Quantum algorithms & simulation
Block encoding, Hamiltonian simulation, circuit synthesis, and error-aware methods for early fault-tolerant quantum computers.
Explore this programPostdoctoral Scholar · Berkeley Lab
Diyi Liu
Applied mathematician developing structure-aware algorithms for quantum simulation and multiscale quantum materials.
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 work with Chao Yang and Lin Lin.
Research
Mathematics across scales and computing paradigms
I develop analysis and algorithms that connect mathematical structure to practical computation—from electronic behavior in aperiodic materials to resource-efficient quantum circuits.
Quantum & moiré materials
Multiscale and aperiodic models for electronic structure and dynamics in twisted two-dimensional materials.
Explore this programScientific machine learning
Operator learning and physics-informed representations grounded in numerical analysis and mathematical well-posedness.
Explore this programSelected 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.
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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.
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