2021 term: Quantum Algorithms for Scientific Computing. It grew out of a seminar he’d been conducting for a few years prior. His view is that classical and quantum algorithms should inevitably work together: classical methods are used to sketch out the “scenery”, and quantum algorithms can be saved for the central details. This would make possible larger scale simulations – thousands of atoms, disordered materials, eventually biomolecules – that are faster and cheaper yet still physically accurate. These developments can encourage cross-disciplinary collaborations among physicists, chemists, mathematicians, and computer scientists.

Professor Lin has more to say about the useful clash of perspectives between mathematicians and physical scientists. Very roughly speaking, math people prefer slow and steady while scientists often throw stuff against the wall to see what sticks. This means different types of problems are attractive to people from different fields. But physicists have been interested in the structure of electronic materials for a long time already, so they bring both vocabulary and ideas that are still new to mathematicians. Lin is happy to be a conduit between the disciplines, to bring mathematical tools to quantum mechanical work. 

How is that going, a decade-plus into his academic career? Cambridge University Press has signed a contract to publish a book version of his quantum computation course. And the College of Chemistry is about to formally acknowledge Lin’s contributions with a joint appointment. Back in graduate school, Lin Lin often wondered whether his combination of interests and skills would fit within traditional academic boundaries. Rather than choosing a single discipline, he pursued an interdisciplinary path, and today his work contributes to the growing dialogue between computational mathematics and quantum science.

Read more about Lin Lin's work in quantum computation here: CIQC's Impact in Action: Building Quantum Careers in Mathematics

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