Quantum algorithms & implementation
Block encoding, Hamiltonian simulation, and circuit synthesis for practical quantum algorithms and many-body simulation.
Postdoctoral Scholar · Berkeley Lab
Diyi Liu
Applied mathematician studying complex quantum systems through applied and numerical analysis, mathematical physics, and fault-tolerant quantum simulation.
I work at the intersection of numerical analysis, mathematical physics, quantum algorithms, and scientific machine learning. My goal is to turn the structure of physical problems into algorithms that are both mathematically rigorous and computationally useful.
At Lawrence Berkeley National Laboratory, I am hosted by Wibe de Jong and also work with Chao Yang and Lin Lin.
Background
Training in applied mathematics and scientific computing
Before joining Berkeley Lab, I earned my Ph.D. in Applied Mathematics from the University of Minnesota, where I was advised by Mitchell Luskin and worked closely with Alexander B. Watson and Stephen Carr.
I completed my B.S. in Mathematics and Applied Mathematics at Shanghai Jiao Tong University, where I was advised by Lei Zhang. As a Visiting Undergraduate Research Program (VURP) student at the California Institute of Technology, I completed my undergraduate thesis under the supervision of Houman Owhadi.
Motivation
Curiosity-driven, problem-driven research for a better world
I want to understand the mathematics and physics of complex quantum systems. Guided by curiosity about both the physical and mathematical worlds, I seek connections across branches of mathematics that can reveal new structure, sharpen our intuition, and deepen our understanding of quantum phenomena.
Research
Computational and theoretical applied mathematics for quantum science
My primary interests are computational mathematics and theoretical applied mathematics. I work at the intersection of fault-tolerant quantum simulation, numerical analysis, applied analysis, quantum many-body systems, and mathematical physics, developing rigorous methods and practical algorithms for quantum science.
Quantum & moiré materials
Multiscale and aperiodic models for electronic structure and dynamics in twisted two-dimensional materials.
Scientific machine learning
Operator learning and physics-informed representations grounded in numerical analysis and mathematical well-posedness.
Fault tolerance & quantum error correction
Quantum codes, magic-state distillation, and logical resource estimation for reliable fault-tolerant quantum computation.
Recent focus
Methods and questions at the center of my current work
Across the broader program above, much of my recent work concentrates in two complementary areas.
Applied analysis & mathematical physics
- Open quantum systems
- Multiscale analysis
- Magnus expansions
- Fault-tolerant analysis
Quantum algorithms & implementation
- Input for Quantum: from State, Hamiltonian to Magic
- Hamiltonian simulation
Selected work
Recent and representative papers
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Logical Resource Estimation for Quantum State Preparation with Compilation
Diyi Liu, Hanyu Wang, Shuchen Zhu, Jason Cong, Wibe A. de Jong, Di Fang, Zhen Huang, Costin Iancu, and Chao Yang
An end-to-end comparison of state-preparation strategies that accounts for compilation overhead, total gate count, and fault-tolerant resources. The work also develops a state-preparation circuit compilation package.
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Time-Dependent Hamiltonian Simulation via Magnus Expansion: Algorithm and Superconvergence
Di Fang, Diyi Liu, and Rahul Sarkar · Communications in Mathematical Physics
A quantum algorithm with commutator scaling and a rigorous fourth-order superconvergence result.
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Learning the Local Density of States of a Bilayer Moire Material
Diyi Liu, Alexander B. Watson, Michael Hott, Stephen Carr, and Mitchell Luskin · Multiscale Modeling & Simulation
Operator learning placed on a mathematical foundation through inverse problems and approximation theory.
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An efficient quantum circuit for block encoding a pairing Hamiltonian
Diyi Liu, Weijie Du, Lin Lin, James P. Vary, and Chao Yang · Journal of Computational Science
A direct block encoding based on controlled swaps, with polynomial gate complexity and an application to density-of-states estimation.
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Computing Free Energies with Fluctuation Relations on Quantum Computers
Lindsay Bassman Oftelie, Katherine Klymko, Diyi Liu, Norm M. Tubman, and Wibe A. de Jong · Physical Review Letters
A Jarzynski-equality algorithm for approximating quantum free-energy differences, demonstrated with the transverse-field Ising model on a real quantum processor.
Teaching
Helping students connect abstraction to computation
I have taught and supported courses from calculus and linear algebra through mathematical modeling and quantum computing. As instructor of record for Calculus I, I focused on making reasoning visible: translating a formula into a picture, an argument, and a computational check.
- Instructor
- Calculus I
- Lab instruction
- Multivariable calculus
- Advanced courses
- Modeling & quantum computing
Contact